Forecasting volatility: Evidence from the Macedonian stock exchange

Kovačić, Zlatko (2007): Forecasting volatility: Evidence from the Macedonian stock exchange.

Abstract

This paper investigates the behavior of stock returns in an emerging stock market namely, the Macedonian Stock Exchange, focusing on the relationship between returns and conditional volatility. The conditional mean follows a GARCH-M model, while for the conditional variance one symmetric (GARCH) and four asymmetric GARCH types of models (EGARCH, GJR, TARCH and PGARCH) were tested. We examine how accurately these GARCH models forecast volatility under various error distributions. Three distributions were assumed, i.e. Gaussian, Student-t and Generalized Error Distribution. The empirical results show the following: (i) the Macedonian stock returns time series display stylized facts such as volatility clustering, high kurtosis, and low starting and slow-decaying autocorrelation function of squared returns; (ii) the asymmetric models show a little evidence on the existence of leverage effect; (iii) the estimated mean equation provide only a weak evidence on the existence of risk premium; (iv) the results are quite robust across different error distributions; and (v) GARCH models with non-Gaussian error distributions are superior to their counterparts estimated under normality in terms of their in-sample and out-of-sample forecasting accuracy.

• Item Type: MPRA Paper
• Institution: The Open Polytechnic of New Zealand
• Language: English
• Keywords: Stock market; forecasting volatility; South-Eastern Europe; GARCH models; non-Gaussian error distribution; Macedonia
• Subjects: G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Ajayi, R. A., Mehdian, S., & Perry, M. J. (2004). The day-of-the-week effect in stock returns - Further evidence from Eastern European emerging markets. Emerging Markets Finance and Trade, 40(4), 53-62. Alexander, C. (2001). Market models: A guide to financial data analysis. New York, NY: John Wiley & Sons. Anatolyev, S. (2006). Nonparametric retrospection and monitoring of predictability of financial returns. Centre for Economic and Financial Research at New Economic School, Moscow. Anatolyev, S., & Shakin, D. (2006). Trade intensity in the Russian stock market: Dynamics, distribution and determinants. Centre for Economic and Financial Research at New Economic School, Moscow. Apolinario, R. M. C., Santana, O. M., Sales, L. J., & Caro, A. R. (2006). Day of the week effect on European stock markets. International Research Journal of Finance and Economics, (2), 53-70. Baele, L., Crombez J., & Schoors, K. (2003). Are Eastern European equity markets integrated? Evidence from a regime-switching shock spillover model. Working Paper, Ghent University. Bekaert, G., & Wu, C. (2000). Asymmetric volatility and risk in equity markets. Review of Financial Studies, 13(1), 1-42. Bera, A. K., & Higgins, M. L. (1993). ARCH models: Properties, estimation, and testing. Journal of Economic Surveys, 7(4), 305-366. Black, F. (1976). Studies in stock price volatility changes. Proceedings of the 1976 Business Meeting of the Business and Economics Statistics Section, American Statistical Association, 177-181. Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307-327. Bollerslev, T., & Wooldridge, J. M. (1992). Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances. Econometric Review, 11, 143-172. Bollerslev, T., Chou, R. Y., & Kroner, K. F. (1992). ARCH modelling in finance, a review of the theory and empirical evidence. Journal of Econometrics, 52, 5–59. Bollerslev, T., Engle, R., & Nelson, D. (1994). ARCH models. In R.F. Engle and D. MacFadden (Eds.), Handbook of Econometrics, IV, Amsterdam: Elsevier. Brailsford, T. J., & Faff, R. W. (1996). An evaluation of volatility forecasting techniques. Journal of Banking & Finance, 20(3), 419-438. Campbell, J. Y., & Hentschel, L. (1992). No news is good news: An asymmetric model of changing volatility in stock returns. Journal of Financial Economics, 31, 281-318. Cappiello, L., Engle, R. F., & Sheppard, K. (2003). Asymmetric dynamics in the correlations of global equity and bond returns. ECB Working Paper No. 204. Chukwuogor-Ndu, C. (2006). Stock market returns analysis, day-of-the-week effect, volatility of returns: Evidence from European financial markets 1997-2004. International Research Journal of Finance and Economics (1), 112-124. Cihak, M., & Janaček, K. (1997). Stock-market volatility and real processes in the Czech economy. Eastern European Economics: A Journal of Translations, 35, 6-34. Claessens, S., Djankov, S., & Klingebiel, D. (2000). Stock markets in transition economies. Financial Sector Discussion Paper No. 5. The World Bank. Cont, R. (2001). Empirical properties of asset returns: Stylized facts and statistical issues. Quantitative Finance, 1(1), 1-14. Cont, R. (2005). Long range dependence in financial markets. In J. Lévy-Véhel & E. Lutton (Eds.), Fractals in engineering: New trends in theory and applications (pp. 159-180): Springer. Cont, R. (2007). Volatility clustering in financial markets: Empirical facts and agent-based models. In G. Teyssière & A. P. Kirman (Eds.), Long Memory in Economics (pp. 289-310): Springer. De Goeij, P., & Marquering, W. (2004). Modelling the conditional covariance between stock and bond returns: A multivariate GARCH approach. Journal of Financial Econometrics, 2(4), 531-564. Deželan, S. (2000). Efficiency of the Slovenian capital market. Economic and Business Review, 2, 61-83. Ding, Z., Granger, C. W. J., & Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1, 83-106. Dumitru, A.-M., Mureşan, A., & Mureşan, V. (2005). The long and short run interdependences between the Romanian equity market and other European equity markets. In S. Poloucek & D. Stavarek (Eds.), Future of Banking after the Year 2000 in the World and in the Czech Republic (Vol. X – Finance and Banking, pp. 592-611): Karvina: Silesian University. Égert, B., & Kočenda, E. (2005). Contagion across and integration of Central Eastern European stock markets: Evidence from intraday data. William Davidson Institute Working Paper Number 798. Égert, B., & Koubaa, Y. (2004). Modelling stock returns in the G-7 and in selected CEE economics: A non-linear GARCH approach. William Davidson Institute Working Paper Number 603. Elliot, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64, 813-836. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4), 987-1007. Engle, R. F., & Ng, V., K. (1993). Measuring and testing the impact of news on volatility. Journal of Finance, 48(5), 1749-1778. Engle, R. F., Lilien, D. M., & Robins, R. P. (1987). Estimating time varying risk premia in the term-structure: The ARCH-M model. Econometrica, 55(2), 391-407. Fama, E. F. (1965). The behaviour of stock market prices. Journal of Business, 38, 34–105. FEAS. (2007). Semi annual report - April 2007. Federation of Euro-Asian Stock Exchanges. Fruk, M. (2004). Sezonalnost prinosa dionica na Zagrebačkoj burzi. Finansijska Teorija i Praksa, 28(4), 435-444. Gelos, G., & Sahay R. (2000). Financial market spillovers in transition economies. Economics of Transition, 91, 53–86. Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48(5), 1779–1801. Grambovas, C. A. (2003). Exchange rate volatility and equity markets. Eastern European Economics, 41(5), 24-48. Guillaume, D. M., Dacorogna, M. M., Davé, R. R., Müller, U. A., Olsen, R. B., & Pictet, O. V. (1997). From the birds eye view to the microscope: A survey of new stylized facts of the intraday foreign exchange markets. Finance and Stochastics, 1(2), 95-131. Harrison, B., & Paton, D. (2005). Transition, the evolution of stock market efficiency and entry into EU: The case of Romania. Economics of Planning, 37(3-4), 203-223. Hasan, T., & Quayes, S. (2005). An empirical analysis of stock prices in the transitional countries of Europe, Russia and the United States. Unpublished paper. Inzinger, D., & Haiss, P. (2006). Integration of European stock markets: A review and extension of quantity-based measures. EI Working Paper No. 74. EuropaInstitut - University of Economics and Business Administration Vienna. Jinho, B., Chang-Jin, K., & Nelson, C. R. (2007). Why are stock returns and volatility negatively correlated? Journal of Empirical Finance, 14(1), 41-58. Jochum, C., Kirchgässner, G., & Platek, M. (1999). A long-run relationship between Eastern European stock markets? Cointegration and the 1997/98 crisis in emerging markets. Weltwirtschaftliches Archiv, 135(3), 454-479. Kanas, A. (1998). Volatility spillovers across equity markets: European evidence. Applied Financial Economics, 8, 245-256. Kasch-Haroutounian, M., & Price, S. (2001). Volatility in the transition markets of Central Europe. Applied Financial Economics, 11, 93-105. Kirchler, M., & Huber, J. (2005). Testing for stylized facts in experimental financial markets (pp. 22): Department of Finance, University of Innsbruck. Krivoruchenko, M. I., Alessio, E., Frappietro, V., & Streckert, L. J. (2004). Modeling stylized facts for financial time series. Physica A, 344(1/2), 263-266. Kuczmarski, J., & Rosenbaum, P. (1999). Quantile plots, partial orders and financial risk. The American Statistician, 53(3), 239-246. Latković, M. (2001). Nesinhrono trgovanje i proračun sistematskog rizika. Hagena. Unpublished paper. Latković, M. (2002). Risk management: Identification, measurement and control. Finansijska Teorija i Praksa, 26(2), 463-477. (in Croatian) Levaj, L., Kamenarić, T., Mišković, J., & Mokrovčak, I. (2005). Metode obrade signala u ekonomiji. Fakultet Elektrotehnike i Računarstva, Sveučilište Zagreb. Ling, S., & McAleer, M. (2002a). Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models. Econometric Theory, 18, 722-729. Ling, S., & McAleer, M. (2002b). Stationarity and the existence of moments of a family of GARCH processes. Journal of Econometrics, 106, 109-117. Malmsten, H., & Teräsvirta, T. (2004). Stylized facts of financial time series and three popluar models of volatility. SSE/EFI Working Paper Series in Economics and Finance No. 563, Department of Economic Statistics, Stockholm School of Economics. Mandelbrot, B. (1963). The variation of certain speculative prices. Journal of Business, 36, 394–419. Miljković, V., & Radović, O. (2006). Stylized facts of asset returns: Case of BELEX. Facta Univertitatis Series: Economics and Organization, 3(2), 189 - 201. Morana, C., & Beltratti, A. (2002). The effects of the introduction of the euro on the volatility of the European stock markets. Journal of Banking & Finance, 26(10), 2047-2064. Müller-Jentsch, D. (2007). Financial sector restructuring and regional integration in the Western Balkans. Office for South East Europe, European Commission - World Bank. Murinde, V., & Poshakwale, S. (2001). Volatility in the emerging stock markets in Central and Eastern Europe: Evidence on Croatia, Czech Republic, Hungary, Poland, Russia and Slovakia. European Research Studies, 4(3-4), 73-101. Nelson, D. B. (1991). Conditional heteroscedasticity in asset returns: a new approach. Econometrica, 59, 347–370. Onay, C. (2006). A co-integration analysis approach to European Union integration: The case of acceding and candidate countries. European Integration Online Papers, 10(7). Pagan, A. R., & Schwert, G. W. (1990). Alternative models for conditional stock volatilities. Journal of Econometrics, 45, 267-290. Palm, F. C. (1996). GARCH models of volatility. In G. S. Maddala & C. R. Rao (Eds.), Handbook of statistics (Vol. 14, pp. 209-240): Elsevier Science. Patev, P., & Kanaryan, N. (2006). Modelling and forecasting the volatility of the Central European stock market. In S. Motamen-Samadian (Ed.), Economic transition in Central and Eastern Europe (pp. 194-215): Palgrave, Macmillan. Patev, P., Kanaryan, N., & Lyroudi, K. (2006). Stock market crises and portfolio diversification in Central and Eastern Europe. Managerial Finance, 32(5), 415-432 Poon, S-H., & Granger, C. W. J. (2003). Forecasting volatility in financial markets: A review. Journal of Economic Literature, 41(2), 478-539. Poon, S-H., & Granger, C. W. J. (2005). Practical issues in forecasting volatility. Financial Analyst Journal, 61(1), 45-56. Posedel, P. (2006). Analysis of the exchange rate and pricing foreign currency options on the Croatian market: The NGARCH model as an alternative to the Black-Scholes model. Financial Theory and Practice, 30(4), 347-368. Poshakwale, S., & Murinde, V. (2001). Modelling the volatility in East European emerging stock markets: evidence in Hungary and Poland. Applied Financial Economics, 11 No. 4, 445-456. Rockinger, M., & Urga, G. (2000). The evolution of stock markets in transition economies. Journal of Comparative Economics, 28(3), 456-472. Rydberg, T. H. (2000). Realistic statistical modelling of financial data. International Statistical Review, 68(3), 233-258. Said, S. E., & Dickey, D. (1984). Testing for unit roots in autoregressive moving-average models with unknown order. Biometrika, 71, 599-607. Samitas, A., Kenourgios, D., & Paltalidis, N. (2006). Short and long run parametric dynamics in the Balkans stock markets. International Journal of Business, Management and Economics, 2(8), 5-20. Scheicher, M. (2001). The comovements of stock markets in Hungary, Poland and the Czech Republic. International Journal of Finance and Economics, 6, No.1, 27-39. Shields, K. K. (1997a). Stock return volatility on emerging Eastern European markets. Manchester School of Economic and Social Studies, 65; Suppl., 118-138. Shields, K. K. (1997b). Threshold modelling of stock return volatility on Eastern European markets. Economics of Planning, 30(2-3), 107-125. Shin, J. (2005). Stock returns and volatility in emerging stock market. International Journal of Business and Economics, 4(1), 31-43. Sian, K. K. (1996). Threshold modelling of stock return volatility on East European markets. Leicester: Faculty of Social Sciences Department of Economics University of Leicester. Syllignakis, M. N., & Kouretas, G. P. (2006). Long and short-run linkages in CEE stock markets: Implications for portfolio diversification and stock market integration. Unpublished paper Šestović, D., & Latković, M. (1998). Modeliranje volatilnosti vrijednosnica na Zagrebačkoj burzi. Ekonomski pregled, 49(4-5), 292-303. Todea, A., & Zoicaş-Ienciu, A. (2005). Random and non-random walks in the Romanian stock market. In S. Poloucek & D. Stavarek (Eds.), Future of Banking after the Year 2000 in the World and in the Czech Republic (Vol. X – Finance and Banking, pp. 634-646): Karvina: Silesian University. Tonchev, D., & Kim, T.-H. (2004). Calendar effects in Eastern European financial markets: Evidence from the Czech Republic, Slovakia and Slovenia. Applied Financial Economics, 14, 1035-1043. Wu, C. (2001). The determinants of asymmetric volatility. Review of Financial Studies, 14(3), 521-547. Xiao, L., & Aydemir, A. (2007). Volatility modelling and forecasting in finance. In J. Knight & S. Satchell (Eds.), Forecasting volatility in the financial markets (3 ed., pp. 1-45). Zakoïan, J.-M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics Control, 18, 931–955. Žiković, S. (2006a). Applying hybrid approach to calculating VaR in Croatia. Paper presented at the International Conference of the Faculty of Economics in Sarajevo: From Transition to Sustainable Development: The Path to European Integration, Sarajevo, Bosnia and Herzegovina. Žiković, S. (2006b). Implications of measuring VaR using historical simulation; An example of Zagreb Stock Exchange index – CROBEX. In J. Roufagalas (Ed.), Resource allocation and institutions: Explorations in economics, finance and law (pp. 367-389). Athens: Athens Institute for Education and Research. Žiković, S. (2007). Measuring market risk in EU new member states. Paper presented at the 13th Dubrovnik Economic Conference, Dubrovnik, Croatia.