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Statistical Inference in Multifractal Random Walk Models for Financial Time Series


Cristina Sattarhoff

The dynamics of financial returns varies with the return period, from high-frequency data to daily, quarterly or annual data. Multifractal Random Walk models can capture the statistical relation between returns and return periods, thus facilitating a more accurate representation of real price changes. This book provides a generalized method of moments estimation technique for the model parameters with enhanced performance in finite samples, and a novel testing procedure for multifractality. The resource-efficient computer-based manipulation of large datasets is a typical challenge in finance. In this connection, this book also proposes a new algorithm for the computation of heteroscedasticity and autocorrelation consistent (HAC) covariance matrix estimators that can cope with large datasets.


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List of abbreviations 9


List of abbreviations ACF autocovariance function ARCH autoregressive conditional heteroscedasticity ARFIMA autoregressive fractionally integrated moving average cf. confer CAC 40 Cotation Assistée en Continu 40 (French stock market index) DAX Deutscher Aktien IndeX (German stock market index) DFT discrete Fourier transform DJIA Dow Jones Industrial Average (U.S. stock market index) etc. et cetera et al. et alteri e.g. exempli gratia EMH Efficient Markets Hypothesis FTSE 100 British stock market index GARCH generalized autoregressive conditional heteroscedasticity GMM generalized method of moments HAC heteroscedasticity and autocorrelation consistent HSI Hang Seng Index (Hong Kong stock market index) i.e. id est i.i.d. independent and identically distributed IBEX 35 Iberia Index 35 (Spanish stock market index) 10 List of abbreviations IDFT inverse discrete Fourier transform KOSPI 200 Korea Composite Stock Price Index 200 (South Korean stock market index) MMAR Multifractal Model of Asset Returns MPCP Multifractal Product of Cylindrical Pulses MRW Multifractal Random Walk MSE mean square error MSM Markov-Switching Multifractal MV multifractal volatility pp. page range p. page QQ quantile quantile s.e. standard error SV stochastic volatility S&P 500 Standard & Poor’s 500 (U.S. stock market index) TSM Time Series and Wavelets for Finance vs. versus

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