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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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B QQ plots 83

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Appendix B QQ plots The GMM estimator is weakly consistent and asymptotically normally distri- buted. In this appendix we investigate whether the normal asymptotic appro- ximation has been reached by the MRW estimates within the framework of the Monte Carlo simulation study in Chapter 5. For this purpose we employ QQ plots of the MRW estimates versus a normal distribution. Each of the following three figures is dedicated to a MRW configuration: MRW1, MRW2 and MRW3 respectively. In each figure the QQ plots of the λ2 estimates were represented at the top, those of the ln (T ) estimates in the middle and those of the ln (σ) estimates at the bottom. At the same time we considered five different sample sizes N ∈ {2048, 4096, 8192, 16384, 32000} from left to right. 84 Appendix B. QQ plots 0 0. 02 0. 04 − 0. 050 0. 050. 1 N = 2 04 8 0. 01 0. 02 0. 03 0 0. 01 0. 02 0. 03 0. 04 0. 05 N = 4 09 6 0. 01 0. 02 0. 03 0 0. 01 0. 02 0. 03 0. 04 N = 8 19 2 0. 01 5 0. 02 0. 02 5 0. 01 0. 01 5 0. 02 0. 02 5 0. 03 N = 1 63 84 0 5 10 0102030 2 4 6 8 0510 4 6 8 246810 4 5 6 7 345678 − 0. 2 0 0. 2 − 0. 4 − 0. 20 0. 2 0. 4 − 0. 2 0 0. 2 − 0....

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