Analysis of the Interrelationships between the Prices of Sri Lankan Rubber, Tea and Coconut Production Using Multivariate Time Series

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1 Advances in Economics and Business 3(2): 50-56, 2015 DOI: /aeb htt:// Analysis of the Interrelationshis between the Prices of Sri Lankan, and Coconut Production Using Multivariate Time Series Kwadwo Agyei Nyantakyi *, B. L. Peiris, L. H. P. Gunaratne Postgraduate Institute of Agriculture, University of Peradeniya, Sri Lanka Coyright 2015 Horizon Research Publishing All rights reserved. Abstract With the globalization of the economy and the financial markets today, rice movement of one market can sread easily and instantly to another market. Because of these financial markets are more or less deendent on each other, there is a need to study their interrelationshis to understand the dynamic structure of the financial economy. In this aer, we use Vector Auto Regression (VAR) Analysis to study the interdeendency of the rice of tea, rubber and coconut roduction in Sri Lanka. We also measured the strength of the linear interrelationshi between the assets using the llllll ll cross-correlation matrix (CCM) and also fit a VAR-model using selection criteria based on the AIC, SIC and HQIC. We examined the individual behaviour of the searate rices of each asset and then analysed the combined effects of the rices. Out of all comuting models, we observed that tea rice was ARIMA (0,1,0), rubber rice was ARIMA (3, 1, 1) and coconut rice is ARIMA (0, 1, 3). Thus they were all integrated of order I(1). We investigate if there is a cointegration between the assets to see if there was a long-run equilibrium, and there was at most one cointgretion equation. Hence we used the Vector Error Correction model (VECM), for the estimation. We observed that coefficients between any of the variables were not equal to zero. The coefficient estimates between tea and rubber were not the same as between rubber and tea at all lags, between tea and coconut, as well as between rubber and coconut. Which indicate that there may be feedback relationshi between all the three series. Further, imulse resonse analyses were used to observe the imacts. There was a fairly strong correlation between them, hence it could be concluded that, there is a linear deendency of all the variables. Keywords Cross-correlation Matrix, Cointegration, Vector Error Correction 1. Introduction Agricultural sector lays very imortant role in Sri Lankan economy. From , it has aroximately emloyed 31.3% annually for the labour force. The sector has also contributed aroximate annual income of Rs million from as a suort to the GDP of Sri Lanka (Deartment of Census and Statistics, 2013)[7]., rubber and coconut are some of the major agricultural commodities that contribute immensely to the GDP of Sri Lanka. They also serve as a key emloyment area for the economy. roduction in Sri Lanka is of high imortance to the Sri Lankan economy and the world market. Sri Lanka is the fourth largest tea roducer in the world. The tea industry is one of the country's main sources of foreign exchange and a significant source for emloyment. is accounting for 12% of the GDP and generated roughly on the average of Rs million annually from The tea sector currently emloys directly or indirectly over one million eole in Sri Lanka and in 1995 directly emloyed 215,338 on tea lantations and estates. Annual Reort ( ) [6,13]. In the world, Sri Lanka is one of the nine major roducers of natural rubber, and in terms of roductivity, is now the third best following India and Indonesia. From , rubber has contributed on the average of Rs million er year to the GDP of Sri Lanka. The rubber sector emloys directly or indirectly over one million eole in Sri Lanka. Coconut is one of the common food roduct found in Sri Lanka. From , coconut has contributed on the average Rs million er year to the GDP of Sri Lanka. The coconut estates emloy directly or indirectly over one million eole in Sri Lanka as well. (Deartment of Census and Statistics, 2013) Various researchers have looked at different estimations of the returns on the individual cros, but we believe that with the globalization of the economy and the financial markets today, rice movement of one market can sread easily and instantly to another market. Since these financial markets are more or less deendent on each other, there is a need to study their interrelationshis to understand the dynamic structure of the financial economy. In this aer we

2 Advances in Economics and Business 3(2): 50-56, use Vector Auto Regression (VAR) Analysis to study the interdeendency of the returns on tea, rubber and coconut which are some of the imortant cash cros in Sri Lanka. The objective of the study is to understand the dynamic structure of the financial economy. In order to achieve this objective, in articular, the study would exlore the following secific objectives, to examine behaviour of the rices of the individual assets, to investigate the interrelationshi between the rices of tea, rubber and coconut and the total behaviour of the effects of the rices on the assets. The study will establish, if the rice movement of one market can sread easily and instantly to another market which makes financial markets more or less deendent on each other, hence the need to study their interrelationshis to understand the dynamic structure of the financial economy. This study is also done to add knowledge to the understanding of the interrelationshi between these imortant lantation cros and their returns on the GDP of the Sri Lankan economy. Hyothesis: H0: There is interrelationshi between the rices of tea, rubber and coconut H1: There is no interrelationshi between the rices of tea, rubber and coconut 2. Materials and Methods Data Source Annual secondary data was collected from FAOSTAT [9], food balance sheet, rice statistics and from, Deartment of Census and Statistic Sri Lanka. These data comrises of the annual rices of tea, rubber and coconut from The estimates in real terms of the ast data series were based on the constant rices of 1958, 1963, 1975 and The current rice estimates were at current factor cost rices until 1975 and thereafter it was at current roducer rices. The National Accounts estimates are comiled based on the UN - guidelines given in the System of National Accounts (SNA), Ministry Of Statistics (2010)[11]. Statistical Software The R software was used in analysing and fitting the VECM models. Behaviour of the Data Figure 1 is the time series lot showing the behaviour of the rice of the variables tea, rubber and coconut between , with rices of rubber having a higher uward growth/movement than the others. and rubber rices exhibit similar characteristics. Initially there was an increase in growth of tea rices from , however, there were shar dros in 1999 and Price in Sri Lanka Rs (Coconu Figure 1. Time series lot of the rice of tea (blue colour), rubber (black colour) and coconut (red colour) in the eriod ( ) 2. Methodology Let XX 1, XX 2 aaaaaa XX 3 be the individual rice of the assets tea, rubber and coconut resectively, and XX tt the total returns with XX tt = (XX 1tt, XX 2tt, XX 3tt ) of the assets at time t, where aa denotes the transose of aa. Then let a stochastic rocess {x it :t Z} be an autoregressive rocess of order ( 1 ) (AR(P)-rocess), X t x t x t 1 = k = 1 2 = k = 1 3 = k = 1 { t α x t k k α x t k k α x t k k + ε t, + ε t, + ε t, where ε } is a white noise. Years 1 < t <, α 0 1 < t <, α 0 1 < t <, α 0 Richard and Johnson (2012) [12] and Anderson (1951, 1984) [3,4] define the mean vector and the covariance matrix as: μμ = EE(XX tt ) is the k-dimensional vector of the unconditional exectations of XX tt and Γ 0 = EE[XX tt μμ][xx tt μμ] where Γ 0 is a kk k matrix and μμ = (μμ 1,, μμ kk ) and the (ii, jj) tth element of Γ 0 is the covariance of XX iiii aaaaaa XX jjjj. Let DD be a kk k matrix diagonal matrix consisting of the standard deviations of XX iiii for ii = 1,, kk. Then DD = dddddddd[ Γ 11 (0), Γ kkkk (0) The lag-zero cross-correlation matrix (CCM) of XX tt is given by ρρ 0 = ρρ iiii (0) = DD 1 Γ 0 DD 1

3 52 Analysis of the Interrelationshis Between the Prices of Sri Lankan, and Coconut Production Using Multivariate Time Series where ρρ iiii (0) = ρρ jjjj (0) aaaaaa 1 ρρ iiii (0) 1 aaaaaa ρρ iiii (0) = 1 for 1 ii, jj kk. Thus ρρ(0) is a symmetric diagonal matrix with unit elements. This is used to measure the strength of the linear deendence between the time series variables. The LLLLLL ll cross-covariance matrix of XX tt is given by Γ ll = Γ iiii (ll) = EE([XX tt μμ][xx tt ll μμ] ) where the (ii, jj) tth element of Γ ll is the covariance of XX iiii aaaaaa XX jj,tt ll. And the llllll ll cross-correlation matrix of XX tt is defined as ρρ ll = ρρ iiii (ll) = DD 1 Γ ll DD 1 the cross covariance matrix can be estimated. Given a time series XX tt, The Vector Autoregressive (VAR) model of order 1 or VAR(1) is defined as: XX tt = φφ 0 + ΦXX tt 1 + aa tt where φφ 0 Is a k-dimensional vector, Φ is a kk kk matrix and {aa tt } is a sequence of serially uncorrelated random vectors with mean zero and covariance matrix Σ, which is required to be ositive definite. Ang. et al (2003),[1]. Therefore, for a VAR(1) with kk = 3, XX tt = (XX 1tt, XX 2tt, XX 3tt ) aaaaaa aa tt = (aa 1tt, aa 2tt, aa 3tt ) Hence, we have the following equations: XX 1tt = φφ 10 + Φ 11 XX 1,tt 1 + Φ 12 XX 2,tt 1 + Φ 13 XX 3,tt 1 + aa 1tt XX 2tt = φφ 20 + Φ 21 XX 1,tt 1 + Φ 22 XX 2,tt 1 + Φ 23 XX 3,tt 1 + aa 2tt XX 3tt = φφ 30 + Φ 31 XX 1,tt 1 + Φ 32 XX 2,tt 1 + Φ 33 XX 3,tt 1 + aa 3tt Where Φ iiii iiii tthee (ii, jj) tth element of Φ and φφ ii0 is the ii tth element of φφ 0. The Error Correction Model Cointegration is a relationshi between two nonstationary, I(1), variables (Reinsel, 1990)[2]. These variables share a common trend and tend to move together in the long-run. A dynamic relationshi between I(0) variables which embeds a cointegrating relationshi known as the short-run error correction model. Consider a k-dimensional VAR() time series XX tt then; XX tt = φφ 0 + Φ 1 XX tt Φ XX tt + aa tt Then an error correction model (ECM) for the VAR() is given by XX tt = φφ 0 + ππxx tt 1 + Φ 1 XX tt Φ 1 XX tt +1 + aa tt where ππ = ααββ = Φ + Φ Φ 1 II = Φ (1) Determination of the Lag Length The otimum lag length was selected based on the selection rocedure roosed by Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC) and Quinn Information Criterion (HQIC). 3. Results and Discussion Descritive statistic of rices of tea, rubber and coconut (in Ruees) between is given in Table 1. Table 1. Ruees) Descritive statistical of return on tea, rubber and coconut (in Variable Obs Mean Price Price Coconut Price Std. Dev Q1 Min Q3 Max From Table 1, it can be seen that the average rice of tea between was Rs er tonne with a minimum rice of Rs 3300 and maximum of Rs er tonne. Also it could be observed that the average rice of rubber between was Rs er tonne with a minimum rice of Rs 1740 and maximum of Rs er tonne. An average coconut rice was Rs 6437 er tonne, with a minimum rice of Rs 180 er tonne and a maximum rice of Rs er tonne. Dickey Fuller Unit-root Test In order to establish the order of the series, the Augmented Dickey Fuller unit-root test was used to investigate whether the series of the rices of tea, rubber and coconut were stationary. Results are given in Table 2. Variable Table 2. Dickey-Fuller test for unit root results Test statistic 1% 5% 10% Coconut Considering the results from Table 2, since - (P>0.05) at all the s, we fail to reject the null hyothesis that there is unit root at all the s ( 1%, 5%, and 10%) for all the variables. Model Selection for the Individual Assets Using Akaike Information Criterion and Schwarz Information Criterion as selection criteria for the individual asset model is summarized below: Model for Price ARIMA(0,1,0) AIC= AICc= BIC=940.3 log likelihood = The best model based on the selection criteria for tea rice

4 Advances in Economics and Business 3(2): 50-56, was ARIMA (0, 1, 0). Model for rubber rice is given in Table 3. ARIMA (3, 1, 1) Table 3. Model for rubber rice Constant ar1 ar2 ar3 ma1 Coefficients Standard Error AIC=952.6, AICc=954.93, BIC=963.16, log likelihood= From Table 3, the best model for the rubber rice is ARIMA (3, 1, 1) based on the selection criteria. Model for coconut rice is given in Table 4. Table 4. Model for coconut rice returns ARIMA (0, 1, 3) Constant ma1 ma2 ma3 Coefficients Standard Error AIC=789.06, AICc=790.68, BIC=797.86, log likelihood = From Table 4, the best model for the coconut rice is ARIMA (0, 1, 3) based on the selection criteria. Johansen tests for cointegration We investigate, whether tea, rubber and coconut rices have a long-run equilibrium by erforming a cointegration test (Johansen, 1988) [10]. Johansen tests results for cointegration are given in Table 5. Maximum rank Table 5. Johansen tests for cointegration Parms LL Eigen Trace statistics 5% * We observe in Table 5 that, at Rank (0) the Trace statistic is 36.8 which is greater than 29.68; hence we reject the hyothesis at 5% that there is no cointegration between tea, rubber and coconut. That is there is a long run association. But at all the other Ranks, the Trace s were less than the 5% s. Therefore, we used the Vector Error Correction model (VECM) (Granger et al., 1987) [8]. Multivariate Analysis for the VECM- Model Lag selection order Using the lag selection rocedure for the maximum lags for the VECM-model, we used the AIC, HQIC, and SBIC selection criteria. The summary is given in Table 6. With tea, rubber and coconut rices as endogenous and the constant as exogenous factors, using the lag selection criteria of AIC, HQIC and SBIC, a maximum of otimal seven lags (7) were selected for the VEC-model as shown on Table 6. Vector Error Correction model (VECM) Table 7 is showing the summary of the otimum model selection for the VECM - Model based on the selection criteria AIC, SBIC, and HQIC, resectively. AIC = , SBIC = , HQIC = , Log likelihood = Table 6. Lag selection using AIC, HQIC and SBIC Lag LL LR df P FPE AIC HQIC SBIC e e e e e e e e Table 7. VECM -model Selection Equation Parms RMSE R-sq chi2 P>chi2 D_ D_ D_Coconut

5 54 Analysis of the Interrelationshis Between the Prices of Sri Lankan, and Coconut Production Using Multivariate Time Series From Table 7 with root mean square error (RMSE) of , and for tea, rubber and coconut and R-square of 0.91, 0.96 and 0.95 for tea, rubber and coconut, resectively. The selected model aroximately exlains about 93% of the variation of the data. Analysis of the equations arameter estimates The summary of the arameter estimation for tea as the deendent variable is given in Table 8. Table 8. Estimated coefficients for tea rices as deendent variable Variables D_ Coef. Std. Err. z P> z L3D L4D L6D L2 D L3D L6D In Table 8, the error correction term was not significant hence there is no long run causality between tea, rubber and coconut. deends on it lags 3,4 and 6 difference and on lags 2,3, and 6 differenced of rubber, hence there is a short run causality between tea and rubber but not coconut. Coconut arameter estimates The summary of the arameter estimation for coconut rices as the deendent variable is given in Table 9. From Table 9, the error correction term is significant; hence there is long run causality between rubber, tea and coconut. Coconut deends on tea at lag 1, rubber at lags 2 and 5 and coconut at lags 1 and 2 difference, resectively. Hence there is short run causality between rubber, tea and coconut. Table 9. Estimated coefficients for coconut rices as the deendent variable Variables D_Coconut Coef. Std. Err. z P> z L LD L2D L5D Coconut LD L2D arameter estimates The summary of the arameter estimation for rubber rices as the deendent variable is given in Table 10. Table 10. Estimated coefficients for rubber rices as the deendent variable Variables D_ Coef. Std. Err. z P> z L LD L2D L3D L4D L5D L6D LD L2D L3D L4D Coconut LD L2D L3D L4D L5D L6D From Table 10 above, the error correction term is significant; indicating the existence of long run causality between rubber, coconut and tea. deends on tea at all the six lags, at lags 1, 2, 3 and 4 and Coconut at lags 1 and 2, 3, 4, 5, and 6 differences resectively. Hence there is short run causality between rubber, tea and coconut. Diagnostic Test Autocorrelation Test Using the Lagrange-multilier test, we tested for autocorrelation at lags 1 and 2. Table 11 shows the summary of results: Table 11. Lagrange-multilier test for autocorrelation Lag chi2 df Prob > chi From Table 11, with robability of and for lags 1 and 2, resectively. This indicates that there is no significant autocorrelation at the lag order.

6 Advances in Economics and Business 3(2): 50-56, Normality Test Using Jarque-Bera, we tested for normality in the residuals. Results of Jarque-Bera normality test for the residuals is given in Table 12, Table 12. Jarque-Bera normality test for the residuals: Equation chi2 df Prob > chi2 D_tea D_rubber D_coconut ALL From Table 12, we observed that all the robability s of the variables including the overall have P>0.05, hence the residuals are normally distributed. Correlation Matrix As roosed by Moynihan (1990) [5], the cross-correlation matrix of the variables is summarized in Table 13. Table 13. Correlation matrix Variable Coconut tea Coconut tea From Table 13, the correlation between rubber and coconut is There is an indication of strong ositive relationshi between the rices of rubber and coconut. The correlation between coconut and tea rices is 0.47 which is fairly strong. And the correlation between rubber and tea rices is 0.42 which is also fairly strong. Imulse Resonses (IR s) The Imulse Resonse (IR s) is given in Figure 2. The first row shows rubber resonses from the shocks of rubber rice, coconut rice and finally tea rices. The second row shows rubber resonses to the shocks of rubber rice, coconut rice and finally tea rices. The third row shows rubber resonses from the shocks of rubber rice, coconut rice and finally tea rices. 4. Conclusions There is also both long run and short run causality among tea, rubber and coconut rices. The coefficient estimates between tea and rubber are not the same as between rubber and tea at all lags, between tea and coconut, as well as between rubber and coconut. This indicates that there is a feedback relationshi between the three series. From the analysis above it could be observed that the coefficients between any of the variables was not equal to zero, that is, there is an indication of linear deendency of all the variables. We could conclude that the rice movement of one market can sread easily and instantly to another market and also there is a fairly strong correlation between the rices of the assets. Therefore, financial markets are more or less deendent on each other; hence there is an interrelationshi between variables which can exlain the dynamic structure of the financial economy varbasic, coconutri, coconutri varbasic, coconutri, rubberri varbasic, coconutri, tearice varbasic, rubberri, coconutri varbasic, rubberri, rubberri varbasic, rubberri, tearice varbasic, tearice, coconutri varbasic, tearice, rubberri varbasic, tearice, tearice ste 95% CI orthogonalized irf Grahs by irfname, imulse variable, and resonse variable Figure 2. Imulse resonse (IR s) of rubber, coconut and tea.

7 56 Analysis of the Interrelationshis Between the Prices of Sri Lankan, and Coconut Production Using Multivariate Time Series Aendix Attached is the time series data of annual rices of tea, rubber and coconut from years coconut rubber tea REFERENCES [1] Ang, M. Piazzesi, (2003), A no-arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables, Journal of Monetary Economics 50: [2] Ahn, SK. and G.C. Reinsel (1990), Estimation for Partially Nonstationary Autoregressive Models, Journal of the American Statistical Association, 85, [3] Anderson, T.W. (1951) Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions, Annals of Mathematical Statistics, 22, [4] Anderson, T.W. (1984), An Introduction to Multivariate Statistical Analysis, 2nd Edition. Wiley: New York. [5] Andrews, D.W.K. and J.C. Moynihan (1990), An Imroved Heteroskedastic and Autocorrelation Consistent Covariance Matrix Estimator, Cowles Foundation Discussion Paer No. 942, Yale University. [6] Annual Reort ( ), Bogawantalawa Estates Ltd. [on line]. [Accessed on ]. Available at [7] Deartment of Census and Statistics, Annual Bulletin 2013, [on line]. [Accessed on ]. Available at [8] Engle, R. F. and Granger, C. W. J. (1987). Co-integration and error correction reresentation, estimation and testing. Econometrica 55: [9] FAOSTAT, Sri Lanka Annual Data( ),[on line]. [Accessed on ]. Available at htt://faostat.fao.org. [10] Johansen, S. (1988). Statistical analysis of co-integration vectors. Journal of Economic Dynamics and Control 12: [11] Manual on Agricultural Prices and Marketing - Ministry Of Statistics (2010), [on line]. [Accessed on ]. Available at Mosi.Nic.In/Mosi.../Manual-On-Agricultural-Prices-And- Marketing.df. [12] Richard A. Johnson, (2012), Alied Multivariate Statistical Analysis, 6 th Edition Willy New Delhi : [13] Sri Lanka Board: Annual Reort. (2010), Sri Lanka Board. 574, Galle Road. Colombo 03. Sri Lanka. Issn: