Memory diagnostic in time series analysis [Elektronische Ressource] / by Simone L. Braun

Simone Pètrement

Sujets

• Psychologie

Informations

• Publié par: ruprecht-karls-universitat_heidelberg
• Publié le: 01 janvier 2010
• Nombre de lectures: 63
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

MEMORY DIAGNOSTIC IN TIME SERIES ANALYSIS

A Dissertation Presented for the Degree of Doktor der Philosophie (Dr. Phil.)
at the Faculty of Verhaltens- und Empirische Kulturwissenschaften of the
Ruprecht-Karls-Universität Heidelberg


by
Simone L. Braun
Born in 75015 Bretten, Germany


Dean of Faculty: Prof. Dr. Andreas Kruse
Advisor/ First Reviewer: Prof. Dr. Joachim Werner
Second Reviewer: Prof. Dr. Andreas Voß


ndOral examination: 2 of June, 2010

ACKNOWLEDGEMENT
The author wishes to express sincere appreciation to Professor Dr. Joachim Werner and Dr.
Tetiana Stadnyska for their assistance in the preparation of this manuscript and their guidance
throughout my research. In addition, special thanks to my very dear collaborators and
colleagues Dipl. Psych. Esther Stroe-Kunold, Dipl. Math. Antje Gruber, and Astrid Milde for
their most valuable input. I owe a special debt of gratitude to Professor Dr. Andreas Voß for
granting his expert opinion.

ABSTRACT I
MEMORY DIAGNOSTIC IN TIME SERIES ANALYSIS
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.

Keywords: time series, time-and frequency domain analyzes, ARFIMA, stationary, long-
range dependence, periodogram analyzes.

CHAPTER 1 INTRODUCTION 1
CONTENTS
ACKNOWLEDGEMENT .................................................................................................. 1-II
1 INTRODUCTION ............................................................................................................3
2 TIME SERIES ANALYSIS: MAJOR APPROACHES ...............................................5
2.1 FREQUENCY-DOMAIN ANALYSIS.................................................................................6
2.1.1 Basic Notation and Principles............................................................................6
2.1.2 Harmonic Analysis .............................................................................................8
2.1.3 Periodogram.......................................................................................................8
2.1.4 Spectral Analysis ..............................................................................................10
2.2 TIME-DOMAIN ANALYSIS..........................................................................................11
2.2.1 Basic Notation and Principles..........................................................................11
2.2.2 Stationary vs. Nonstationary Processes ...........................................................12
2.2.3 Sample (Partial-) Autocorrelation Function ....................................................13
2.2.4 Box-Jenkins ARIMA Modeling .........................................................................16
2.2.5 Automated Model Identification .......................................................................20
3 LONG-RANGE DEPENDENCE ..................................................................................23
3.1 DEFINITION................................................................................................................23
3.2 MODELING LONG-RANGE DEPENDENCE ...................................................................24
3.2.1 ARFIMA Methodology......................................................................................24
3.2.2 Fractal Analysis................................................................................................26
3.3 IDENTIFYING LONG-RANGE DEPENDENCE ..................................................................29
3.3.1 Time Domain Methods .....................................................................................29
3.3.2 Frequency Domain ...........................................................................................31
3.3.3 Relation between Measures..............................................................................33
3.4 ESTIMATING LONG-RANGE DEPENDENCE...................................................................37
CHAPTER 1 INTRODUCTION 2
3.4.1 Software............................................................................................................41
4 TIME SERIES RESEARCH IN PSYCHOLOGY ......................................................42
4.1 REVIEW OF EMPIRICAL FINDINGS ..............................................................................42
4.2 RESPONSE VARIABILITY IN ATTENTION-DEFICIT DISORDER .....................................46
4.3 LONG-RANGE TEMPORAL CORRELATIONS AND MAJOR DEPRESSION........................51
5 SIMULATION STUDIES..............................................................................................54
5.1 STUDY 1: DISTINGUISHING FRACTAL SIGNALS..........................................................56
5.1.1 Introduction ......................................................................................................56
5.1.2 Background.......................................................................................................57
5.1.3 Modifications of Estimation Methods...............................................................58
5.1.4 Method..............................................................................................................62
5.1.5 Results...............................................................................................................63
5.1.6 Conclusions92
5.2 STUDY 2: DISTINGUISHING (NON-)STATIONARY PROCESSES ....................................94
5.2.1 Introduction ......................................................................................................94
5.2.2 Method97
5.2.3 Results...............................................................................................................98
5.2.4 Conclusions ....................................................................................................131
5.3 STUDY 3: DISTINGUISHING SHORT AND LONG MEMORY.........................................133
5.3.1 Introduction133
5.3.2 Method............................................................................................................134
5.3.3 Results.............................................................................................................135
5.3.4 Conclusions ....................................................................................................146
6 GENERAL DISCUSSION...........................................................................................148
REFERENCES .....................................................................................................................155
APPENDIX ...........................................................................................................................170
CHAPTER 1 INTRODUCTION 3
1 INTRODUCTION
Glass, Willson, and Gottman (1975), McCleary and Hay (1980), and Gottman (1981)
introduced time series procedures to social and behavioral sciences three decades ago and thus
challenged the popular view that most psychological phenomena can be viewed as randomly
distributed in time around a more or less stable mean. Since then researchers from different
fields of psychology have recognized the advantages of time series methods to capture
dependence and instability in their empirical data. Persistent autocorrelations in the data
generating process indicates long-range dependence (LRD) or, in other words, a process with
long memory. Long memory implies statistical dependence between observations separated
by a large number of time units (Beran, 1994) as opposed to processes with short-range
dependence (SRD), whose autocorrelations decay quickly as the number of observation
increases. Gilden et al. (Gilden, 1997, 2001; Gilden & Wilson, 1995a,b; Gilden et al., 1995)
demonstrated in experiments including mental rotation,