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Statistical Inference in Multifractal Random Walk Models for Financial Time Series

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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 tables 17

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List of Tables 5.1 Model configurations . . . . . . . . . . . . . . . . . . . . . . . . 48 5.2 Estimated biases and MSEs for the model MRW1 . . . . . . . . 49 5.3 Estimated biases and MSEs for the model MRW2 . . . . . . . . 50 5.4 Estimated biases and MSEs for the model MRW3 . . . . . . . . 50 5.5 The mean distance and the mean square distance . . . . . . . . 52 5.6 Estimated biases and MSEs when using the starting value θ . . 53 5.7 Estimated biases and MSEs when using the starting value θ and the moments function f∗ . . . . . . . . . . . . . . . . . . . . . . 54 6.1 Estimated significance levels and powers for the multifractality test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.1 The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.2 Sample values of the statistic M . . . . . . . . . . . . . . . . . . 64 7.3 Estimates and approximate 0.95 confidence intervals . . . . . . . 65 8.1 Computing times for different sample sizes . . . . . . . . . . . . 72 8.2 Computing times for different moment conditions and bandwidths 72

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