Long Memory in Stock Market Volatility:Evidence from India

Hiremath, Gourishankar S and Bandi, Kamaiah (2010): Long Memory in Stock Market Volatility:Evidence from India. Published in: Artha Vijnana , Vol. 52, No. 4 (2010): pp. 332-345.

Abstract

Long memory in variance or volatility refers to a slow hyperbolic decay in auto-correlation functions of the squared or log-squared returns. GARCH models extensively used in empirical analysis do not account for long memory in volatility. The present paper examines the issue of long memory in volatility in the context of Indian stock market using the fractionally integrated generalized autoregressive conditional heteroscedasticity (FIGARCH) model. For the purpose, daily values of 38 indices from both National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) are used. The results of the study confirm presence of long memory in volatility of all the index returns. This shows that FIGARCH model better describes the persistence in volatility than the conventional ARCH-GARCH models.

• Item Type: MPRA Paper
• Language: English
• Keywords: Fractional integration, Long memory, Volatility, FIGARCH, hyperbolic decay, Indian Stock Market, NSE, BSE.
• Subjects: G - Financial Economics > G0 - General; G - Financial Economics > G1 - General Financial Markets > G12 - Asset Pricing ; Trading Volume ; Bond Interest Rates; G - Financial Economics > G1 - General Financial Markets > G14 - Information and Market Efficiency ; Event Studies ; Insider Trading; G - Financial Economics > G1 - General Financial Markets > G17 - Financial Forecasting and Simulation

References

Andersen, T. G. and T. Bollerslev (1997), Intraday Periodicity and Volatility Persistence in Financial Markets. Journal of Empirical Finance, 4, pp. 115-158.

Andersen, T. G., T. Bollerslev., F. X. Diebold., and P. Labys (2003), Modeling and Forecasting Realized Volatility, Econometrica, 71, pp. 579–625.

Andreano, M. S. (2005), Common Long Memory in the Italian Stock Market, Quaderni de Statistica, 7, pp. 107-119.

Assaf, A. (2007), Fractional Integration in Equity Markets of MENA Region, Applied Financial Economics, 17 (9), pp. 709-723.

Baillie, R. T., T. Bollerslev and H. O. Mikkelsen (1996), Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 74, pp. 3-30.

Bollerslev, T (1986), Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31, pp. 307-327.

Cavalcante, J and A. Assaf (2005), Long-range Dependence in the Returns and Volatility of the Brazilian Stock Market, European Review of Economics and Finance, 5, pp. 5–20.

Comte, F. and E. Renault (1998), Long-memory in Continuous Time Stochastic Volatility Models. Mathematical Finance, 8, pp. 291-323.

Crato, N. and P. de Lima (1994), Long range Dependence in the Conditional Variance of Stock Returns, Economic Letters, 45, pp. 281-285.

Ding, Z. and C. W. J. Granger (1996), Modeling Volatility Persistence of Speculative Returns: A New Approach, Journal of Econometrics, 73, pp. 185-215.

Ding, Z., C.W.J. Granger and R. F. Engle (1993), A Long Memory Property of Stock Returns and A New Model, Journal of Empirical Finance, 1, pp. 83–106.

DiSario, R., H. Saragolu., J. McCarthy and H. Li (2008), Long Memory in the Volatility of An Emerging Equity Market: The Case of Turkey, Intentional Financial Markets, Institutions and Money, 18, pp. 305-312.

Engle, R. F (1982), Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K Inflation, Econometrica, 50, pp. 987-1008.

Engle, R. F and T. Bollerslev (1986), Modelling the Persistence of Conditional Variances, Econometric Review, 5, pp. 1-50

Floros, C., S. Jaffry and G.V. Lima (2007), Long Memory in Portuguese Stock Market, Studies in Economics and Finance, 24 (3), pp. 220-232.

Granger, C. W. J., Z. Ding, and S. Spear (1997), Stylized Facts of the Temporal and Distributional Properties of Daily Speculative Markets. San Diego (US): Unpublished manuscript.

Granger, C.W.J. and R. Joyeux (1980), An introduction to Long-memory Time Series Models and Fractional Differencing, Journal of Time Series Analysis, 1, pp. 15-29.

Gurgul, H and T. Wojtowicz (2006), Long Memory on the German Stock Exchange, Czeck Journal of Economics and Finance, 56 (9-10), pp. 447-468.

Hosking, J (1981), Fractional Differencing, Biometrika, 68, pp. 165-176.

Jefferis, K and P. Thupayagale (2008), Long Memory in Southern African Stock Markets, South African Journal of Economics, 75(3), pp. 384-398

Kang, S. H. and S. M. Yoon (2008), Long Memory Features in the High Frequency Data of the Korean Stock Market, Physica A, 5, pp. 189-196.

Kasman, A. and E. Torun (2007), Long Memory in the Turkish Stock Market Return and Volatility. Central Bank Review, 2, pp. 13-27.

Killic, R (2004), On the Long Memory Properties of Emerging Capital Markets: Evidence from Istanbul Stock Exchange. Applied Financial Economics, 14, pp. 915-922.

Korkmaz, T., E. I. Cevik and N. Ozatae (2009), Testing for Long Memory in ISE using ARFIMA-FIGARCH Model and Structural Break Test. International Research Journal of Finance and Economics, 26, pp. 187-191.

Ljung, G. M., and G. P. E. Box (1978), On a Measurement of Lack of fit in Time Series Models”. Biometricka, 66; 66-72.

Lobato I. N and N. E. Savin (1998), Real and Spurious Long Memory Properties of Stock Market Data, Working Paper, Department of Economics, University of Iowa, Iowa city.

Mandelbrot, B (1971), When can Price be Arbitraged Efficiently? A limit to the Validity of the Random walk and Martingale Models, Review of Economics and Statistics, 53, pp. 225-236.

McMillan, D. G. and P. Thupayagale (2008), Efficiency of African Equity Markets. Studies in Economics and Finance, 26(4), pp. 275-292.

McMillan, D. G. and P. Thupayagale (2009), Efficiency of the South African Equity Market, Applied Financial Economics Letters, 4(5), pp. 327-330.

Mendes, B. V. de M., and N. Kolev (2006), How Long Memory in Volatility Affects True Dependence Structure, Working Paper, Department of Statistics, Federal University, Brazil.

Oh, GabJin, Cheol-Jun Eom, and S. Kim (2006). “Long-term memory and volatility clustering in daily and high-frequency price changes”. Department of Statistics. arXiv:physics/0601174v2

Poon, S. H. and C. W. J. Granger, (2003), Forecasting Volatility in Financial Markets: A Review, Journal of Economic Literature, 41(2), pp. 478-539.