ARIMA Models on Forecasting Sri Lankan Share Market Returns

Transcription

1 ISSN Vol. 2, Issue, pp: (6-2), Monh: January - April 5, Available a: Models on Forecasing Sri Lankan Share Marke Reurns W.G. S. Konarasinghe, 2 N. R. Abeynayake, 3 L.H.P.Gunarane Posgraduae Insiue of Agriculure,Universiy of Peradeniya, Sri Lanka. 2 Faculies of Agriculure and Planaion Managemen,Wayamba Universiy of Sri Lanka, Makandura, Gonawila (NWP), Sri Lanka. 3 Deparmens of Agriculural Economics and Business Managemen,Faculy of Agriculure, Universiy of Peradeniya, Peradeniya, Sri Lanka. Absrac: Sri Lankan share marke reurns have wave like paerns. A wave can be viewed eiher in ime domain or frequency domain. The ime domain is a record of wha happens o a parameer of he sysem versus ime or space. Box-Jenkins mehodology or Auo Regressive Inegraed Moving Average () mehodology was widely applied in explaining wave like paerns when wave is saionary ype. This sudy was focused on esing models on forecasing Sri Lankan share marke reurns. Saionary of he series were esed by Auo Correlaion Funcions and Parial Auo correlaion Funcions. models were esed on oal marke reurns, secor reurns and individual company reurns of Colombo Sock Exchange. Mean Square Error, Mean Absolue Deviaion, residual plos and Anderson Darling es were used in model validaion. Keywords:, Auo correlaion, Fundamenal analysis, Saionary, Technical analysis I. INTRODUCTION Share marke invesmen is considered as high reurn, bu high risk invesmen. As such predicabiliy of share reurns in a secondary marke is of immense imporance o he invesors. A one ime share marke forecasing was oally depend on knowledge and inuiion of he marke expers. Bu laer in 95 s scienific forecasing became more popular in he field. Scienific forecasing is based on mahemaical modeling. A mahemaical model is a simplificaion of a real world siuaion ino an equaion or a se of equaions. Mahemaical models can be classified in many ways. Some of hem are: saic models, dynamic models, deerminisic models and sochasic models. A model is said o be saic when i does no have ime-dependen componen. In conras, dynamic models conain ime-dependen componen. A deerminisic model is one in which every se of variable saes is uniquely deermined by parameers in he model and by ses of previous saes of hese variables. Deerminisic models are no associaed wih any randomness. Conversely, in a sochasic model, randomness is presen and variable saes are described by associaed probabiliy disribuions. In general sochasic models are referred as Saisical models. Saisical models can be broadly classified ino univariae saisical models and mulivariae saisical models. Univariae saisical model is an equaion or se of equaions ha explain he behavior of single random variable over ime while mulivariae saisical models explain he join behavior of wo or more random variables. Univariae saisical modeling procedure is based on he pas inernal paerns in daa o forecas he fuure and no exernal variables are required in forecasing. Auo Regressive Inegraed Moving Average () mehod is a widely applied univariae forecasing echnique in many fields (Sephen, 998). mehodology explained presen value of a series (Y) by pas values of Y iself and he sochasic error erms. According o Gujarai (3), model consiue a flexible class of models for describing he behavior of economic and financial ime series. Various researchers have forecased he behavior of financial ime series using he mehod. Some of he sudies were: Rosangela, Ivee, Lilian and Rodrigo (), Rahman and Hossain (6), Emenike () and Jeffrey and Eric (). Page 6

2 ISSN Vol. 2, Issue, pp: (6-2), Monh: January - April 5, Available a: II. PROBLEM STATEMENT Scienific forecasing in share marke can be mainly divided in o wo pars. They are fundamenal analysis and echnical analysis. Fundamenal analysis involves analyzing he economic facors of a company while echnical analysis ineresed in he price movemens and / or rading volume in he marke. Sri Lankan share marke forecasing has been based on Capial Asse Pricing Model (CAPM), which is derived hrough fundamenal analysis. Bu forecasing abiliy of CAPM has been debaed over he las decades and sudies based on many sock markes given evidence for he incapabiliy of CAPM. Nimal (997), Samarakoon (997) and Konarasinghe and Abeynayake (4-a) have given evidence for he same in Sri Lankan conex. Therefore, Sri Lankan sock marke is in need of finding suiable echniques for forecasing share reurns. Box-Jenkins (976) mehodology or he mehodology has also been widely esed for forecasing share reurns, bu such sudies have been limied in he Sri Lankan conex. However Konarasinghe and Abeynayake (4-b) has shown ha Sri Lankan share marke reurns are saionary ype. Therefore models may suiable in forecasing Sri Lankan sock marke reurns. III. METHODOLOGY models are he mos general class of models for forecasing a ime series which is eiher saionary or can be made o be saionary by differencing. A ime series is saionary if i has no rend, has consan mean and consan variance. The forecasing equaion for a saionary ime series is a linear equaion in which he predicors consis of lags of he dependen variable and/or lags of he forecas errors given by: d p ( B) Y q ( B) Where, Y = presen value, ε : presen error, B = backshif operaor. Lised companies of Colombo Sock Exchange (CSE) in year 3 were he populaion of sudy. The populaion consis business secors. They were; Planaion (PLT), Oil palms (OIL), Land and Propery (L&P), Moors (MTR), Manufacuring (MFG), Telecommunicaion (TLE), Sores supplies (S&S), Trading (TRD), Services (SRV), Power and energy (P&E), Invesmen rus (INV), Hoels and Travels (H&T), Heah care (HLT), Foowear and Texile (F&T), Informaion Technology (IT), Diversified Holdings (DIV), Consrucion and engineering (C&E), Chemicals and Pharmaceuicals (C&P), Beverage Food and Tobacco (BFT), Bank, Finance and Insurance (BFI). models were esed on oal marke reurns, reurns of random sample of four business secors and random sample of 5 companies of CSE. Auo Correlaion Funcions (ACF) and Parial Auocorrelaion Funcions (PACF) were obained o es he saionary of he series. When saionary was confirmed, several models were esed on each series and bes fiing model was seleced by comparing MSE, MAD and resuls of goodness of fi ess. Monhly All Share Price Index (ASPI) daa, secor indices and daily closing share prices of individual companies from year 3 o 3 were obained from CSE daa library. Toal Marke Reurn on monh, (R, m, ) was calculaed by: () R m ASPI ASPI ASPI. Where, ASPI is All Share Price Index on monh. (2) R S I I I. Where, I is he secor index of he monh. (3) Page 7

3 Toal Marke Reurns ISSN Vol. 2, Issue, pp: (6-2), Monh: January - April 5, Available a: Monhly average share prices were calculaed for individual companies and monhly reurns were calculaed by formula: R P P P. (4) Where P is he share price of monh IV. STATISTICAL MODELS AND TECHNIQUES USED IN THE STUDY Generalized Linear Models have been esed in he sudy. Hisogram of residuals, normal plo of residuals and residuals versus fis were obained o examine he goodness of model fi. In addiion Anderson Darling es was used o es he normaliy of residuals. Forecasing abiliy of he models was assessed by wo absolue measures of errors, Mean Square Error (MSE) and Mean Absolue Deviaion (MAD). Goodness of Fi Tess: The goodness of fi of a saisical model describes how well i fis a se of observaions. Measures of goodness of fi ypically summarize he discrepancy beween observed values and he values expeced under he model in quesion. plos; Hisogram of residuals, Normal plo of residuals and residuals versus fis were obained o examine he goodness of model fi. In addiion Anderson Darling es is used for normaliy of residuals. Measuremens of Forecasing Errors: Forecasing is a par of a larger process of planning, conrolling and/ or opimizaion. Forecas is a poin esimae, inerval esimae or a probabiliy esimae. One of he fundamenal assumpions of saisical forecasing mehods is ha an acual value consiss of forecas plus error; In oher words, Error = Acual value Forecas. This error componen is known as he residual. A good forecasing model should have a mean error of zero because i should over forecas and under forecas approximaely he same (Sephen, 998). Measuring errors is vial in forecasing process. Measuremens of errors are divided ino wo pars as absolue measures of errors and relaive measures of errors. V. FINDINGS Daa analysis consiss hree pars: es on oal marke reurns, es on secor reurns and es on individual company reurns. Daa analysis was done by saisical sofware MINITAB. Tes Arima Models On Toal Marke Reurns: Ou liars of he oal marke reurns were removed from he daa se by observing he box plo of daa se. Figure is he ime series plo of ou liar free oal marke reurns. Time Series Plo of Toal Marke Reurns Index Fig. Page 8

4 Frequency Percen Auocorrelaion Parial Auocorrelaion ISSN Vol. 2, Issue, pp: (6-2), Monh: January - April 5, Available a: Fig. shows a wave like paern does no show any rend and suggess a saionary series. Therefore ACF (Fig. 2) and PACF (Fig. 3) of firs difference series were obained: Auocorrelaion Funcion for d (wih 5% significance limis for he auocorrelaions) Parial Auocorrelaion Funcion for d (wih 5% significance limis for he parial auocorrelaions) Lag Lag Fig. 2 Fig. 3 Fig.2 shows one significan spike a lag and confirmed he saionary of he series. Fig. 2 shows decreasing paern and confirm he same. Also above figures suggesed he suiabiliy of Auo Regressive (AR) models and Moving Average (MA) models. Hence several models were esed and summary of resuls are given in Table I. Table I Model Model Fiing Model Verificaion MSE MAD MSE MAD Remarks Model parameers were significan. s were normally disribued and uncorrelaed (,,2) MA 2 was no significan. (,,) AR was no significan. The goodness of fi of a saisical model describes how well i fis a se of observaions. Measures of goodness of fi ypically summarize he discrepancy beween observed values and he values expeced under he model in quesion. plos; Hisogram of residuals, Normal plo of residuals and residuals versus fis were obained o examine he goodness of model fi. In addiion Anderson Darling es was used for normaliy of residuals. Figure 4 is he residual plos of (,, ): Plos for Toal Marke Reurns Normal Probabiliy Plo of he s s Versus he Fied Values Fied Value 2 Hisogram of he s s Versus he Order of he Daa Observaion Order 8 2 Fig. 4 Page 9

5 ISSN Vol. 2, Issue, pp: (6-2), Monh: January - April 5, Available a: In Normal Probabiliy Plo of s, almos all he poins were on a sraigh line. Hisogram of s was symmerical. Also p value of Anderson Darling es (.58) was greaer han he significance level (.5). Therefore i was concluded ha he residuals of he model are normally disribued. Plo of Vs Fied Values did no show any paern and hey lie on boh sides of zero. I suggess he independence of residuals. Modified Box-Pierce (Ljung- Box) Chi-Square saisic was greaer han significance level (.5), confirmed he independence of residuals. Hence (,, ) is he bes fiing model for forecasing oal marke reurns of CSE. Same procedure was repeaed wih secor reurns and individual company reurns. Table II gives he summary of oupus of secor reurns and Table 3 gives he summary of oupus of individual company reurns. Business Secor Bes Fiing Model Secor DIV Secor L&P Secor MFG Secor MTR Table II: Bes Fiing Models for Secor reurns Model Fiing Model Verificaion Remarks of residuals MSE MAD MSE MAD Normal, uncorrelaed Normal, uncorrelaed Normal, uncorrelaed Normal, uncorrelaed MAD of all he models was saisfacory in boh model fiing and model verificaion, bu MSE s of he models were high. Sill residuals of all he models were normally disribued and uncorrelaed. Therefore (,, ) are he bes fiing models for all he four secors. Company Bes Fiing Model Table III: Bes Fiing Models for Individual Company reurns Model Fiing Model Verificaion Remarks of residuals MSE MAD MSE MAD COMBANK (,,) Normal, uncorrelaed HNB No normal, uncorrelaed BREW (,,) Normal, uncorrelaed LMF AGAL BOGA WATA JKH Normal, uncorrelaed Normal, uncorrelaed Normal, uncorrelaed Normal, uncorrelaed Normal, uncorrelaed Page

6 ISSN Vol. 2, Issue, pp: (6-2), Monh: January - April 5, Available a: DIAL (,,) Normal, uncorrelaed CIC Normal, uncorrelaed HAYL (,,) Normal, uncorrelaed GALAD TWOD TAJ RICH No normal, uncorrelaed No normal, uncorrelaed Normal, uncorrelaed Normal, uncorrelaed MAD of all he models was saisfacory in boh model fiing and model verificaion, bu MSE s of he models were high in some models. s of all he models were normally disribued and uncorrelaed. (,, ) is suiable for forecasing reurns of 2 companies and (,, ) suiable for forecasing reurns of he oher 3 companies. According o he resuls, (,, ) model: Y (5) Y is he bes fiing model for forecasing Sri Lankan sock marke reurns. VI. CONCLUSION Share rading is an imporan par of he economy of a counry from boh he indusry s poin of view as well as he invesor s poin of view. For example, whenever a company wans o raise funds for furher expansion or seling up a new business venure, insead of aking loans i can issue shares of he company. On he oher hand an invesor can ge he par ownership of he company hrough buying shares. Also invesors have he abiliy o quickly and easily sell securiies. Bu Share marke invesmen is involved wih high risk, compared o he oher forms of invesmen such as invesmen in real esae, reasury bills ec. Therefore forecasing share reurns were immensely imporan o he invesors. Scienific forecasing in share marke reurns based on wo main caegories: fundamenal analysis or echnical analysis. Forecasing Sri Lankan share marke reurns has been based on fundamenal analysis, bu has been proved unreliable. As such i is essenial o find a suiable forecasing echnique for Sri Lankan share marke. models have been successfully used in forecasing economic ime series; however such sudies were limied in Sri Lankan conex. This sudy was focused on esing models in forecasing Sri Lankan share marke reurns. Saionary of oal marke reurns, secor reurns and individual company reurns were confirmed by ACF s and PACF s. Based on he resuls, i was concluded ha models are suiable in forecasing Sri Lankan sock marke reurns. REFERENCES [] Box, G.P.E., & Jenkins, G.M. (976).Time Series Analysis: Forecasing and Conrol. Holden Day, San Francisco. [2] Emenike, K., O.Forecasing Nigerian Sock Exchange Reurns: Evidence from auoregressive Inegraed Moving Average () Model. Deparmen of Banking and Finance, Universiy of Nigeria, Enugu Campus, Enugu Sae, Nigeria,. [3] Gujarai, D.N. Basic Economerics (4h Ed), Delhi: McGraw Hill Inc., (3). Page

7 ISSN Vol. 2, Issue, pp: (6-2), Monh: January - April 5, Available a: [4] Jeffrey, E. J., Eric, K.,). Modeling Wih Inervenion o Forecas and Analyze Chinese Sock Prices. om In. j. eng. bus. manag.,, Vol. 3, No. 3, pp ,. [5] Konarasinghe, W.G.S., & Abeynayake, N.R., Modeling Sock Reurns of Individual Companies of Colombo Sock Exchange. Conference Proceedings of he s Inernaional Forum for Mahemaical Modeling 4, Deparmen of Mahemaics, Universiy of Colombo, Sri Lanka, pp -4, 4-a. [6] Konarasinghe, W.G.S. & Abeynayake, N.R., Time Series Paerns of Sri Lankan Sock Reurns. Proceedings of Docoral Consorium, h Inernaional Conference in Business & Managemen, Universiy of Sri Jayewardenepura, Sri Lanka, pp , 4-b. [7] Nimal, P.D., Relaionship beween Sock Reurns and Seleced Fundamenal Variables; Evidence from Sri Lanka. Sri Lankan Journal of Managemen, 2(3), 997. [8] Rahman, S., & Hossain, M.F.Weak Form Efficiency: Tesimony of Dhaka Sock Exchange.Journal of Business Research, Vol.8, pp. -2, 2. [9] Rosangela, B., Ivee L., Lilian M.,& Rodrigo, L.A comparaive analysis of Eurofuzzy, ANN and models for Brazilian sock index forecasing. Deparmen of Economic Theory, Insiue of Economics, Universiy of Campinas, Brazil,. [] Samarakoon, M. P., The Cross Secion of Expeced Sock Reurns of Sri Lanka. Sri Lankan Journal of Managemen, 2(3), 997. [] Sephen, A., D., (998). Forecasing Principles and Applicaions. Firs Ediion. Irwin McGraw-Hill, USA. Page 2