Statistical analysis of domestic price volatility of sugar in Ethiopia

Transcription

1 American Journal of Theoreical and Applied Saisics 04; 3(6): Published online Ocober 30, 04 (hp:// doi: 0.648/.aas ISSN: (Prin); ISSN: (Online) Saisical analysis of domesic price volailiy of sugar in Ehiopia Aneneh Asmare Godana *, Yibelal Arega Ashebir, Tewodros Geine Yiraw Universiy of Gondar, College of Naural and Compuaional Science, Deparmen of Saisics, Gondar, Ehiopia address: (A. Asmare), (Y. Arega), (T. Geine) To cie his aricle: Aneneh Asmare Godana, Yibelal Arega Ashebir, Tewodros Geine Yiraw. Saisical Analysis of Domesic Price Volailiy of Sugar in Ehiopia. American Journal of Theoreical and Applied Saisics. Vol. 3, No. 6, 04, pp doi: 0.648/.aas Absrac: The aim of his sudy was o model and idenify deerminans of monhly domesic price volailiy of sugar in Ehiopia over he sudy period from December 00 o December 0 GC. The volailiy in he domesic price of Sugar has been found o vary over monhs suggesing he use of GARCH family approach. Thus, family of special characerisics of ime series models, namely ARCH, GARCH, TGARCH and EGARCH models wih ARIMA mean euaions were fied o he daa. The bes fiing model among each family of models was seleced based on how well he model capures he variaion in he daa and he opimal lag specificaion accessed via AIC and SBIC. Comparisons of he symmeric and asymmeric model were carried ou based on he significance of asymmeric erm in TGARCH and EGARCH models. The analysis showed ha: saisically significance asymmeric erm and leas forecas error from he model esablished ha EGARCH model wih Suden- disribuional assumpions for residual were superior o he GARCH and TGARCH models. Therefore, ARIMA (0,0,)-EGARCH(,3) wih Suden- were chosen o be he bes fiing models for monhly domesic price volailiy of Sugar. Moreover, i was found ha from candidae explanaory variables, impor price for sugar, fuel oil price, exchange rae (dollar-birr), general inflaion, inflaion for non food iems, inflaion for food iems, pas shock, and volailiy on monhly domesic price had saisically significan effec on he curren monh domesic price volailiy on sugar. Keywords: Price Volailiy, Time Series Daa, ARIMA, ARCH, GARCH, TGARCH, EGARCH Models. Inroducion Food price volailiy has srong and long-lasing effecs on emerging economies and low income people; Ensuring food securiy o a growing human populaion is a op prioriy among he challenges facing he world oday. Managing food price insabiliy is a long sanding policy challenge, which, wih mixed experiences of agriculural price policy reforms, has re-emerged as a conemporary policy issue. This is paricularly rue for Ehiopia, where managing food price insabiliy coninues o be a formidable policy challenge. Cereals (eff, whea, maize, sorghum and barley) and cash crops (coffee, oil seeds and sugar) producion and markeing are he means of livelihood for millions of households in Ehiopia. I forms he lion share by being half of food consumpion and one-fourh of average expendiure across various household groups. More specifically, for his sudy I was employ economeric mehods o explore he paerns and deerminae of domesic price volailiy of sugar under consideraion in Ehiopia over he sudy period from December 00 o December 0G.C by developing separae GARCH, TGARCH and EGARCH model wih Box-Jenkins model for condiional mean specificaion... Volailiy Volailiy provides a measure of he possible variaion or movemen in a paricular economic variable. In economic heory, volailiy connecs wo principal conceps: variabiliy and uncerainy; he former describing overall movemen and he laer referring o movemen ha is unpredicable. Lack of predicabiliy and uncerainy associaed wih increased volailiy may influence boh producers and consumers. The review share s monhly closing prices of commodiies over a period of ime; hese observed ne changes, also called reurns. These changing or flucuaing commodiy prices represen a share s volailiy. Reurn: Le P be he price of a commodiy a ime period ( in days, monhs, ec). The price reurn in ime period is defined as

2 78 Aneneh Asmare Godana e al.: Saisical Analysis of Domesic Price Volailiy of Sugar in Ehiopia R ( P P ) = P log( P ) log( P ) T S = (r µ ) T i = is he coninuously compounded reurns. Volailiy: Volailiy is a measure of price variaion from period o ime period. If here is a large price variaion from period o hen R is large (in above value) and hence, we speak of large reurns or large volailiy. Hence, exreme values for reurns reflec exreme price variaion (volailiy) and vice versa. Clearly, if here is no price variaion over ime (volailiy) P = P 0 and R = 0. Noe, ha a period of susained price increases (or decreases) may be characerized by low or high volailiy. Volailiy is ofen measured as he sample sandard deviaion where r is he reurn a ime and µ is he average reurn over he T period. Since variance is he suare of sandard deviaion, i makes no difference which ever measure S or S we use o compare he volailiies of wo commodiies. Two ypes of volailiy are he following:. Mehodology.. Daa To assess he average monhly domesic price volailiy and is deerminans on sugar in Ehiopia, he daa for he sudy were obained from CSA, NBE, ECX and EPE, as secondary daa on monhly basis. They were domesic prices of sugar colleced from 9 sample marke place in he counry, exchange rae, ineres rae, fuel oil price index, general inflaion rae, food inflaion rae, non food inflaion rae, and impor price for sugar observed from December 00 o December 0 GC... Saisical Models The Box-Jenkins ime series model such as Auoregressive (AR), Moving Average (MA) and ARMA are ofen very useful in modeling general ime series daa. However; hey all reuire he assumpion of homoskedaiciy (or consan variance) for he error erm in he model. Bu, his may no be appropriae when dealing wih some special characerisics in he financial and agriculural price ime series and his causes he inroducion o ARCH Auoregressive Condiional Heeroskedasiciy model which was proposed by Engle (98) and generalized by Bollerslev (986) and Taylor (986). Therefore, o come up wih he obecives of he sudy, Afer idenifying he presence of ARCH effecs, he separae GARCH, TGARCH and EGARCH models has been employed in his sudy o invesigae he paern of domesic price volailiy and is deerminans on sugar under consideraion wih oin esimaion of a mean and a condiional variance euaion as model specificaion given below. Le Y be he reurns of average monhly domesic price for sugar under sudy a ime, be error erm (residual) from mean euaion wih mean zero and condiional variance σ and given he hisorical informaion on he average domesic price reurn series as ( Y Y,..., ), Y, under he presence of ARCH effec, for GARCH(p,) family model he condiional mean euaion, The ARMA (m, s) mean model (Box-Jenkins, 976) is given as: m Y = ϖ + ψ y θ + i i i= = s () An Auoregressive Condiionally Heeroskedasiciy model for he variance of he errors which is known as an ARCH () model proposed by Engle (98), he condiional variance is given by 0 αi i i= σ = α + () Generalized by Bollerslev(986) as GARCH(p, ) which allow he condiional variance o be dependen upon previous own lags as model, hen he full model for GARCH(p,) has wo pars he mean model and he condiional variance model given below; p 0 i i i= = (3) σ = α + α + β σ α > 0, α 0, β 0 fori =,... 0 i and =,... p EGARCH (p, ) models wih mean euaion and he variance of residuals a a ime given as: Y = lo g ϖ + ( ) m s ψ i y i θ + i = = σ = α + α + i o i i = σ p i λ i + β lo g σ i = σ = ( ) The full model of TGARCH model wih mean euaion and condiional variance euaion is given as: (5 m s Y = ϖ + ψ y θ + i i i= = 0 i i i = σ = α + α + p λ i S i i + β σ i = = (4) )

3 American Journal of Theoreical and Applied Saisics 04; 3(6): S i if i < 0 = 0if i 0 α > 0, α 0, β 0 fori =,... 0 i and =,... p if i < 0 where S i = Tha is, depending on wheher 0if i 0 is above or below he hreshold value of zero. i More specifically, he general inflaion rae, food inflaion rae, non food inflaion rae, exchange rae, saving ineres rae, fuel oil price, impor price, expor price and monhly seasonal dummies were inroduced ino he condiional variance euaion as exogenous variables in order o deermine he volailiy spillover on he average monhly domesic prices reurns for sugar under consideraion..3. Procedures for Model Building The basic frameworks ha were followed in order o invesigae he paern of domesic price volailiy and is deerminans on, sugar were follows he following Box and Jenkins approach: Tes for he presence of uni roo (non-saionary) case Tes for ARCH effecs Model order selecion for GARCH family model Model parameer esimaion Model adeuacy checking 3. Resuls and Discussion 3.. Descripive Saisics Price Sugar Price Year Figure 3.. Average Monhly Domesic Price Trend for Sugar from December 00 o December 0 GC. The daa se used in his research were average monhly domesic prices in Birr per kg for sugar observed from December 00 o December 0 GC observed a sample of 9 seleced markes in he counry. The reurn series were consruced for sugar prices o allow a marke wide measure of volailiy o be examined. They were calculaed as he coninuously compounded reurns which are he firs difference in logarihms of closing prices on successive monhs. From Figure 3., i can be observed ha monhly domesic prices in Birr per Kg show an increasing rend over he sudy period. In paricular, high increases of domesic prices are observed in he year Table 3.. Summary Resuls for Average Monhly Domesic Prices (in Birr) per kg and Price reurns for Sugar. Saisics Price of Sugar Reurn Series of Sugar Price Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Jarue- Bera Probabiliy Observaions 0 Table 3. displays summary saisics and normaliy es for he prices under sudy. Thus, he empirical resul shows ha he average monhly domesic price (in birr) per kg for sugar was 9.5 wih sandard deviaion of Also displays summary saisics and normaliy es for he reurn compued. The reurns were posiive skewness and longer ails. The coefficien of skewness indicaes ha he series ypically had asymmeric disribuions skewed o he righ. Also he excess kurosis coefficiens indicaed ha he disribuion of price reurn series for sugar possess lepokuric characerisics. Moreover, he implicaion of non-normaliy is suppored by he Jarue-Bera es saisic which poins ou ha he null hypohesis of normal disribuion is reeced a 5% level of significance for reurn series. Hence, he price reurns appropriaely conain financial and agriculural ime series characerisics such as, long ails and lepokurosis as documened by Mandelbro (963), Cornew e al. (984) and Hudson e al. (987). 3.. Tes for Saionariy As many lieraures indicae, mos of he ime series daa possesses non-saionariy propery or uni roo problem. Thus, in order o check for non-saionariy of prices and heir reurns ACF, Augmened Dickey-Fuller and Phillips-Perron ess were used ADF and PP Uni Roo Tess ADF and PP uni roo ess revealed ha all he price series considered were non-saionary as we see in Table 3. This is because of heir corresponding p-values from boh ADF and PP es saisic were greaer han However, es resuls presened in Table 3.3 shows ha monhly domesic prices appear saionary afer firs difference of logarihmic

4 80 Aneneh Asmare Godana e al.: Saisical Analysis of Domesic Price Volailiy of Sugar in Ehiopia ransformaions of average monhly closing prices in o reurn series for he sugar under sudy which were reuired for furher analysis. This is because of heir corresponding p-values from boh ADF and PP es saisics were less han A 5% level of significance, he null hypohesis of non-saionariy was reeced. Table 3.3. ADF Uni Roo Tes a level Price ADF Tes Saisic Criical Value (α = 0.05) p-value Sugar price Table 3.4. ADF Uni Roo Tes a s Difference Table 3.. Mean euaion for monhly domesic price reurn Variable Coefficien Sd. Error -Saisic Prob. C MA() MA() Mean Euaion Deerminaions for Tesing ARCH Effec Based on euaion () hiry six combinaion of (AR 0-5) by (MA 0-5) were compued for each price reurn series.. Opimal lag lengh was seleced based on SBIC provided ha no serial auocorrelaion in he residuals from specified mean model. Therefore mean euaion for average monhly domesic price reurn series for sugar were formed o be ARIMA(0,0,) as shown Table 3. above. Table 3.5 shown below ARIMA(0,0,) model has he smalles SBIC = and so far seleced o be he bes fied model. Bu all he oher fied AR(0-5) and MA(0-5) combinaion of models had greaer SBIC. To verify he adeuacy of seleced mean euaion, he Lung-Box Q(k)-es was performed o check for absence of auocorrelaion in he residuals for correc specificaion as he residuals from a model ha fis he daa well should be uncorrelaed Prices Sugar price Reurns ADF Tes Saisic Criical Value (α = 0.05) p-value * 3.5. Tess for ARCH Effecs To proceed wih volailiy modeling ARCH effecs (wheher or no volailiy varies over ime) in he residuals from he seleced ARIMA model should be esed. The confirmaion of he presence of ARCH effec indicaes ha he volailiy in he average monhly domesic price of sugar is ime varying and appropriaeness of employing GARCH family models Opimal Order Selecion and Parameer Esimaion of GARCH Family Model Once he ARCH effecs are deermined, hen he opimal lag specificaions for GARCH family models were deermined prior o he consrucion of he final model o invesigae he deerminans of domesic price volailiy. Afer esing for differen orders of p and of GARCH family, i was found ha EGARCH(,) under GED disribuional assumpions for residuals, EGARCH(,3) under Suden- disribuional assumpions for residuals and EGARCH(,4) under Normal disribuional assumpions for residuals for domesic price volailiy of sugar were seleced o be bes model o describe he daa as hey possess minimum SBIC. Table 3.5. Opimal Lag seleced Based on SBIC under Differen Disribuional Assumpions of Residuals for Sugar. Model Error Disribuion SBIC Asymmeric erm (α = 0.05) ARIMA(0,0,)-EGARCH(,) GED No significan ARIMA(0,0,)-EGARCH(,3) Suden Significan ARIMA(0,0,)-EGARCH(,4) Normal Significan The above Table shows opimal lag specificaion for EGARCH (p,) models and resul reveals ha asymmeric erms are saisically significan a 5% level of significance for seleced models under specified error disribuions excep monhly domesic price reurn series for sugar under GED disribuional assumpion for residuals. This indicaes ha asymmeric GARCH class models, specifically EGARCH model are appropriae o assess he deerminans of domesic price volailiy for sugar. Moreover, o selec appropriae error disribuion for seleced asymmeric GARCH class models assuming normal, unresriced Suden- and GED disribuions for he error erms from mean euaion, he four error saisics: RMSE, MAE, MAPE and Thail Ineualiy coefficien was applied o evaluae he forecas abiliy of models using in-sample forecas. Thus, empirical resuls show ha EGARCH(,3) model wih disribuional assumpions for residuals under Suden- performs bes as compared o ohers, since in all cases RMSE, MAE, MAPE and Thail Ineualiy Coefficien of EGARCH(,3) for monhly domesic price reurns of sugar, formulaed he model wih he smalles measure of forecas errors.

5 American Journal of Theoreical and Applied Saisics 04; 3(6): Table 3.6. Maximum Likelihood Parameer Esimaes of he Volailiy Models for Seleced Orders wih he Incorporaed Exogenous Variables for Sugar. Parameer Consan AR() MA() MA() ARCH(-) ARCH(-) Asymmeric(-) Asymmeric(-) EGARCH(-) EGARCH(-) EGARCH(-3) Food inflaion rae Non food inflaion rae General inflaion rae Exchange rae Saving ineres rae Fuel oil price Impor price for sugar Ocober November December January February March April May June July Augus Sugar Mean (0.54) * (0.006) * (0.040) Variance * (0.04) * (0.0383) 0.006* (0.0347) * (0.043) (0.5993) (0.6873) * (0.08) (0.938) * (0.0384).06664* (0.047) (0.444) * (0.05) * (0.0399) (0.8) (0.854).76988* (0.0488).8950* (0.034) (0.0660) (0.37).43440* (0.0494) * (0.094) (0.987) (0.3957) 4.389* (0.0008) * are saisically significan a 5% level of significance and values inside he bracke denoes p-values of corresponding o es saisic. A he naional level, a posiive and significance coefficien is eviden for exchange rae (dollar-birr). This is because of is corresponding p-value of o es null hypohesis of coefficien for exchange rae is zero in he variance euaion of domesic price reurns for sugar, respecively were less han 5% level of significance. Thus, here is no evidence o accep null hypohesis a 5% level of significance and he link beween exchange rae and increase in domesic price volailiy a curren monh was likely o be hrough he impac ha exchange rae affec he purchasing power of domesic money. Changes in exchange raes reallocae he purchasing power and price incenives across counries wihou changing

6 8 Aneneh Asmare Godana e al.: Saisical Analysis of Domesic Price Volailiy of Sugar in Ehiopia he overall agriculural commodiies supply demand balance. Dollar devaluaion raises prices US producers and consumer s lowers prices of consumers ouside he dollar area. This implies ha he dollar price of commodiies on world marke were rises as a resul of depreciaion, implying a fall in domesic currency say in, Birr and serling prices (Ridler& Yandle,97). This resul was consisen wih finding by Loening e al. (009), Gilber (989), Chambers (984) and Sarris and Morrison (009). Therefore, a uni increase in he exchange rae of he U.S. dollar s in o birr serves o increases domesic price volailiy for sugar by.0664 unis. Coefficiens of fuel oil price is posiive and saisically significan a 5% level of significance, indicaing ha he change in fuel oil price was also deerminan of curren monh volailiy of domesic price for sugar in he counry over he sudy period. The link beween fuel oil prices and sugar domesic price volailiy is likely o be hrough he fac ha a flucuaion on he fuel oil prices affecs he coss of ransporaion. This finding was consisen wih finding by Swaray (007) and Baffes (007) in he domesic price volailiy for agriculural crops and sugar. Therefore, a uni increase in he fuel oil price serves o increase curren monh domesic price volailiy for sugar by unis. The coefficien of impor price for sugar in he variance euaion was posiive and saisically significan a 5% level of significance since is corresponding p-value (0.0399) was less han 5% level of significance o es null hypohesis of coefficien for impor price is zero was reeced a 5% level of significance. Thus, here is ransmission of impor price for sugar o he domesic price volailiy in he counry over he sudy period. This resul also inline findings by Harald Grehe and Sephan Nole (005) and Rashid e al (006) ha impor price was one of he deerminans of domesic price volailiy. Therefore, a uni increase in he impor price serves o increases domesic price volailiy a curren monh for sugar by unis. The coefficiens of food inflaion rae on price reurn series for sugar were posiive and saisically significan a 5% level of significance. This is because of is corresponding p-value of 0.08, o es null hypohesis of coefficien for inflaion rae for food iems is zero in he variance euaion of domesic price for sugar, were less han 5% level of significance. Likewise, he coefficien of general inflaion rae in he variance euaion for sugar was posiive and saisically significan a 5% level of significance. Among he seasonal dummies added o he EGARCH model price during December, January, April, May and Augus monhs had posiive coefficiens and saisically significan a 5% level of significance, indicaing ha domesic prices during hose monhs had increasing effecs on he curren monh variabiliy of domesic price for sugar. However, price during Sepember monh had negaive coefficien as refleced hrough consan parameer in variance euaion for sugar and saisically significan a 5% level of significance. As p-value of 0.04 was less han 5% level of significance, indicaing ha null hypohesis of consan parameer is zero was reeced, indicaing ha domesic prices during Sepember had decreasing effecs on he curren monh variabiliy of domesic price for sugar. 4. Conclusions and Recommendaions 4.. Conclusions This sudy invesigaes he average monhly domesic price volailiy and is deerminans on sugar in Ehiopia, over he sudy period from December 00 o December 0 GC. The resuls from his sudy provides evidence o show volailiy clusering, lepokuric disribuions and asymmeric effec for average monhly domesic price reurn series for sugar. Thus, from empirical resul i can be conclude ha, he volailiy in he monhly domesic price of rape sugar has been found o vary from monh o monh suggesing he use of GARCH family approach, here is srong evidence ha here is a persisen volailiy in sugar. The forecas performances of he model were evaluaed using he MAE, MAPE, RMAPE and Thail ineualiy coefficien. Asymmeric EGARCH model wih GED and Suden disribuional assumpion for residual was found o fi beer han GARCH and TGARCH models. Therefore, ARIMA(0,0,)-EGARCH(,3) model wih Suden- for Sugar were found o be he bes models for fiing daa on monhly domesic price reurn series. There was evidence o conclude ha he variance of domesic price reurns a curren monh influenced by is previous one monh s lagged volailiy for sugar. There is also significan evidence ha many of he candidae explanaory variables have an impac on monhly domesic price reurn volailiies of sugar, over he sudy period. In monhly series, fuel oil price had a posiive impac on domesic price volailiy for sugar. Likewise, exchange rae (dollar-birr) had posiive influence on monhly domesic price volailiy of sugar, respecively. Also, i can be conclude ha, general inflaion rae, non-food inflaion rae and food inflaion rae had a significan effec on monhly domesic price volailiy of sugar, impor price for sugar had a posiive impac on he domesic price volailiy of sugar. Among he seasonal dummies added o he EGARCH model for sugar, price during December, January, April, May and Augus monhs had significan increasing effecs on he curren monh variabiliy of domesic price of sugar. 4.. Recommendaions As many sudies indicaed price volailiy on sugar has a negaive impac on he economy of he counry by making income insabiliy, for producers, consumers, whole sellers as well as governmens in boh developing and developed counries and also leads o a maor decline in he fuure oupu, if hey are unpredicable, unreliable and if no idenify is deerminans. The aim of his sudy was o model average monhly domesic price volailiy and heir deerminans on sugar. Thus from empirical findings, his sudy draws he following recommendaions: Insabiliy in domesic prices for sugar can occur due o flucuaions in inernaional marke price of impor. In

7 American Journal of Theoreical and Applied Saisics 04; 3(6): such a case, he governmen should ake measure o balance he ineres of consumers o mee he obecives of price sabilizaion. Impor price for fuel oil also had saisically significan increasing effec on he domesic price volailiy. Thus, he governmen should ake some measures o regulae and reduce demand of impor price for fuel oil o mee obecive of domesic price sabilizaion. Exchange rae (dollar-birr) had saisically significan increasing effec on he insabiliy of domesic price; herefore, policy makers and concerned bodies should ake his in o consideraion during exchange rae (dollar-birr) moneary policy seing, o mee he obecives of domesic price sabilizaion. Food inflaion rae, non-food inflaion rae and general inflaion rae had saisically significan increasing impac on he insabiliy of domesic price. Therefore, he governmen, policy makers and concerned bodies should ake some measures o underake inflaion due o food iems, non-food iems as well as general inflaions o alleviae domesic price volailiy. The volailiy in he average monhly domesic price of sugar was varying over ime from monh o monh. Sepember, December, January, April, May and Augus monhs had affeced he average monhly domesic price volailiy of sugar. Thus, he governmen and concerned bodies should follow and conrol he price of sugar during hose monhs. References [] Bollerslev, T. (986). Generalized Auoregressive Condiional Heeroskedasiciy, Journal of Economerics, Vol 3, P [] Engle, R. and Fadng, V. K. (993). Tesing and Measuring he Impac of News on Volailiy, Journal of Finance Vol 48, P [3] Engle, R. F. (98). Auoregressive Condiional Heeroskedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion, Journal of Economerics, Vol 50, P [4] Swaray, R. (007). How did he Demise of Inernaional Commodiy Agreemens Affec Volailiy of Primary Commodiy Prices? Applied Economics, Vol 7, P [5] Ridler, D. and Yandle, C. A. (97). A Simplified Mehod for Analyzing he Effec of Exchange Rae on Expor of Primary Commodiy IMF Saff Paper 9, [6] Loening, J., Durevall, D. and Birru, Y. A. (009). Inflaion Dynamics and Food Prices in an Agriculural Economy: The Case of Ehiopia. World Bank Policy Research Working Paper Series, No [7] Gilber, C. L. (989). The Impac of Exchange Raes and Developing Counry Deb on Commodiy Prices. Journal of Economics, Vol 99, P [8] Chambers, R. G. and Jus, R. E. (984). Effecs of Exchange Rae Changes on U.S. Agriculure. Journals of Agriculural Economics, Vol 73, P [9] Saris, A. and Morisson, J. (009). The Evolving Srucure of World Agriculure Trade: Implicaion for Trade Policy and Trade Agreemens Food and Agriculural Organizaion of Unied Naions (FAO). [0] Baffes, J. (007). Oil Spills on Oher Commodiies. World Bank Policy Research Working Paper. [] Shahidur Rashid (007). Inercommuniy Price Transmission and Food price policies, an analysis of Ehiopian Cereal Markes, Inernaional food policy Research Insiue. [] Harald, G. and Sephan, N. (005). Agriculural Impor Surges in Developing Counries: Exogenous Facors in heir Emergence, Humbold-Universiy of Berlin.