Academy of Economic Studies Doctoral School of Finance and Banking- DOFIN

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.

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