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Exploring Dual Long Memory in Returns and Volatility across the Central and Eastern European stock markets

Academy of Economic Studies Doctoral School of Finance and Banking- DOFIN. Exploring Dual Long Memory in Returns and Volatility across the Central and Eastern European stock markets . Msc. Student: Mihaela Sandu Supervisor: PhD.Professor Mois ă Alt ă r. Bucharest, July 2009.

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Exploring Dual Long Memory in Returns and Volatility across the Central and Eastern European stock markets

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  1. Academy of Economic Studies Doctoral School of Finance and Banking- DOFIN Exploring Dual Long Memory in Returns and Volatility across the Central and Eastern European stock markets Msc. Student: Mihaela Sandu Supervisor: PhD.Professor Moisă Altăr Bucharest, July 2009

  2. Dissertation paper outline • Importance of long memory • Aims of the paper • Data & Methodology • Nonparametric & semiparametric aproaches • Parametric approach: ARFIMA / FIGARCH • Structural breaks • The joint ARFIMA-FIGARCH model • Model distributions • Empirical results • Conclusions and further improvements • References

  3. Long memory • Contradicts the EMH weak-form by allowing investors and portfolio managers to make prediction and to construct speculative strategies • The price of an asset determined in an efficient market should follow a martingale process in which each price change is unaffected by its predecessor and has no memory . Pricing derivative securities with martingale methods may not be appropriate if the underlying continuous stochastic processes exhibit long memory • Implications to assest allocation decisions and risk management

  4. Aims of the paper • To ivestigate the presence of long memory in stock returns via non-, semi- and parametric techniques • To distinguish between long memory and structural breaks within return series • To found evidences of dual long memory processes within CEE emerging stock markets

  5. Short vs. Long memory processes vs.

  6. The Data • Six indices representing five CEE emerging stock markets: BET, BET-FI, SOFIX, BUX, WIG, PX • Daily closing stock prices transformed into continuously compounded returns • The estimations and tests were performed in R version 2.9.0. • For estimating ARFIMA-FIGARCH model, the Ox Console version 5.10, together with the G@rch Console 4.2 were used.

  7. Methodology • Unit root tests: ADF KPSS statistic: • Rescaled range statistic • Wavelet based estimator • Log-periodogram estimator (GPH) • ARFIMA model:

  8. Methodology • FIGARCH model: • Model distributions: • Pearson goodness-of-fit test

  9. Unit root tests Empirical results • For all indices we can reject the null of a I(1) process, as well as the null of I(0) process

  10. Nonparametric and semiparametric estimates • For most of the indices, the estimates indicate the presence of long memory in returns, squared and absolute returns • In case of SOFIX, the estimate of H using R/S and wavelet analysis indicate no long memory in return series.

  11. Parametric estimates - ARFIMA model Following Cheung(1993), we estimate different specifications of the ARFIMA (p, ξ, q) with p,q=0:2 for each return series. The Akaike’s information Criterion (AIC), is used to choose the best model that describes the data. Ln(L) is the value of the maximized Gaussian Likelihood; AIC is the Akaike information criteria; the Q(20) is the Ljung-Box test statistic with 20 degrees of freedom based on the standardized residuals

  12. Parametric estimates - ARFIMA model • the long memory parameter ξ significantly differs from zero for all return series (for WIG at 5% level of significance) • the results seem to confirm the idea that long memory is a property of emerging markets rather than developed markets. • the standardized residuals display skewness and excess kurtosis, the departure from normality beeing also confirmed by the J-B statistic • Q-statistic indicate that the residuals are not independent, except for BET-FI and WIG , for which we cannot reject the null of independent residuals

  13. Testing for structural breaks We use the Supremum F test proposed by Andrews and the methodology of Bai and Perron for detecting structural breaks in return series • for BET, BET-FI, SOFIX and WIG the breakpoint corespond to the historical maximum value of the index. • For BUX, the F statistic indicate that the null hypothesis of no structural break cannot be rejected • we further split the sample in two subsamples depending on the breakdate, and we reestimate all the procedures for each subsample

  14. Subsamples technique – non and semiparametric procedures For most of the series, the subsamples appear to keep the full sample properties For SOFIX although the Hurst exponent is still below 0.5 for each subsample , indicating no long memory properties, the log-periodogram estimate indicate a significant value for ξ on the second subsample. We therefore examine the ARFIMA estimates on each subsample in order to conclude upon the reliability of the initially findings.

  15. Subsamples technique – ARFIMA estimates For BET, BET-FI and PX the estimate of fractional parameter is significant for both subsamples In case of SOFIX and WIG it can be clearly observed that the long memory patterns of the full sample are based in fact only on the second subsample, after the structural break

  16. ARFIMA-FIGARCH for the Romanian stock market indices

  17. ARFIMA-FIGARCH- Remarks • the sum of the estimates of α1 and β1 in the ARFIMA–GARCH model is very close to one, indicating that the volatility process is highly persistent • the estimates of β1 in the GARCH model are very high, suggesting a strong autoregressive component in the conditional variance process • in the ARFIMA–FIGARCH model, the estimates of both long memory parameters ξ and d are significantly different from zero • the results indicate that the β1 estimates are lower in the FIGARCH than those of in the GARCH model. • according to the AIC, the FIGARCH models fit the return series better than the GARCH models • P(60) test statistics reconfirm the relevance of skewed Student-t

  18. ARFIMA-FIGARCH estimates for PX and BUX FIGARCH estimates for WIG and SOFIX

  19. Conclusions and further improvements • The tests and estimated models show evidence of dual long memory in Romanian, Czech Republic and Hungarian stock markets, while Bulgarian and Poland’s markets show evidence of long memory in volatility. • The results support the idea that the detection of long memory properties in emerging markes is more likely than in developed markets, having implications in portfolio diversification, speculative strategies and risk management. • However, one should use various methods and techniques when investingating the presence of long memory, due to the sensitivity of the results to the selected estimation method. • Structural breaks and regime shifts can significantly affect the results. Therefore, one should use such techniques designed to account for these processes which could induce to a short memory process similar patterns with a long memory process. • Further research could be conducted using the models developed by Baillie and Morana (2007,2009), namely Adaptive-FIGARCH and Adaptive-ARFIMA, and their generalisation for dual long memory processes, the A2-ARFIMA-FIGARCH model, beeing designed to take into account for both long memory and structural change in the conditional mean and variance.

  20. References Andrews, D.W.K. (1993), ”Tests for parameter instability and structural change with unknown change point”, Econometrica 61, 821-856 Bai, J., and P. Perron (2003), “Computation and Analysis of Multiple Structural-Change Models”, Journal of Applied Econometrics, 18, 1-22 Baillie,R.T. (1996), “Long memory processes and fractional integration in econometrics”, Journal of Econometrics 73, 5-59 Baillie,R.T., T. Bollerslev and H.O. Mikkelsen (1996), “Fractionally integrated generalized autoregressive conditional heteroskedasticity”, Journal of Econometrics, 74, 3-30 Baillie, R. T., and C. Morana (2007), “Modelling long memory and structural breaks in conditional variances: An adaptive FIGARCH approach”, Journal of economic, dynamics & control, 33, 1577-1592 Baillie, R. T., and C. Morana (2009), “Investigating inflation dynamics and structural change with an adaptive arfima approach”, Applied mathematics working paper series. Barkoulas, J. T., C. F. Baum and N. Travlos, “Long memory in the greek stock market”, Applied Financial Economics, 10, 177-184(8) Beine, M., S. Laurent, and C. Lecourt (1999), “Accounting for conditional leptokurtosis and closing days effects in FIGARCH models of daily exchange rates”

  21. References Bolerslev, T., and H.O. Mikkelsen (1996) , “Modeling and pricing long memory in stock market volatility”, Journal of Econometrics, 73,151-154 Breidt, F.J., N. Crato, and P. Lima (1998), “The detection and estimation of long memory in stochastic volatility”, Journal of Econometrics, 83, 325-348 Cajueiro, D. O., and B. M. Tabak (2005), “Possible causes of long-range dependence in the Brazilian stock-market”, Physica A, 345, 635-645 Cheung, Y. W. (1995), “A search for long-memory”, Journal of International Money and Finance, 14, 597-615 Diebold, F. X., and A. Inoue (2001), “Long memory and regime switching”, Journal of econometrics, 105, 131-159 Geweke ,J. and S. Porter-Hudak (1983),”The estimation and application of long-memory Time series models”, Journal of Time Series Analysis, 4, 221-238 Granger, C.W.J and R.Joyeux (1980), “An introduction to long-memory times series modrls and fractional differencing”,”Journal of time series analysis 1,15-29 Granger, C.W.J and N. Hyung (1999), “Occasional structural breaks and long memory” , Discussion Paper 99-14 Granger, C.W.J and N. Hyung (2004), “Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns”, Journal of Empirical Finance, 11, 399 – 421.

  22. References Granger, C.W.J., Z. Ding (1996), “Varieties of long memory models”, Journal of econometrics, 73, 61-76 Henry, O.T. (2002), “Long memory in stock returns: some international evidence”, Applied Financial Economics, 12, 725-729 Kang, S. H., and S. M. Yoon (2007), “Long memory properties in return and volatility - Evidence from the Korean stock market”, Physica A, 385, 591-600 Kasman, A., S. Kasman and E.Torun (2008), “Dual long memory property in returns and volatility: Evidence from the CEE countries’ stock markets”, Emerging Markets Review, Liu, M. (2000), “Modeling long memory in stock market volatility”, Journal of econometrics, 99, 139-171 Lo, A. W. (1991), “Long-Term Memory in Stock Market Prices”, Econometrica, 59, 1279-1313 Lobato, I. N., and N. E. Savin (1998), “Real and spurious long memory properties of stock-market data”, Journal of business & economic statistics, 16, 261-268 McMillan, D.G., and I. Ruiz (2009), “Volatility persistence, long memory and time-varying unconditional mean: Evidence from 10 equity indices”, The Quarterly Review of Economics and finance, 49, 578-595 Shimotsu, K. (2006), “Simple (but effective) tests of long-memory versus structural breaks”, Queen’s Economics Department Working Paper, 1101

  23. References Sowell, F. (1992), “Maximum likelihood estimation of stationary univariate fractionally integrated time series models”, Journal of econometrics, 53, 165-188 Taqqu, M., V. Teverovsky and W. Willinger (1995), “Estimators for long-range dependence: an empirical study” Teyssiere, G. (1997), “Double long memory financial time series”, GREQAM (Groupement de Recherche en Economie Quantitative d’Aix-Marseille ) Teyssiere, G., A.P.Kirman (2007), “Long memory in economics”, Springer editure Turhan, K., E.I.Cevik, N. Ozatac (2009), “Testing for long memory in ISE using ARFIMA-FIGARCH model and structural break test”, International Research Journal of Finance and Economics, 26 Willinger, W., Taqqu, M.S. andV. Teverovsky (1999), “Stock market prices and long-range dependence”, Finance and Stochastics, 3, 1-13

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