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RELATIONSHIP BETWEEN CULTIVATED AREA, PRODUCTION AND EXPORT OF CITRUS FRUIT OF PAKISTAN: A TIME SERIES APPROACH M. Phil Thesis
By
MUHAMMAD IBRAHIM 2013S-MUMPL-STAT-07 Supervised By Dr. Zahid Ahmad
Department of Statistics Faculty of Basic Sciences and Mathematics Minhaj University Lahore, Pakistan
March, 2015
i
RELATIONSHIP BETWEEN CULTIVATED AREA, PRODUCTION AND EXPORT OF CITRUS FRUIT OF PAKISTAN: A TIME SERIES APPROACH M. Phil Thesis
By
MUHAMMAD IBRAHIM 2013S-MUMPL-STAT-07 Supervised By Dr. Zahid Ahmad
Department of Statistics Faculty of Basic Sciences and Mathematics Minhaj University Lahore, Pakistan
March, 2015
ii
RELATIONSHIP BETWEEN CULTIVATED AREA, PRODUCTION AND EXPORT OF CITRUS FRUIT OF PAKISTAN: A TIME SERIES APPROACH
By
MUHAMMAD IBRAHIM 2013S-MUMPL-STAT-07 A thesis submitted in the partial fulfillment of the requirement for the degree of Master of Philosophy in Statistics
Department of Statistics Faculty of Basic Sciences and Mathematics
MINHAJ UNIVERSITY LAHORE, Pakistan. March 2015
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In the name of ALLAH, The most beneficent and the most merciful
iv
DECLARATION
I, Muhammad Ibrahim, Registration No. 2013S-MUMPL-STAT-07, student of M.Phil in the subject of Statistics, session 2013-15, hereby declare that the printed material
in
thesis
“RELATIONSHIP
BETWEEN
CULTIVATED
AREA,
PRODUCTION AND EXPORT OF CITRUS FRUIT OF PAKISTAN: A TIME SERIES APPROACH” is my own research work and not yet been printed, published and submitted as Research work, thesis or publication in any form in any university or in any Research institution in Pakistan or elsewhere.
MUHAMMAD IBRAHIM
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CERTIFICATE The work contained in this dissertation titled” RELATIONSHIP BETWEEN CULTIVATED AREA, PRODUCTION AND EXPORT OF CITRUS FRUIT OF PAKISTAN: A TIME SERIES APPROACH” submitted by Muhammad Ibrahim, M. Phil Statistics, Reg. No. 2013S-MUMPL-STAT-07, session 2013-15 is accepted as confirming to the required standard in Partial fulfillment of the requirement for the degree of M. Phil in Statistics.
________________________ SUPERVISOR Dr. Zahid Ahmad Associate Professor of Statistics UCP, Lahore
External Examiner ……………………… Professor of Statistics
Chairperson ……………………. …………………….
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Dedicated This thesis is affectionately dedicated to my My Parents & Teachers Whose inspiration towards knowledge served me as “Beacon of Light”
ACKNOWLEDGMENT vii
Firstly, I would like to thanks Allah Almighty for giving me courage to complete this research project. Apart from the efforts of me, the success of my study depends largely on the encouragement and guidelines of many others who have always given their valuable advice or lent a helping hand. I sincerely appreciate the inspiration; support and guidance of all those people who have been instrumental in the successful completion of this study.
It has been great honor and privilege to The administration and management of Minhaj University Lahore for providing me such opportunity, I am extremely grateful to Dr. Rukhshanda, Chairman person Mathematics Department Minhaj University. I would like to express my profound gratitude and deep regards to Teachers Dr. Afzal Baig, Dr. Ismail, Mr. Irfan Aslam, Dr. Syed Azeem, Mr. Maqsood Ahmad, Mr. Muhammad Awais, and Mr. Iaasac Shaehzad. for their exemplary guidance, monitoring and constant encouragement throughout the study duration. I also express my gratitude to my research supervisor Dr. Zahid Ahmad for the useful comments, remarks and engagement through the learning process of this study and also for providing all facilities and support to meet my study requirements. I also acknowledge my class fellows who have willingly helped me out with their abilities in class room and out of class room.
At last but not least a special thanks to my family. Words cannot express how grateful I am to my wife, son and daughter who helped me in encouraging for completing my education when I am going to finish my service career.
MUHAMMAD IBRAHIM 2013S-MUMPL-STAT-07
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ABSTRACT Objective of the study was to investigate the empirical relationship between three variables (export of citrus, cultivated area of citrus and production of citrus in Pakistan). Time series data from 1961 to 2012 of all three variables was taken from Economic Survey of Pakistan 2013. In this study time series approach was used to test the causal linkage between all three variables rather than classical regression approach using unit root (ADF & PP Test), co-integration (JJ test), Vector Error Correction (VEC) model and Granger Causality test. The key finding of the data is that all three variables are stationary at first difference (I (1)) at 5% level of significance, the JJ cointegration test showed that all three variables are co-integrated and moved together in long-run and there is only one co-integrating equation of all three variables in which Export of citrus from Pakistan was taken as dependent variable and other two as explanatory variables. VEC model also suggested a short-run dynamics. The Granger causality test deduced from VEC Model revealed that there is uni-directional causality in Export and production at Lag 4. The relationship showed that there is a strong impact of export on production. From above results we may conclude that export of citrus fruit has a significant impact on production of citrus fruits in Pakistan.
Keywords: Citrus fruit, Pakistan, Co-integration, Granger Causality, Stationarity.
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TABLE OF CONTENTS Title
Page No.
Acknowledgment ....................................................................................................... viii Abstract ........................................................................................................................ ix CHAPTER NO. 1........................................................................................................... 1 INTRODUCTION ......................................................................................................... 1 1.1 TYPES OF CITRUS FRUITS ............................................................................. 2 1.2 LAND OF CITRUS FRUITS ............................................................................ 14 1.3 CITRUS FRUIT PAKISTAN‟S PERSPECTIVE ............................................. 17 CHAPTER NO. 2......................................................................................................... 24 LITERATURE REVIEW ............................................................................................ 24 CHAPTER NO. 3......................................................................................................... 38 METHODOLOGY ...................................................................................................... 38 3.1 TIME SERIES APPROACH ............................................................................. 40 3.2 TESTING FOR STATIONARITY .................................................................... 41 3.3 COINTEGRATION ........................................................................................... 47 3.4 VECTOR AUTREGRESSIVE (VAR) MODEL ............................................... 49 3.5 ESTIMATION OF VAR MODEL COEFFICIENTS ....................................... 51 3.6 LAG SELECTION CRITERIA OF VAR MODEL .......................................... 52 3.7 ERROR CORRECTION MODEL .................................................................... 53 3.8 COINTEGRATION TEST ................................................................................ 57 3.9 ENGLE & GRANGER TWO STEP MODELING METHOD ......................... 57 3.10 JOHANSEN METHOD USING VAR MODEL ............................................. 58 3.11 GRANGER CAUSALITY .............................................................................. 59 3.12 DESCRIPTION OF VARIABLES .................................................................. 60 3.13 DATA ACQUISITION.................................................................................... 61 3.14 DATA ANALYSIS STRATEGY .................................................................... 61 3.15 EXAMINATION OF STATIONARITY......................................................... 61 3.16 LAG SELECTION .......................................................................................... 62 3.17 JOHANSEN TEST OF CO-INTEGRATION ................................................. 62 3.18 ESTIMATE OF ERROR CORRECTION MODEL ....................................... 62 3.19 DIAGNOSTICS CHECK ................................................................................ 62 CHAPTER NO 4.......................................................................................................... 68 EMPIRICAL RESULTS .............................................................................................. 68 4.1 DESCRIPTIVE ANALYSIS ............................................................................. 68 4.2 TIME SERIES ANALYSIS............................................................................... 70 4.2.1 TEST OF STATIONARITY ....................................................................... 70 4.2.2 LAG SELECTION ...................................................................................... 71 4.2.3 C0INTEGRATION TEST .......................................................................... 72 4.2.4 ERROR CORRECTION MODEL (short –run dynamics) ......................... 75 4.2.5 GRANGER CAUSALITY TEST ............................................................... 80 4.2.6 DIAGNOSTIC CHECKS ........................................................................... 82 Conclusion ................................................................................................................... 86 Summary ...................................................................................................................... 87
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CHAPTER .1 INTRODUCTION
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CHAPTER NO. 1 INTRODUCTION Citrus fruits has pivotal role in providing nutrition to mankind since ancient times, citrus fruits has also medicinal values besides the nutritional values. Citrus fruits are well familiar for their refreshing aroma, vitamin C provider and thirstquenching ability. Citrus fruits contain ascorbic acid, phytochemicals, which are main ingredients of catenoides, limonoides, vitamin B complex and related nutrients. Certain components of citrus fruits especially oranges and grapefruits are very help for human body for improving blood circulation and to reduce the risk of heart attack. Fresh grapefruits and orange provide the fiber and pectin. (Spreen 2001) Citrus is cultivated more than 80 countries all around the world (Change 1992) and most produced fruit with its several species like Orange, Lemon, Sweet lime, Grape fruit, Mandarin Kinnows, Mosambi, Blood-Red and Tangelo. Citrus cultivation is beneficent in earning money, producing jobs, minimizing unemployment, and said earlier; fruits have nutritive and remedial worth. Citrus fruits are at top among all fruit harvesting products worldwide in production above the fruits like Mango, grapes, apples, and banana. Worldwide its production augmented at the rate of 4.5 % for every year reported in 1990s, which consequent in an yield of 98.35 x 106 tons in year 2001–02, and that number reached at the 100 x 106 tons in year 2003–04 (FAO, 2006). According to FAO (2012) Brazil is the largest citrus producing country and processed major quantity of orange in to juices and small portion of its production exported as fresh fruit. America (North & South) produces about 40% production of the total world and about 10–12 % is produced by Europe (Mediterranean), whereas Asia produces 23% production of citrus fruits (FAO, 2006). In 2012 trend changed in 1
production and Asia gained first position in the production of citrus fruit. Mexico is the largest producer of Lemon its market share for lemon is 27% of the world production. Grape fruit is the major product of China, most of production is consumed in its homeland. Like other countries Pakistan has not gained any prominent position for cultivated area and production of citrus fruits as it is largest producer of Kinnow in the world. The total production of citrus worldwide was 57.78 Million MT in 1981-82 and became 115.52 million MT in 2010-11 (FAO, 2012), the domestic use of citrus for both producing orange juice and for public was 50.59 Million MT and reaming 7.19 million MT was exported while in 2010-11, the worldwide total production was 115.52 million MT, for this period the export was 12.91 million and domestic use was 102.61 million MT. The worldwide total production of orange juice is 1.847 million MT at 65 degree brix. In early 1960‟s the cultivated area in Pakistan was only 33000 Hectares and became 197450 Hectares in 2012. The total production of citrus was 365 MT in 1961 and 2147 MT in 2011.
1.1 TYPES OF CITRUS FRUITS Citrus fruits are acidic and are rich source of vitamin C with lot of health benefits. Citrus fruits are available in several types, taste and colors. The color depends upon environment and climate. Somewhere its color is yellow, somewhere green; this delicious fruit has a lot of varieties globally. These are mentioned below a) Sweet Orange b) Mandarin c) Grape fruit d) Lemon 2
e) Sweet Lime f) Citron g) Acid Lime a. SWEET ORANGE Orange, which is spherical in shape and one of the most popular citrus fruit with low fat, sodium, cholesterol and is rich in fiber and vitamin C. one Orange, only, contains 62 calories on the average in one orange. It is prepared in September to October and be harvested up to January. The yellow-orange is juicy, seedless and having excellent quality food ingredients (Fig No. 1.1). There are many regional names of orange which are Ambersweet, Valencia, Shamouti, Masombi, Sathgudi, Malta, Bonanza, Hongjiang, Marrs, Jaffa, Diller and Beledi. These all are non-blood or non-pigmented orange.
Fig No 1.1: Different shape of orange.
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Other than above mentioned variety of sweet orange, there is blood or pigmented oranges because of deep red color or may be light red color. Red color grows in hot days and cold nights. This type of orange is product of tropical areas. The widespread blood oranges are “Malta” or blood red, Moro, Sanuinello and Sanguinnelli. All types of blood-orange are round, good taste, and skin thin, juicy and medium to large size (Fig No. 1.2). Another type of orange is Navel orange fruits. This fresh fruit orange has excellent quality for eating, because of its small size it is called navel orange and can be seen in Fig No 1.3. it is mainly grown in Brazil.
Fig No 1.2: Different shape of Red-blood orange.
Fig No 1.3: Navel orange
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b. MANDARIN This genus of citrus fruit is most delicious, pleasant taste with attractive shape and aroma. The most prominent characteristic of Mandarin is its easy peeling and seedlessness. It originally belongs to South-eastern Asia, mostly cultivated in Japan, China, Philippine, India and Pakistan. It is also cultivated in Alabama, Florida, Mississippi, Texas, Georgia and California USA (Reynaldo, I.M. 1999). The mandarin is shown in different form in Fig No.1.4
Fig No 1.4: Mandarin citrus fruit 5
Mandarin falls in different categories as common mandarin, Mediterranean Mandarin, King Mandarin and Satsuma mandarin. Category I (Common Mandarin) This is the product of China, India, Pakistan and other south Asian countries with different names. This mandarin is very tasty and is seeded. This category contains Chagsa, Darjeeling, Khasi, Clementisne, Emperor, Dancy and Murcott. Category II (Mediterranean Mandarin) Its main home is China but it is cultivated in Mediterranean region that‟s why its name is Mediterranean Mandarin. It is also grown in USA with name Willow leaf Mandarin. This citrus is seeded, oblate in shape, medium size with good taste. The fruit is shown in Fig No.1.5.
Fig No 1.5: Mediterranean Mandarin citrus fruit
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Category III (King Mandarin) It is large in size, seeded with thick orange color, juicy and tasty. Its origin is China, India, Malaysia and Pakistan. In Pakistan its name is Kinnow , very famous fruit of late winter. The photo of Kinnow is displayed in Fig No. 1.6.
Fig No 1.6: King Mandarin (Kinnow) citrus fruit
Category IV (Satsuma Mandarin) A very famous mandarin (Satsuma mandarin) of Japan, China and Mediterranean region, it is considered that its main homeland is Japan then other soil
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adopted it. It is product of cool places where temperature is less than 0C o. other species are Miyagawa, Owari Satsuma and Sugiyama Unshu. The Satsuma mandarin is shown in Fig No.1.7
Fig No 1.7: King Mandarin (Kinnow) citrus fruit
c. GRAPEFRUIT Its name is combination of two words fruit and grape because it looks like cluster of grapes on tree. It a large in size, the diameter of grapefruit is 10-15 cm. due to its nutritional and medicinal values it is liked everywhere and every age group people globally. It is full of juice, rich in fiber, pleasant fragrance, low in cholesterol, sodium and full of vitamin A & C. Grapefruit has two colors, red-fleshed and whitefleshed. Red-fleshed grapefruit is more preferred than white fleshed. Grapefruit is cultivated all over the world (Iwahori, S. 1991). The grapefruit is presented in Fig No. 1.8.
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Fig No 1.8: Grapefruits
d.
LEMON A fruit which is essential part of kitchen, It is used for cooking, beverages, juices
and also for to garnish. Lemon is excellent natural source of fiber, vitamin C, and low in cholesterol, fat and sodium. Lemon is a citrus fruit with several health benefits. It is used to make germ-free injuries, infections and cuts. It also acts an harsh apart from an anti-inflammatory effect. Lemon mixed with water is used in treating sore throats and anti-bacterial infections. The fruit is also used in a range of foodstuff provision and in cleaning purposes, lemon is blessing of God as it has multipurpose uses. It has lot of varieties and colors.
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Fig No 1.9: Lemon
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e.
SWEET LIME It is product of Pakistan, India, Egypt and Palestine. In Punjab, Pakistan it is
known as “Mitha”. It is sweet full of juice, vitamin C and full of taste. It is small in size and its color is green. The season of sweet lemon is July to September (rainy season), it protects human being from various diseases in rainy seasons. Different sweet lemon are shown in Fig No.1.10
Fig No 1.10: Sweet Lemon
f. ACID LIME Acid lime is commercially cultivated in Pakistan, India, Bangladesh, Mexico and USA, Acid lime is highly acidic with acidity level of 8%. This fruit is mostly seeded but seedless is also available in market. Acid lime is grown in moderate temperature. 11
It is green in color and of medium size. In yellow color, acid lime is also available. In Pakistan and India it is known as “kagzi” lemon. The juice content is very high and it is used for garnishing salad, making squashes and home drinks “Sakenbeen” in summer.
Fig No 1.11: Acid Lime 12
g. CITRON The citrus fruit “Citron” is oblong in shape as looking like lemons. It is full of seeds, moderately large in size with yellow color. It is native product of Pakistan and India. It is used for drinking and making candies.
Fig No 1.12: Citron
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1.2 LAND OF CITRUS FRUITS Citrus organic products are created in more than 80 nations of the world, however pretty much 20 of the creating nations contribute around 90% of the aggregate world generation and exchange (FAO, 2012). Main citrus-producing areas of the world are South East Asia, China, Japan, and USA, Brazil, Mexico and Mediterranean countries. In south Asia real delivering nations are India, Pakistan, Bangladesh, Nepal, Bhutan, and Sri Lanka (Ladaniya, 2004) contribute 33% of citrus created in the Asia-Pacific locale.
Major areas of Citrus production (Courtesy FAO)
In production Brazil is at the top of the list in citrus producing countries and contributes 20%, India, China and Mexico are in lower order than Brazil. Pakistan is enjoying 6th position in production of citrus with volume of production 4%.
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Courtesy Google Images (FAO 2012-13)
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Courtesy by Zaraimedia.com
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1.3 CITRUS FRUIT PAKISTAN’S PERSPECTIVE Pakistan is an agro-based country and agricultural sector has big share in national economy. Though its share is continuously declined, even then agriculturalsector assumes a significant position in the socio-economic expansion of Pakistan. According to 2012-13 Economic survey of Pakistan, this sector contributes 21.4% share to GDP (Gross domestic product) and 45% workforce is directly or indirectly engaged in this area (Economic Survey of Pakistan 2013). More than Rs. 100 billions is the worth of fruit economy in national business. Besides income the fruit industry also generates employment through various activities like transportation, packaging, accounts and HRM. Nature has given a climate to Pakistan which is conducive and favorable for the growth of fruits and vegetables. In cool temperature we grow apple, plum, pear and cherries, in warm climate we grow apricot, grapes, melon and in subtropical climate we grow citrus, mango, dates, banana and guava. Approximately 811800 hectares (4% of cultivated area) area is used for the cultivation of fruits and vegetables in Pakistan. In agricultural sector the contribution of Punjab is 59.6%, Sind has 8.6%. Baluchistan has 25.6% and KPK has 6.2%. According to Agricultural Statistics Govt. of Pakistan (2013), the total production of all fruits is 4772000 MT with expected increase of 6.85% per annum. The export of all fruits is 592000 MT with worth of Rs.30.930 billions. Table No. 1.2 shows some previous data on various fruits with production and export (Economic Survey of Pakistan 2013).
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Production of Important Fruit (000 tones) Export CitrusMango Apple BananaApricotAlmonds GrapesGuava (000 Value tones) (Mln. Rs) 1990-91 1,609 776 243 202 81 32 33 355 112 935 1991-92 1,630 787 295 44 109 38 36 373 125 966 1992-93 1,665 794 339 52 122 40 38 384 121 1,179 1993-94 1,849 839 442 53 153 45 40 402 127 1,324 1994-95 1,933 884 533 80 178 49 43 420 139 1,256 1995-96 1,960 908 554 82 191 49 72 442 135 1,487 1996-97 2,003 915 569 83 188 49 74 448 219 2,776 1997-98 2,037 917 573 94 189 49 74 455 202 2,793 1998-99 1,862 916 589 95 191 50 76 468 181 2,773 1999-00 1,943 938 377 125 121 32 40 494 240 4,130 2000-01 1,898 990 439 139 126 33 51 526 260 4,575 2001-02 1,830 1,037 367 150 125 26 53 539 290 5,084 2002-03 1,702 1,035 315 143 130 24 52 532 263 4,815 2003-04 1,760 1,056 334 175 211 24 51 550 354 5,913 2004-05 1,944 1,671 352 148 205 23 49 571 281 5,408 2005-06 2,458 1,754 351 164 197 23 49 552 455 7,508 2006-07 1,472 1,719 348 151 177 23 47 555 343 6,894 2007-08 2,294 1,754 442 158 240 27 75 539 411 9,085 2008-09 2,132 1,728 441 157 238 26 76 512 469 12,519 2009-10 2,150 1,846 366 155 194 22 65 509 687 20,094 2010-11 1,982 1,889 526 139 190 22 64 547 669 25,017 2011-12 2,147 1,700 599 97 189 21 64 495 723 32,058 2012-13 Provisional 2,334 1,680 684 69 189 21 64 508 592 30,932 Source: Bureau of Statistics
Fiscal Year
Table No. 1.2: Production and Export of Fruit
Fig No. 1.13: The graph of value of export of fruits
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Fig No. 1.14: The graph of production of fruits
Fig No. 1.15: The graph of volume of fruits
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God has sanctified Pakistan with a number of delicious fruits and vegetables. Pakistan grows 11 crops, 40 different vegetables and 21 fruits around the year. Major agricultural commodities are cotton, wheat, rice, maize, mango, dates, citrus, apple, grapes, and flowers. The annual production of fruits and vegetables is about 13.67 X 106 MT per year. Pakistan exports rice, cotton, mango, date and citrus fruits. After Mango, Citrus fruits are the 2nd largest exporting fruit of Pakistan. Pakistan produces 2334 X 103 MT citrus fruits annually and Pakistan is 6th largest producer of citrus fruit in the world. Pakistan earns 100M US$ from the export of citrus fruits.
The
cultivated area of citrus fruit is 199.9 X 103 hectares (100x100 meters), with increasing trend. Citrus fruits have various varieties, sweet kinnows, lemons, grape fruits (Khushk 2001) Pakistan produces about 4% citrus of world production and its contribution in Export is only 0.8% (Ayesha, T. 2014). Almost around the Pakistan the citrus is cultivated but the major contribution of production is Punjab. The province Punjab produces about 70% of the citrus fruit and about 95% of Kinnow (Nawaz 2007). According to some recent survey the specie of citrus known as “Kinnow” is at the top in production worldwide. This unique variety is produced in Sargodha division of Punjab. Bhalwal city is the centre of Kinnow. Other verities of citrus are Musambi, blood red and lemon but leading is Kinnow. Only 60-80% produced citrus is utilized locally and export, remaining is wasted during pre-and-post harvesting procedure, bad and unfavorable weather, uncontrolled diseases, late access to market and poor infrastructure (Naseer, M. 2010).
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Source: Federal Bureau of Statistics (2001-02) The prices variation of agro-products/commodities not only affects the national economy but also affect he production decision of the growers and related agricultural business entity. Fluctuation in prices of agro-based products, crops, fruits & vegetables is a big problem of Pakistan as case around the world. The prices of crops/fruits/vegetables depend on export of agro products, local and international demand, supply/production, climate, consumer‟s trend, seasons. Price variation has significance influence on decision regarding production and cultivated area. At planting time of any crop, the grower/farmer decision for cultivation area depends on price of any commodity, whereas the prices of any commodity depend on its export volume and price (GoP. 2013)
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The export of citrus fruits and its production has increasing trend since last many years so the question is, whether there is any significance relationship between production of citrus and its export, any causality linkage between citrus fruit production and cultivated area.
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CHAPTER.2 LITERATURE REVIEW
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CHAPTER NO. 2 LITERATURE REVIEW In this chapter an attempt is made for discussion
on
the
previously
conducted studies on economics variables and used time series tools like cointegration, VEC Models, Granger causality for diretion of relationship.
Different
authors took different variables for causal relationship, some took food related variables, some took variables related to energy and consuption with commodity prices. The ultimate purpose of this chapter is to take guidelines for data analysis and discussion regarding empirical results. Haleem & Sheik (2005) worked on Estimation of Export Supply Function for Citrus Fruit in Pakistan and they conclude that export of citrus products from Pakistan caused by such calculates as changes local and export price, local products, foreign exchage rate etc, using time series technique like co-integration and VEC Model. In this study they used time series data for the period 1975–2004 for citrus trades and related local price, export price, GDP, and foreign exchange rate. Kiran (2011) conducted a study to investigate the long-run equilibrium (relationship) between oil prices and their stock market values of G7 Countries through integration and co-integration technique instead of the classical linear regression. They found that the unit root null hypothesis was not rejected for any individual series at level; it is examined whether oil prices and stock market prices have a co-integration relationship. Test results on the residuals from the co-integrating regressions indicate that there is evidence of fractional co-integration between oil prices and DAX 30, Dow Jones, FTSE 100 and SP-TSX indices while there is no evidence of fractional co-integration for others.
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Areshia, A. (2011) investigated linear and non linear Granger causality between export and growth rate in a new way using Geo-statistical model (Kiriging and Inverse distance weighting). Geo-statistical methods are the usual methods for prediction/forecasting the positions and developing map in water engineering, climatic changes, environmental pollution, rock and earth mining, bionetwork, geology and topography. In classical econometrics, there are not available any estimator which have the capability to find the best functional form in the estimation. Geo-statistical techniques, tools and models investigate simultaneous linear and various nonlinear categories of causality test, which cause to decrease the effects of choosing functional form in autoregressive model. This approach imitates the Granger definition and structure but improve it to have better ability to investigate nonlinear causality. Results of two Vector Error Correction Models and Improved-Vector Error Correction models (with geo-statistical tecniques) are similar and show a long run one-directional causality from exports and imports to economic development, but Fstatistic of Improved-VEC for this relationships is more bigger than VEC. Analyzing the geo-statistical methods show that there are some Exponential and Spherical functions in VEC structure instead of linear form. KHALID, M (2006) conducted a study to forecast export of Kinnow from Pakistan to other countries. Pakistan‟s Kinnow market is Europe and Middle East. They used ARIMA model to forecast the export of Kinnow. On the basis of estimated model they forecast the export of Kinnow up to 2023. They suggested that in 2023 the export of Kinnow will be 1.11 X 106 MT. Jam (2013) carried out a study to develop an appropriate Univariate ARIMA model employing Box-Jenkins methodology to estimate the cultivated area of mangoes in Pakistan. Data for the year 1961-2009 was used in this
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study to develop the model. An ARIMA (0,1,0) model was established based on the available data to forecast the cultivated area. The estimated area for the year 2025 was found to be 318.5 thousands hectares for mangoes in Pakistan. The results of this study suggested an increasing trend in the area of mangoes in Pakistan for coming years. The ultimate results of this task will Government institutions, policy making authorities, Mango exporters, Growers, producers, and importing countries. Ghafoor, A (2013) carried out a study to determine the influence of different factors on export of mangos. They applied ADF test to examine the stationrity in the data and Johansen‟s co-integration test for short-run and long-run relationship in economic variables. They also used Granger Causality test to point out the trend of the relationship. They found that significant estimates of the parameters in the shortrun and long-run for mango production chased by actual agri GDP. Burhan A, (2005) was embraced a study to estimate the past growth trend in production and Export of Kinnow and to estimate the production and export of Kinnow. The log linear model was connected to gauge the past pattern of production and export of Kinnow. ARIMA model was utilized to speculate the production and export of Kinnow for next 20 years. The estimated value of production and export of Kinnow for 2022-23 was reported as
2617450 tons and 1.11081 x 106 tons,
respectively. Shahbaz & Ahmad (2011) conducted the study on exports-led growth using three month quarterly data over the period 1990-2008 of Pakistan. They used PP unit root test, Autoregressive Distributed Lag bounds testing technique for co-integration and Error Correction Model (ECM) for short-run dynamics were employed. The outcome of the study showed that exports and economic growth is positively
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correlated, also verifying the strength of exports-led growth hypothesis. Exchange rate downgrading decreases and genuine capital stock progress economic growth. Haleem et al. (2005) conducted a study to investigate the variables influencing citrus trades. These incorporate local and international trade prices, local production, and currency exchange rates. They utilize data for the period 1975–2004, and utilize co integration and an Error Correction Model (ECM). The assessed export value versatility is 1.48 while local value flexibility is –0.98. Among non-price variables, the evaluated flexibility of local citrus production, the conversion standard, and GDP are 1.37, 1.31, and 0.35. Aktaş & Yilmaz (2008) conducted study to observe the short-run and longrun relationship between oil utilization and GNP for Turkey using time series data for 1970-2004. Economic variable economic growth and variable oil consumption used for analysis showed order of integration (I(1)) employed for causality testing. In this working it was indicated that there is bidirectional Granger causality between oil consumption and economic growth in the short-run and long-run. Quddus & Saeed (2005) examined the export groth rate and GDP growth rate using OLS with AR(1) and concluded that growth rate of export has postily effeted the GDP growth rate. Ogazi C G, (2009) carried out study and used error correction version of ARDL approach to co-integration and concluded that rice output is regressed as a function of area, weather and time trend. Mahmood & Zahid (2012) conducted a study to find an appropriate Univariate ARIMA model to anticipate the cultivated area of mangoes in Pakistan. Time series data for 49 years from 1961 to 2009 were taken. The results of study recommended that ARIMA (0,1,0) as appropriate model to predict the cultivated area of mango.
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Moreover, this study suggested that in the year 2025 the forecasted cultivated area of mangoes in Pakistan will be 318500 hectares. AWAL M. A. (2011) was carriedout a study to guess the growth pattern and also observe the best ARIMA model to efficiently forecasting Aus, Aman and Boro rice production in Bangladesh.It appeared that the timeseries data for Aus and Aman were 1st order homogenous stationary but Boro was 2nd order stationary. The study revealed that the best models were ARIMA (4,1,4),ARIMA (2,1,1), and ARIMA (2,2,3) for Aus, Aman,and Boro rice production, respectively. The analysis indicated that short-run predictions were much better for ARIMA models compared to the nonprobablistc models. The doubts about of rice production could be reduced if production were forecasted sound and essential steps were taken against losses.The findings of this study would be more useful for policy makers, researchers as well asproducers in order to forecast future national rice production more accurately in the short run. Munir & Mustafa (2008) carried out study and found that production of Mango in Pakistan has been improved due to use of improved infrastructure and superior supervision systems. Beyond an increased production and rising demand in the export market, the prospective of Mango export has, however, not yet wholly achieved. Pakistan has comparatively superior benefit in the production of Mango with massive probable exists for its export in the big Gulf and other Arabian markets. The study was carried to estimate production of Mango for the years 2005 through 2024. The Log linear and ARIMA models were used to predict production of Mango. The predicted value of production of Mango for the year 2024 worked out as 1431010 MT‟s, which means that an increased yield of Mango would be offered for utilization as well as for export. The paper underlines the need for taking steps to
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boost export of Mango by improving its class, wrapping and fulfilling with international standards recommended by WTO. Duc & Tram (2008) examined
the relationship with evidence from
fisheries exports of Vietnam during 1997 to 2008. The contribution of fishery sector in Vietnamese Gross Domestic Products (GDP) was determined with statistical dsta. the effects of fishery exports on the economic growth was observed yet to be thoroughly studied in an econometric time series approach. Descriptive and time series analyses in this study revealed a direct influence of fishery trade on the Vietnamese economic development in long run. The modern econometric approach with unit root test for stationary and co integration approach and vector error correction model (VECM) used in this study for long run and short run association between fish trade & Vietnamese Gross Domestic Production of different seasonal phase business. For the long run estimation, a double increase in its fishery exports value would raise the GDP by 7%. This has a great economic meaning in developing process of the economy. In reverse side, Vietnamese fishery exports would increase by 5.2% with 10% increase in its GDP. Ramos (2001) carried a study to investigate the causal linkage between different economic variables like exports, imports, and economic growth in Portugal for 1865 to 1998. The influence of import on export output was observed. No unidirectional casualty was observed between the variables included in the study. Bidirectional consequence between export-output growth and imports-output growth was observed. Import and export did not exhibit any relationship. Vaezi & Moghaddasi (2009) carried out a study to establish the relationships between agriculture, manufacturing and export of Iran using data for the period 1959-2007. The results showed the unit root present in all variables at level, including
29
log of exports, agri GDP and manufacturing GDP. However, at first difference the data became stationary. They concluded that those economic variables were integrated at order one (I (1)). It was also reported that manufacturing causes both exports and agriculture by using causality test. Exports did not cause any other economic variable as agri GDP and manufacturing GDP. Sean & Nicholos, (2008) researched causal linkage among horticulture, assembling and export trade in Tanzania by utilizing information for the time of 19702005. The outcomes indicated in both divisions Granger causality was watched where agribusiness causes both export and assembling areas. Export additionally caused both farming GDP and assembling GDP. It was likewise watched that assembling did not bring about Export and horticulture. Horticultural GDP and Export were linearly co-integrated; Export and production were additionally co-integrated. Agribusiness and assembling was co-integrated however they were lag touchy. On the other hand, three variables, assembling, Export and farming all together were cointegrated demonstrating that they shared long run connection and this has critical financial ramifications. Kumari & Malhotra (2014) carried out the study to examine the causal linkage among exports and economic growth employing Johansen co-integration and Granger causality approach. Annual data for exports and GDP per- capita stemming for 19802012 was used in analysis. The tests on the long-run and short-run linkage between exports and economic growth were performed. concentrating on the findings of cointegration approach this paper concluded that there did not exist long-run linkage
between
exports
and per
capita.
Granger causality test exhibited
bidirectional causality between exports with GDP per capita and GDP per capita with exports.
30
Saban & Ekrem (2011) examined the function of currency rate on Turkey's fresh fruits and vegetables export trade balance with 14 trading countries in the (EC) European Union. It was already reported that currency rate affect the trade equilibrium and was best displayed by J-curve effect, so it was emphasized that Jcurve effect was really observed for the data. Finally they employed the bounds testing co-integration approach for trade balance model to the period of 1995–2007. The Results of the study supported verification of the J-curve effect in two cases for the short-run. In the long-run, the currency rate has a positive influence on the trade balance. Mohammadi & Mahasa (2013) Pistachios is the main product of Iran‟s major export products, this product is still limited offered by rest of the world. The study was carried by taking advantage of the statistics of Iranian products from 1980 to 2010 and with Vector Auto Regression approach (VAR), (IRA) Impulse Response Analysis and Forecast Error Variance ( FEV) Decomposition; factors affecting Iran‟s export supply and demand were analyzed. The results of co-integration model exposed the fact that each of the variables of average income of importing countries, the real exchange rate and domestic production of pistachios has a significant as well as positive relation in long-term while production in other countries in addition to the domestic price of the product has a significant and negative relation with supply and demand of the exporting product in long-term. The analysis of forecast error variance decomposition, additionally, manifests the most effect on the fluctuations of supply of pistachios export in Iran is due to the variable itself, while the most effective factor on fluctuations of the global demand of the export, was the variable of Iran‟s exporting supply factor, after which the same is true for the exporting price in long-term.
31
Abad & Mofrad (2012) carried out a study to compare the relationship using long-term and short-term approach between Gross domestic production, export and FDI for years 1991-2008. Outcome exhibited a direct and strong long term association between investments and export. The association between investment and export was found inverse. Results of the vector error correction (VEC) model for GDP indicated an error correction coefficient showed negative which due to the big value of the Gross domestic production in the short-run than long-term linkage value. the impact of investment and exports on GDP was positive. Impact of domestic production on investment was positive, but on export was not positive. Paul, C. W. C. (2013) conducted the study to re-explores the association between export and economic development in South Africa utilizing econometric strategies of co-integration and Granger causality over the period 1970Q1-2012Q4. The Johansen approach revealed that export and Gross domestic production moved together with time, there might be short-run association among those economic variables. It was found in the study that Causality covered by VECM, there was a short-run association and causality between these two economic variables. Vector auto regressive (VAR) also confirmed that both Export and GDP cause each other, as the Granger casualty test reported above. .
Atef & Mounir (2014) did a study to determine the causal linkage between
fossil powers utilization, CO2 emissions and financial movement at total and disaggregates levels in Saudi Arabia utilizing the multivariate co-integration approach. Their results indicated the presence of a long-run balance relationship between
fossil
fills
utilization,
carbon
dioxide
outflows
and
monetary
development. In addition, in the long-run the causality was unidirectional running from financial development to vitality utilization and regular gas
32
utilization while there no confirmation of causality in the case of oil utilization. Our results show that vitality protection strategies may be authorized without influencing monetary development. Arrangements pointed at decreasing fossil fuel utilization and controlling for CO2 discharges may not influence adversely Saudi's monetary development. Henceforth, arrangement changes went for lessening fossil energizes (oil and characteristic gas) sponsorships turn into a critical need soon keeping in mind the end goal to take out fossil fuel fritter away. Mohammadi, H (2009) carried out a study to examine the long-run association and short-run dynamics between power costs and three fossil fuel costs - coal, common gas and unrefined petroleum - utilizing yearly information of U.S. for 19602007. The outcomes proposed (1) a stable long-run connection between true costs for power and coal (2) Bi-directional long-run causality between coal and power costs. (3) Insignificant long-run relations between of power and unrefined petroleum and/or regular gas costs. Furthermore, (4) no confirmation of asymmetries in the alteration of power costs to deviations from harmony Martínez & Perez (2015) accomplished a study and the objective of this study was to find the short-run and long-run impacts on cigarette request in Argentina taking into account changes in cigarette cost and wage. They took information from the Ministry of Economy and Production of Argentina. Examination was taking into account month to month time-arrangement information somewhere around 1994 and 2004. The econometrics particular is a direct twofold logarithmic structure utilizing cigarettes utilization per individual more established than 14 years, as dependent variable and genuine salary per individual more seasoned than 14 years, and the genuine normal cost of cigarettes deals as free variables. Exact investigations were done in three stages: 1) To confirm the integration the variables utilizing the ADF
33
test; 2) To test for co-integration utilizing the Johansen-Jullius (JJ) maximumlikelihood technique to catch the long –run impacts; and 3) To use the Vector Error Correction (VEC) model to catch the short-run dynamics of the variables. The results demonstrated that in the long-term period the demand for cigarettes in Argentina being influenced by changes in genuine pay and genuine normal cost of cigarettes. The estimation of pay flexibility was to be equivalent to 0.54 while the estimation of own-value versatility discovered equivalent to –0.34. The outcomes utilizing vector slip revision model estimation recommend that the fleeting cigarette request in Argentina was discovered autonomous of cost (not statistically significant). The estimation of the transient salary flexibility was equivalent to 0.49. Esso, L. (2010) carried a study to examine the long-run and the causality relationship between vitality utilization and monetary development for seven SubSaharan African nations amid the period 1970-2007. Utilizing the Gregory and Hansen (1996a, 1996b) testing way to deal with threshold co-integration, they found that vitality utilization was co-integrated with economic development in Cameroon, Cote d'Ivoire, Ghana, Nigeria and South Africa. In addition, this test recommended that economic growth has a significant positive long-run affect on vitality utilization in these nations before 1988 and this impact gets to be negative after 1988 in Ghana and South Africa. Besides, causality tests likewise proposed bidirectional causality between vitality utilization and genuine GDP in Cote d'Ivoire and unidirectional causality running from genuine GDP to vitality use on account of Congo and Ghana.
Research Question
34
Pakistan is lacking in modern infrastructure of handling, packaging, harvesting for fresh fruits & vegetables. Almost 20-30% fresh fruits & vegetables are destroyed without usage due to lack of facilities. This study will focus on the question, whether there is any significant linkage/relationship between production of citrus fruits and export using some appropriate time series approach.
Objectives The objectives of study are to: 1. Investigate short-run & long-run relationship between cultivated area, production and export of citrus fruits using appropriate model. 2. Determine the direction of relationship between variables using Granger Casualty test. Significance of study For efficient decision regarding future planning in business or any usual activity, someone should know the previous behavior/pattern of the phenomenon of interest. When the phenomenon of interest is risky in nature, the accurate forecasting/prediction needs some concrete techniques and tools. Because agricultural output is highly volatile in its nature & behavior and farmers/growers always experience a low price for their products / commodities / crops. Time series models (ARMA, ARIMA, and VAR, VECM, co-integration) have ability to help the farmers/growers in forecasting/prediction of any phenomenon which is linked with time for future planning. Various researchers used these models and found significant results of the fitted models in agricultural activities like production, price.
HYPOTHESIS 35
The necessary hypotheses are given below and all are tested and their results are in result section. The level of significance in our study is 5%. Hypothesis 1: Regarding Unit root testing Hypothesis 2: Regarding Cointegration Hypothesis 3: Regarding Granger Causality Hypothesis 4: Regarding Autocorrelation Hypothesis 5: Regarding Hetroskedisticity Hypothesis 6: Regarding Normality
Hypothesis 1: all variables are non-stationary Hypothesis 2: There is no co-integration relationship between Export, Area and Production of citrus Hypothesis 3: Lagged values of coefficients in each equation are zero Hypothesis 4: There is no correlation between error terms Hypothesis 5: There is the constant variance of error term Hypothesis 6: The error term follows normal distribution
36
CHAPTER .3 METHODOLOGY
37
CHAPTER NO. 3 METHODOLOGY In most of the social sciences studies/researches, the researcher endeavor to establish relationship between variables and then to predict study variable using other set of explanatory variables. Like other discipline the economists and financial analysts are also interested prediction and forecasting of economic and financial variable using appropriate techniques. Two kinds of data are usually employed in data analysis, one cross-sectional data and other is time series data, in some cases pooled is also used for such purpose. Time series is frequently used in economic/financial studies. Since for a long time, Classical Linear Regression Models (CLRM) were used for prediction and forecasting Time series & Econometric data. It was assumed that the data is stationary and errors are normally distributed with zero mean and constant variance, but sometimes the data shows trend which may be shown spurious (nonsense) relationship (Granger & Newbold 1974),which consequently produced spurious regression. This type of relationship can be found in social sciences research especially in Psychology, Education, Medical and Environment.
1.
2.
38
Spurious Regression: - Trend in data leads to spurious relationship, which causes a non-sense or spurious regression. In time series data if errors or residuals show a strong autocorrelation or serial correlation, then there is a serious problem in interpreting the coefficients of model. 2 Spurious regression occurs when we have high value of “R ” and low value of Durbin-Watson “d” statistics. This indicates that there is no real relationship occurs among variables and independent variables nothing contributes towards the explanation of variation in dependent variable. We may conclude that the strong relationship be due to some other variable. Lagged variable:- A variable is called lagged variable which is predicted on the basis of its past values, this process is called auto regression or auto regressive (AR) model, the AR(p) can be described as Yt = β0 + β1 Yt-1+β2Yt-2+………………….+ βp Yt-p + Zt
This type of relationship may be due to appalling selection of variables, it may a relationship due to third variable which is actually part of study (for example there is significant direct association between number of psycho patients and number of Psychiatrics in different cities of Pakistan, this is non-relationship as we assume if we increase number of psychiatrics so patients will also increased, definitely answer is “No”, so what happen, we may interpret this as that the relationship may due to some third variable which may be “Awareness” in public regarding psycho-disorder and people get contact with psychiatrics in general than before), This spurious relationship may be due to biased sample or wrong data collection techniques which were used in research. This relationship may cause a staid problem in economic/financial forecasting. Granger & Newbold (1974) pointed out in their paper that sometimes significant relationship found between variables in regression analysis, but there is no relationship exists in fact. They then suggested some remedial measures for such nonsense relationship as:a) Inclusion of lagged variable b) Taking differenced variable involved in the model.
3. 4.
39
Stochastic process:- Collection of random variables gathered with respect to time in equal intervals. Cross-sectional data is that which is collected any time and same time for example weight of students, whereas time series data is that which is collected over regular interval of time for example hourly temperature, monthly stock, annual production. Time series is realization of a variable in stochastic variable.
Lagged variable is used when present observation/measurements depend upon past or previous observations/measurements of the same variable. Differenced variable is also used to overcome this issue. But using differenced, some useful information
may
probably
lost
during
data
analysis.
In
dealing
with
economic/financial data analysis, the prime interest of researcher is to forecast/predict the economic variable. For prediction/forecasting of economic variable, the researcher necessitates an appropriate model which is based on previous data/history of variable under study. For modeling time series, the precondition is that, the series or data must be stationary, in practical approach, the data is stationary if it tends to wonder more or less uniformly about some fixed level. A stochastic process or series is said to be stationary when its arithmetic mean and variance are constant over time and value of covariance depends on gap (lag) between two time periods and not actual time at which the covariance is captured. Staionarity may strict (strong) or weak, for a strict stationary data, the distribution of Yt is independent of time, distribution does not depend on time (Madala & Kim, 2007). In everyday affairs and scenarios, the majority of the time series data are non-stationary. The non-stationary time data is that which has clear trend (either upward or downward). Now the question is that how can we say that data is stationary or not?
3.1 TIME SERIES APPROACH An econometric data may be cross-sectional or time series. In cross sectional data,
Pearson‟s
correlation
coefficient
is
employed
to
determine
relationship/association between variables, cross sectional approach has limitation that correlation may not be suitable some time for testing causality even if correlation between variables is very high (as previously discussed example of pycho-patients 40
and Psychiatrists ). Time series approach is appropriate and has ability to solve the limitations of cross sectional data, and also impose no prior restriction on relationship between variables of interest regarding direction of causality. Most of the time series involve three steps. These are as:1) Testing of unit root (stationarity or integration) 2) Testing of co integration 3) Testing of causality All these steps are discussed below for clarity in concepts of stationarity.
3.2 TESTING FOR STATIONARITY In econometric time series analysis, it is essential to know, is the series stationary or not. Presence of stationarity in a series can strongly influence its behavior. The non-stationary behavior leads to spurious regression (A high R2 with no logic of relationship between independent and dependent variables). Time plot (a primary choice which is graph of time series data) and correlogram (a graph between lag and ACF & PACF) provide a rough idea about trend that is present in the series or non-stationary behavior. Below Fig No 3.1 time plot shows a trend in data and quite possible series is non-stationary and Fig No 3.2 does not exhibit any trend and this series may be a stationary.
41
Fig No. 3.1: Time plot with trend
Fig No. 3.2: Time plot without trend (likely a stationary series) Non-stationary issues were discussed by (J Hamilton 1994), (R. Harrison 1995), (Fuller 1996), (Endres 1995, 2004), and (Verbeek 2004). Unit root test is a numerical procedure to detect the existence of stationarity in the series and to determine that its presence is significant or not as it is detected. Now question is what is unit root test? To explain the concept of unit root, consider an AR (1) model
Yt Yt 1 Z t
………………………….3.1
Here φ is autoregressive regression coefficient and can take any value. Equation (3.1) is AR of lag one and now take AR of two periods lag 2 & 3.
Yt 1 Yt 2 Z t 1 42
………………………3.2
Yt 2 Yt 3 Z t 2
……………………….3.3
Putting (3.2) into (3.2) for getting Yt new equation
Yt (Yt 2 Z t 1 ) Z t
……………………….3.4
Yt 2Yt 2 Zt 1 Zt
……………………….3.5
Putting again (3.3) into (3.5) for getting Yt new equation
Yt 2 (Yt 3 Zt 2 ) Zt 1 Zt ……………………...3.6
Yt 3Yt 3 2 Zt 2 Zt 1 Zt ……………………….3.7 K successive substitutions lead to
Yt K 1Yt ( K 1) K Z t K .......... .......... . Z t 1 Z t ………..3.8 There are three possibilities for 3.8 1)
1 K 0 as K
This is a stationary case as shocks in the data/series die gradually. 2)
1 K 1 for all K The equation 3.1 is random walk when φ=1, and process is non-stationary.
This is the thought at the support of the unit root. The shocks are remained in the system and we have the new form of 3.8
Yt Y0 Z t
as K
………………..3.9
t 0
The Yt (the present value of series) is simply an infinite summation of previous shocks and some initial value of Y. this is unit root case and is null hypothesis in ADF test.
43
3) ɸ>1, in this case there is a systematic upward change in the series as shocks are more significant with time. For φ > 1, φ4 > φ3 > φ2 > φ, for this data shows a clear trend which is not desirable. Above discussion is all about the value of “φ” which is less or equal to one. So, when to discuss about stationarity of a process, it is essential to test the existence of unit root to avoid the problem like fake relationship. When we are discussing about unit root, in fact we are discussing about serial/autocorrelation correlation. Early work on unit root test was carried out by Dickey (1976), Dickey & Fuller (1979), Philips & Perron (1988) developed non-parametric procedure for testing of unit root which is based on Phillips (1987) Z-test to remove any serial correlation in the series. PP tests are considered more lenient regarding distribution of error terms. The DF test is more popular because its simplicity. The necessary purpose of the test was that the null hypothesis is φ = 1, in the AR (1) model
Yt Yt 1 Z t Under the assumption that “Zt “ is white noise errors, against the alternative hypothesis φ < 1. The hypothesis can be written as H0: The process/series is non-stationary or series does contain unit root H1: The series is stationary The test is called DF test or ϯ (tau) test. The test statistic is
44
1 SE( )
………………………………………… 3.10
α level
10%
Critical Value for constant but no -2.57
5%
1%
-2.86
-3.43
-3.41
-3.96
trend Critical Value for constant and -3.12 trend
Table No. 3.1: CV’s for DF tests (Fuller, 1976, p. 373) In practice, the following model is used rather than model stated in 3.1 for computations Yt Yt 1 Z t
…………………………………….3.11
The test φ =1 is equivalent to ψ = 0.The Dickey & Fuller (DF) test is based on three regression models. The first model is stated as in equation 3.11 where DF is used. The second regression model is that when random walk is with drift and model is written as Yt Yt 1 Z t …………………………………………………3.12
When we add linear variable in equation 3.12 it becomes as
Yt t Yt 1 Z t ……………………………………………3.13
Dickey & Fuller (1981) provided another test statistic to test the hypothesis for all three models
test statistic
SE ( )
………………………………….3.14
The DF test is based on the assumption that the errors “Zt “are independent and is a stationary process, also there is no serial correlation in errors, if present that must has to be removed from the errors Zt. Further DF test is only applicable when sample size is large (Banerjee, 1993), (Dickey & Fuller 1981), (Said- Dickey 1984), (Phillips, 1987), (Phillips & Perron 1988) suggested modification in DF test when Zt 45
is not white noise. The developed tested was named as ADF (Augmented Dickey Fuller) test. To remove serial correlation in the process, higher order differencing may be required in order to transfer Zt into white noise, p-lags of dependent variable is used augmented the DF test , which is based on equation 3.11 to 3.13. p
Yt Yt 1 j Yt j Z t j 1
…………………..3.15
p
Yt Yt 1 j Yt j Z t ………………….3.16 j 1 p
Yt t Yt 1 j Yt j Z t ……………..3.17 j 1 Where Zt is error term with independent and stationary process and p is number of lags (Zuo, 1997). The testing procedure is same as DF test and the test statistic 3.14 is also used in ADF test and with same critical values in table no. 3.1. Still there is problem in using ADF test for example lag length selection, as before performing ADF test we must know the lag length “p”, there is no hard and fast rule for lag length selection, however as a simple thumb rule we may take lag as 12 (p=12) when data in monthly, pas 4 when data is quarterly. But for other time periods like years, days, hours, we have some criterion known as AIC (Akaike information criterion) and BIC (Baysian information criterion) which are often use to select the lag length (Brook 2008). For small sample ADF test cannot work efficiently. Philips & Perron (1988) suggested more comprehensive non parametric test as alternative to the ADF test and which works similar to ADF test. In PP test, Phipps & Perron incorporated an automatic correction to DF procedure to allow for serial errors as ADF assumes that errors are statistically independent. If residuals of unit root 46
process are not homogenous or weakly dependent the Philips & Perron (1988) test can be used. E-view and other software facilitate users to test unit root using both ADF and PP tests.
3.3 COINTEGRATION Many series are highly correlated over time, for example UK Pound and Euro exchange rate, Personal Disposal Income (PDI) and Personal Consumption Expenditure (PCI), National Income and Investment. In said example both variables show relationship. If variables are measured over fixed interval of time, then the relationship is called co-movement or co-integration. In common practice, independent series are often related to each other and with high degree of correlation. When economic series are highly correlated even then there is warning that two series contain unit roots and be related. In other words, series has high R2 than DurbinWatson “d” statistic. In this situation there is chance of spurious relationship which was addressed (Hornik 2009) and introduced by Granger and others during 1980‟s to investigate the presence of equilibrium in two or more variables over time. They introduced co-integration concept in Econometric modeling. AIC:- Akaike information criteria after the name of developer
Mr. Akaike 1969 and
BIC
(Schwartz 1978) Baysian information criteria. AIC is an important statistic to determine the lag length selection in regression models. The AIC takes into account both how well model fits the series and the number of parameters estimated. BIC is also works on same lines as AIC but both have slightly different formula. Let p is number of parameter estimated and n I sample size.
AIC ( p) n ln | ( p) | 2 p
BIC ( p) n ln | ( p) | p logn
QC( p) n ln | ( p) | p ln ln n Lower the value of AIC or BIC, better the model. For lag selection these criteria are also used.
47
Two or more processes are said to be cointegrated if they stay close to each other even if they “drift about” as individual processes (Rachev 2007). The existence of co-integration relationship between two or more variables indicates that the series move together in the long run and so they share a common stochastic trend although in short run the series may diverge from each other. The co integration property is a long term property . Before proceeding next, we should first define the word integration. A series is said to be integrated if it gathers past effects (Banerjee 1993). The word integration means that a Yt series is said to be integrated of order “d”, if Yt is stationary of “d” difference. Co-integration is linear combination of non stationary variables (Walter. 2004), two non-stationary time series Yt & Xt are co-integrated if some linear combination aXt +bYt is a stationary series. (Hornik 2009). The idea of co-integration is influential one because it allows us to explain the existence of equilibrium relationship among two or more time series, as each one is non-stationary (Banerjee 1993). As an example, let we have two series Yt & Xt are Yt = µt + Zxt
…………………………………….3.18
Xt = µt + Zyt
…………………………………… 3.19
Where µt is random walk and Zxt & Zyt are white noise with zero mean. Both series are non-stationary and their difference (Yt - Xt) is stationary. Thus the linear combination of Yt & Xt with a = 1 and b = −1, produced a stationary series, (Zyt – Zxt). Hence Yt & Xt are co-integrated and share the underlying stochastic trend {µt} (Hornik 2009).
48
3.4 VECTOR AUTREGRESSIVE (VAR) MODEL Process Yt is called an autoregressive (AR) model of order “p” if
Yt 0 1Yt 1 .......... ..... pYt p Z t
……………3.20
Where “Zt “ is a random process (error or residual) with zero mean and variance σ2. This is like regression model where Yt is not regressed on independent variable (Exogenous variable) but the past values of Yt. The equation 3.20 may be written as p
Yt 0 jYt j Z t
……………………………………3.21
j 1
When we have several time series and we need to investigate relationship among them simultaneously, for such problem Sims (1980) introduced a VAR approach, which is generalized form of simple AR process. Vector autoregressive (VAR) models are those economic models where each variable depends linearly on its own lagged values and those of the other variables in the system. This means that the future values of the stochastic process are a weighted sum of past and present values plus some noise (Rachev 2007). Let we have two Y1t and Y2t, each depends on different combinations of previous “p” values of both variables and error term
Y1t 1 11Y1t 1 ............... 1 pY1t p 11Y211 ........ 1 pY2t p Z1t …3.22 Y2t 2 21Y2t 1 .......... ..... 2 pY2t p 21Y1t 1 ........ 1 pY1t p Z 2t .3.23 Both 3.22 & 3.23 can be written in for 3.21 as p
p
j 1
j 1
Y1t 1 1 j Y1t j 1 j Y21 j .Z1t
49
………………….3.24
p
p
j 1
j 1
Y2t 2 2 j Y2 t j 2 j Y11 j .Z 2 t
…………………3.25
The equations 3.24 & 3.25 are used for testing of causality which was introduced by (Grnager 1969) and slightly modified by Sims (1972). Causality test is used to answer the question “changes in Y1 causes change in Y2 or vice versa”. (Brooks, 2008). Since we are concerning with two variables and dealing bilateral causality. Four types of causality can be distinguished (Gujrati 2004) 1) Unidirectional causality from Y2 to Y1 is indicated if the estimated coefficients on the lagged Y2 in (3.24) are statistically different from zero as a group ((∑φj ≠ 0) and the set of estimated coefficients on the lagged Y1 in (3.25) is not statistically significant (∑βj =0). 2) Conversely, Unidirectional causality from Y1 to Y2 exist if the set of lagged Y1 coefficient in (3.24) is not statistically different from zero ((∑φj = 0) and the set of lagged Y1 coefficient in (3.25) is statistically significant from zero (∑βj ≠0). 3) Feedback, or bilateral causality, is suggested when the sets of Y2 and Y1 coefficients are statistically significantly different from zero in both regressions. 4) Finally, independence is suggested when the sets of Y2 and Y1 coefficients are not statistically significant in both the regressions (neither set of lags are statistically significant in model for other variable). Finally, the word „causality‟ is really means only a correlation between the current value of one variable and the past values of others (Brooks 2008).
50
If we have more than two series with “p” lags and “k” variables, then the VAR model is written as Yt A1Yt 1 . A2Yt 2 .............. Ap Yt p Z t
………………………………3.26
Where Yt , its lagged variables, Zt are Kx1 ordered vectors and A1, A2……………Ap are KxK order matrix of coefficients to be estimated. (Maddala & Kim), if exogenous variable is also included in the model then equation 3.26 is written as Yt A1Yt 1 . A2Yt 2 .............. A p Yt p X t Z t
…………….3.27
Where β and Xt (exogenous variable) both are vector of Kx1 order. This is also known as VARX (p,b) model.
3.5 ESTIMATION OF VAR MODEL COEFFICIENTS The equation 3.27 be written as Y = Tβ +Z ……………………………………… 3.28 Where Y is vector and T is matrix of lagged values of Y and exogenous variable. The least square solution for β (Zellner 1962) is given as
(T / T ) 1 T / Y ……………………………….. 3.29 If the model has intercept then 3.29 may be written as
(T / T ) 1 T / Y ………………………….. 3.30
The set of is tested using t-statistic given below with df K-(p+1)
51
t
……………………….3.31
SE ( )
3.6 LAG SELECTION CRITERIA OF VAR MODEL The most important component of VAR model is the selection of appropriate lag length. There are several alternative criteria are available to select the appropriate VAR model lag length such as the likelihood ratio, the Final Prediction Error (FPE), the Akaike‟s (1969) Information Criterion (AIC), the Schwarz‟s (1978) Baysian Information Criterion (BIC), and Hannan and Quinn‟s (1979) (HQ) statistic. In all criteria, that model is best fits the data for “p” lag is the one that minimizes the Information Criterion Function (ICF) or simply, the model that minimizes the overall sum of squared residuals or maximizes the likelihood ratio. LR (Likelihood Ratio) test statistic is used to determine appropriate order or lag of VAR model, the test is of the form as
LR (T c)(log| k | log | p |) or LR (T c)(log| r | log | u |) Where “T” is number of observations, “c” is the maximum number of regressor in the unrestricted system of equations, ∑ k or ∑r are residuals variance/co-variance matrices of VAR (k) or restricted system of equations,
∑ p or ∑u are variance/covariance
matrices of VAR (p) OR unrestricted system of equations. LR follows chi-square distribution with “k” as degree of freedom. Final prediction error: FPE is used to select the optimal lag length for proposed model. Lesser the FPE value for different lag is considered as most optimal value for the model. The formula of FPE is as T N p 1 FPE det( ( p)) T N 1 p
AIC, BIC and QH methods are as below
AIC ( p) T ln | ( p) | 2 p
BIC ( p) T ln | ( p) | p logT 52
HQ( p) T ln | ( p) | p ln ln T
Where
( p) is residuals variance/covariance matrix. T is number of observation, p is lag length, N
is number of parameters.
3.7 ERROR CORRECTION MODEL Error correction model (ECM) was first introduced by Sargon (1964), Hendry & Anderson (1977) and Davidson (1978). The recent revival of ECM in based on work by Granger & Weiss (1983). One feature of co-integration is long run or equilibrium relationship, but sometimes relationship move away from equilibrium. Now the question is why relationship is not always in equilibrium. If there is short run relationship in variables then there may be disequilibrium. This is because of that the current value of dependent variable is not only being determined by current value of some independent variable but also past values of independent variables. A lot of information is also lost when we apply differences for making the series stationary. The difference between VAR and ECM is the concept of long run relationship and the previous disequilibrium as independent variable in the dynamic behavior of the existing variable. Let we have two variables Yt & Xt, both are said to be co-integrated, such that Yt – βXt is I(0), consider the equation Yt X t Z t ……………………………………. 3.32
The equation 3.32 shows that for any relationship between Yt & Xt, a difference Yt – βXt must be stationary for any value of β. If there a long run equilibrium exists between Yt & Xt, the error Yt – βXt contains some useful information since on the average the process will move towards equilibrium if not
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already there and called “equilibrium error” whereas the term Yt-1 – βXt-1 is known as past disequilibrium and is “error correction term”. The error correction model (ECM) is used where there is need for correction in present, previous and anticipated disequilibrium.
Error correction model estimate the speed at which dependent
variable returns to equilibrium after change in lagged variable. A basic ECM for the co-integration equation 3.32 can be formulated as Yt X t (Yt 1 X t 1 ) Z t ……………… 3.33 Yt X t EC term Z t
……………….. 3.34
If EC term is zero (Yt-1 – βXt-1 =0) then both variables are in equilibrium state. Where the coefficients are interpreted as The coefficient “α” estimates the short term effect of an increase in X on Y The coefficient “ϒ” estimates the speed of return to equilibrium after a difference, if ECM is proper then “ϒ” lies between -1 & 0 (1
