Time series research in psychology [Elektronische Ressource] : conceptual and methodological issues / Tetiana Stadnytska

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RUPRECHT-KARLS –UNIVERSITÄT-HEIDELBERG

TIME SERIES RESEARCH IN PSYCHOLOGY:
CONCEPTUAL AND METHODOLOGICAL ISSUES

TETIANA STADNYTSKA

Inaugural-Dissertation zur Erlangung des akademischen Grades
„Doktor der Philosophie“ (Dr. Phil.) in der Fakultät für
Verhaltens- und Empirische Kulturwissenschaften
der Universität Heidelberg

Tag der Disputation: 14. 11. 2006

Dekan: Prof. Dr. Klaus Roth
Berater/ 1.Gutachter: Prof. Dr. Joachim Werner
2.Gutachter: Prof. Dr. Joachim Funke

DANKSAGUNG
Mein besonderer Dank gilt meinem wissenschaftlichen Betreuer, Herrn Prof. Dr.
Joachim Werner, der mich für das methodische Thema begeisterte, diese Arbeit mit
hilfreichen Diskussionen und konstruktiver Kritik begleitete und mir stets als
interessierter Gesprächspartner zur Verfügung stand.
Für die Übernahme des zweiten Gutachtens bin ich dem Herrn Prof. Dr. Joachim Funke
zu Dank verpflichtet.
Meinen Kommilitonen aus der „Zeitreihengruppe“ bin ich für die hervorragende
Zusammenarbeit sehr verbunden. Besonders erwähnt seien an dieser Stelle Simone
Braun und Esther Stroe-Kunold. Die zahleichen Diskussionen mit ihnen haben viel zum
Fortschritt der Arbeit beigetragen. ABSTRACT I
TIME SERIES RESEARCH IN PSYCHOLOGY:
CONTENTS AND METHODOLOGICAL ISSUES
The objectives of this paper are (1) demonstrate the superiority of the time series analysis over
the traditional methods in dealing with dynamical phenomena; (2) discuss various possible
research applications of time series procedures in psychology; and (3) solve some
methodological problems occurring in applied settings. After a brief introduction into time-
and frequency-domain analyses, a range of applications of time series procedures in
psychology was discussed; theories and empirical studies from different fields of psychology
employing time-series terminology and methods were presented. Three simulation studies
designed to solve methodological problems typical for time series research in psychology,
such as handling of instationary time series, identifying of appropriate dynamical models and
reliable detection of long-range dependencies between successive observations in a series,
represented the main field of the paper.

Keywords: time series, time-and frequency domain analyses, ARFIMA, unit root tests,
automated methods for ARIMA model identification, 1/f noise

CONTENTS II
CONTENTS
1 INTRODUCTION ............................................................................................................1
2 BASIC CONCEPTS .........................................................................................................3
2.1 TIME-DOMAIN ANALYSIS............................................................................................4
2.1.1 Autocorrelation and Partial Autocorrelation Functions....................................5
2.1.2 Time-Domain Models .........................................................................................6
2.1.3 Box-Jenkins ARIMA Methodology......................................................................8
2.2 FREQUENCY-DOMAIN ANALYSIS...............................................................................10
2.2.1 Modeling Repeating Phenomena......................................................................11
2.2.2 Detecting Deterministic Cycles: Periodogram.................................................12
2.2.3 Detecting Probabilistic Cycles: Spectral Analysis...........................................15
2.3 STATIONARITY ..........................................................................................................19
3 RESEARCH APPLICATIONS.....................................................................................21
3.1 PROCESS ANALYSIS...................................................................................................22
3.1.1 Stability.............................................................................................................22
3.1.2 Memory24
3.1.3 Dependency Structure.......................................................................................27
3.2 TIME-SERIES EXPERIMENT ........................................................................................30
3.3 FORECASTING............................................................................................................33
4 TIME-SERIES RESEARCH IN PSYCHOLOGY......................................................35
4.1 MODELING AND ASSESSING CHANGE IN ADDICTIVE BEHAVIOR................................36
4.1.1 Testing Theories Explaining Smoking Habits ..................................................36
4.1.2 Assessing Change in Addictive Behavior .........................................................38
4.2 SELF-ESTEEM AS DYNAMICAL CONCEPT...................................................................41
4.3 LONG-RANGE DEPENDENCIES IN PSYCHOLOGICAL TIME SERIES ..............................46
CONTENTS III
4.3.1 Review of Empirical Findings ..........................................................................46
4.3.2 Explanations for Long-Range Dependencies ...................................................52
5 METHODOLOGICAL ISSUES ...................................................................................57
5.1 STUDY 1: DETERMINISTIC OR STOCHASTIC TREND: DECISION ON THE BASIS OF THE
AUGMENTED DICKEY-FULLER TEST......................................................................................58
5.1.1 Introduction ......................................................................................................58
5.1.2 Unit Root Testing..............................................................................................64
5.1.3 Deterministic or Stochastic Trend....................................................................66
5.1.4 Method..............................................................................................................69
5.1.5 Results...............................................................................................................70
5.1.6 Conclusions ......................................................................................................72
5.2 STUDY 2: MODEL IDENTIFICATION OF INTEGRATED ARMA PROCESSES ..................73
5.2.1 Introduction73
5.2.2 Method..............................................................................................................83
5.2.3 Results84
5.2.4 Conclusions ......................................................................................................95
5.3 STUDY 3: SAMPLE SIZE AND ACCURACY OF ESTIMATION OF THE FRACTIONAL
DIFFERENCING PARAMETER ..................................................................................................99
5.3.1 Introduction99
5.3.2 Method............................................................................................................102
5.3.3 Results.............................................................................................................103
5.3.4 Conclusions ....................................................................................................112
6 GENERAL DISCUSSION...........................................................................................113
REFERENCES .....................................................................................................................117
APPENDIX ...........................................................................................................................132
CHAPTER 1 INTRODUCTION 1
1 INTRODUCTION
Time series analysis is widely used in econometrics, physic, astronomy, or seismology. To
most psychologists, this methodology remains unfamiliar despite the fact that Glass, Willson,
and Gottman (1975), McCleary and Hay (1980), and Gottman (1981) introduced time series
procedures to social and behavioral sciences three decades ago. The standard research strategy
in psychology consists in the attempt to infer general models from the average behavior of a
large sample of individuals. As a result, employing classical statistics ignoring the dimension
of time is characteristic of psychological research. This neglect of variation in time is rather
surprising, since change, development, or growth represent typical signatures of most
psychological phenomena. Traditionally, psychologists assess evolution or development
through repeated measurements using mean and variance. By this procedure however,
possible dependences between subsequent values remain indiscernible. Comparing means and
standard deviations does not reveal the true nature of variability or change. In contrast, time
series analysis is able to provide profound insight into properties of dynamical concepts. In
the last few years, more and more researchers from different fields of psychology seem to
recognize advantages of time series methods and increasingly apply these techniques in their
empirical studies. The objectives of this thesis are to demonstrate the superiority of the time
series analysis over the traditional methods in dealing with dynamical phenomena; dis