This paper aims to study the long memory behaviour of major equity markets globally with respect to long persistence characteristics of return and volatility during global financial crisis. For returns, the fractal dimension of these equity markets is estimated by employing the Levy stable distribution’s alpha and its special relationship to Hurst exponent. However, different estimation methods were undertaken to approximate the fractional parameter, d, in ARFIMA(p,d,q) model. With respect to volatility, the study is more extensive and considers the GARCH(p,q) for volatility persistence and EGARCH(p,q) for asymmetry and persistence in contrast with the fractionally integrated counterpart of GARCH model, FIGARCH(p,d,q) with two approaches of BBM and Chung. Similarly, the fractional component of major equity markets were tested using HYGARCH(p,d,q), and to also examine the stationarity condition of FIGARCHs. The behaviour of the markets in relation to efficient market hypothesis (EMH) is also highlighted in this study. The results from the empirical investigation confirmed the long memory in global financial markets’ return, while the results for volatility achieved in this study remained indeed controversial. Although traditional models GARCH and EGARCH approved the persistence in volatility, the fractional models fail to fulfil basic conditions. Similarities observed along the study between both markets, with regard to EMH.

1. Testing Long Memory in Stock Market Return and Volatility during Global Financial Crisis: International Evidence Author; Amir Kheirollah Supervisor: PhD. Sabur Mollah Master DissertationStockholm Business School Stockholm University

2. Painting Title: The Disintegration of the Persistence of Memory, 1952/54Salvador DaliFamous Spanish Painter – Surrealist Abstract

3. Does Long Memory exist in Crisis Time? Does Equity Markets Behave Differently? Long Memory, EMH & Emerging vs. Developed Markets in Crisis Period Are our Measures and Models Consistent? Does all Models Fulfil their Assumptions and Objectives?

4. Self similarity Slow decay of autocorrelations Persistence and Information A Martingale Process, Stationarity and EMH. What is long memory (persistence)?

5. Data & Methodoly Crisis Period 01/01/2007 – 31/12/2009 Equity Markets Indices from FTSE Emerging vs. Developed Categories including 12 countries each Data under investigation: Continuously Compounded Rate of Daily Returns

6. Data & Methodoly Statistical Analysis ACF/PACF/Periodograms Non-normality; Skewness, Kurtosis, Jarque Bera Test Stationarity; ADF and PP Tests ARCH Effect; Lagrange Multiplier Test Long Memory in Return; Hurst Exponent & ARFIMA Model Long Memory in Volatility; GARCH Family Models (GARCH, EGARCH, FIGARCH (BBM & Chung), HYGARCH

7. Long Memory in Return Levy Index & Hurst Exponent Revered Relationship confirmed persistence in all financial timeseries under investigation

8. Long Memory in Return ARFIMA Model for Return Maximum Likelihood Estimation Geweke Porter-Hudak Estimation Smoothed Periodogram Estmiation All three methods of estimation confirmed existence of long-memory Limitations and Further Research

9. Long Memory in Volatility GARCH(1,1), confirmed long memory in all markets in similar way. EGARCH(1,1) confirmed long memory and assymmetry of data. FIGARCH.BBM(1,1) produced d estimates in the expected range. (Chung produced smaller d parameter, still in expected range) HYGARCH(1,1) produced d parameters equal to FIGARCH.BBM, with no significant results for log alpha.

10. Long Memory in Volatility GARCH & EGARCH models confirm the long memory, and prior to this, fulfil the covariance stationarity condition (CS). FIGARCH models produing results for fractal parameter in long memory range, fail to account for CS. Emerging and developed market seems not to be differrent from each other, in the matter of quanititative results.

11. Long Memory in Volatility Limitations and Further Research The number of orders p & q. Gaussian distribution vs. Other distributions recommended for financial data series. The behavior of fractional models Seperate study on behaviour of particularely emerging markets with respect to long memory.

12. EMH & Emerging vs. Developed Markets No difference observed between resutls from emerging and developed economies. This might be due to reaching a level of maturedness by emerging economies relative to developed ones. Does Emerging Markets deriving the world economy during global financial crisis?

13. Thank you!And Your Questions Please! Painting Title: The Persistence of Memory, 1931Salvador DaliFamous Spanish Painter – Surrealist