Work detail

Long-term memory detection with bootstrapping techniques: empirical analysis

Author: Bc. Branislav Albert
Year: 2012 - summer
Leaders: prof. PhDr. Ladislav Krištoufek Ph.D.
Work type: Bachelors
Language: English
Pages: 62
Awards and prizes: B.A. with distinction from the Dean of the Faculty of Social Sciences for an extraordinarily good bachelors diploma thesis.
Abstract: A time series has long range dependence if its autocorrelation function is not absolutely convergent.
Presence of long memory in a time series has important consequences for consistency of several time
series estimators and forecasting. We present a self-contained theoretical treatment of time series models
necessary for study of long range dependence and survey a large list of parametric and semiparametric
estimators of long range dependence. In a Monte Carlo study, we compare size and power properties of
four estimators, namely R/S, DFA, GPH and Wavelet based method, when relying on asymptotic
normality of the estimators and distributions obtained from the moving block bootstrap. We find out that
the moving block bootstrap can improve the size of the R/S estimator. In general however, the moving
block bootstrap did not perform satisfactorily for other estimators. GPH and Wavelet estimators offer the
most reliable asymptotic confidence intervals.
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