Memory Diagnostic in Time Series

Abstract

The objectives of this thesis is to evaluate the reliability of different periodogram-based estimation techniques and their non-spectral alternatives, implemented in the free software environment for statistical computing and graphics R, in distinguishing time series sequences with different memory processes, specifically to discriminate (1) two different classes of persistent signals within fractal analysis, fractional Brownian motions (fBm) and fractional Gaussian noises (fGn) (2) nonstationary and stationary ARFIMA (p,d,q) processes as well as (3) short- and long-term memory properties of the latter, and to assess the accuracy of the corresponding estimates. After a brief introduction into time- and frequency-domain analyzes fundamental concepts such as the ARFIMA methodology and fractal analysis for modeling and estimating long-(LRD) and short-range dependence (SRD) as well as (non)stationary of time series are presented. Furthermore, empirical studies utilizing time series analysis of long memory processes as diagnostic tools within psychological research are demonstrated. Three simulation studies designed to solve the abovementioned methodological problems represent the main field of this thesis, i.e., the reliable identification of different memory as well as specific statistical properties of ARFIMA and fractal time series and the assessment of estimation accuracy of the procedures under evaluation, and thus, based on the empirical findings, recommending the most reliable procedures for the task at hand.