Multivariate Analyse instationärer Zeitreihen : Integration und Kointegration in Theorie und Simulation

Mit Hilfe der Kointegrationsmethodologie ist die multivariate Modellierung und Analyse instationärer Zeitreihen möglich. Für die Begründung des Kointegrationskonzepts erhielt der Ökonometriker Granger 2003 den Nobelpreis. Kointegrierte Modelle und deren Fehlerkorrekturrepräsentationen ermöglichen die Betrachtung der beiden Prozesseigenschaften des Gleichgewichts und der dynamischen Anpassungsprozesse. Dabei ist der multivariate Prozess, der sich aus den kointegrierten Komponentenprozessen zusammensetzt, als stabiles System - repräsentiert durch eine durch den Kointegrationsvektor gewichtete Linearkombination - aufzufassen. Abweichungen vom langfristigen Gleichgewicht sind nur vorübergehender Natur. Das methodologische Thema wird im Rahmen der Arbeit für die psychologische Forschungspraxis erarbeitet, in deren Zusammenhang zeitbezogene und entsprechend zu modellierende Phänomene eine nicht unbedeutende Rolle spielen, die nicht selten miteinander in (Wechsel-)Beziehungen stehen. Übergeordnetes Ziel der Darstellung des Kointegrationsansatzes ist die theoretische und empirische Überprüfung notwendiger Bedingungen für das Vorliegen von Kointegration. Nach der Darstellung der für das Verständnis des Ansatzes notwendigen Grundlagen der Zeitreihenanalyse werden die in der Fachliteratur in einigen Punkten uneinheitlichen Definitionen von Kointegration theoretisch kontrastiert. Außerdem werden einige Spezifika des Konzepts (Kointegration vs. Scheinregression, Funktion des Anpassungskoeffizienten und Kointegrationsvektors, Testverfahren) beschrieben und untersucht. Der theoretische Teil wird durch einen Literaturüberblick und die Erläuterung fraktional integrierter und kointegrierter Modelle und aktuelle Anwendungsbeispiele abgerundet. Im empirischen Teil werden Hypothesen zur Schätzung von Kointegrationsvektor und Anpassungskoeffizient sowie zu den Testverfahren durch Monte-Carlo-Simulationen überprüft. Eine Schlussbetrachtung vor psychologischem Kontext beschließt die Diplomarbeit

Analyzing Dynamic Process Systems : Cointegration Methodology as a Tool of Psychological Research

The present paper-based thesis puts forward cointegration methodology as a multivariate tool of psychological research. Aiming at familiarizing psychologists with the toolbox of cointegration techniques, the studies conducted here provide strategies to analyze complex dynamic process systems. Within the framework of these systems, integrated processes displaying an unpredictable course due to stochastic trends interact over time. If these non-stationary series are co-integrated, their interaction is driven by common stochastic trends with the systems returning to stable equilibrium states in the long run. Vector error-correction (VEC) modeling, a frequently used representation of cointegrated systems, allows insights into these short- and long-term dynamics at a glance. The objectives of this thesis are (a) to adapt this econometric approach to psychological circumstances based on conceptual considerations; (b) to provide a systematic investigation of the mathematical models behind integrated and cointegrated processes as well as their VEC representation, thus clarifying how their parameters are to be interpreted from a psychological perspective; and (c) to address issues of research practice such as spurious relations or long memory characteristics. By means of simulated as well as empirical data from different domains of psychology, this work is designed as a step-by-step guideline inducing psychological applications

Pain and psyche in a patient with irritable bowel syndrome: chicken or egg? A time series case report

Background!#!Irritable bowel syndrome (IBS) appears to have a bidirectional interaction with both depressive and anxiety-related complaints. However, it remains unclear how exactly the psychological complaints, at the individual level, are related to somatic symptoms on a daily basis. This single case study investigates how somatic and psychological variables are temporally related in a patient with irritable bowel syndrome.!##!Case report!#!The patient was a woman in her mid-twenties with an IBS diagnosis. She reported frequent soft bowel movements (5-6 times per day), as well as flatulence and abdominal pain. She resembled a typical IBS patient; however, a marked feature of the patient was her high motivation for psychosomatic treatment as well as her willingness to try new strategies regarding the management of her symptoms. As an innovative approach this single case study used a longitudinal, observational, time series design. The patient answered questions regarding somatic and psychological variables daily over a period of twelve weeks with an online diary. The diary data was analysed using an autoregressive (VAR) modeling approach. Time series analyses showed that in most variables, strong same-day correlations between somatic (abdominal pain, daily impairment) and psychological time series (including coping strategies) were present. The day-lagged relationships indicated that higher values in abdominal pain on one day were predictive of higher values in the psychological variables on the following day (e.g. nervousness, tension, catastrophizing, hopelessness). The use of positive thinking as a coping strategy was helpful in reducing the pain on the following days.!##!Conclusion!#!In the presented case we found a high correlation between variables, with somatic symptoms temporally preceding psychological variables. In addition, for this patient, the use of positive thoughts as a coping strategy was helpful in reducing pain

Patients with Multiple Functional Gastrointestinal Disorders (FGIDs) Show Increased Illness Severity: A Cross-Sectional Study in a Tertiary Care FGID Specialty Clinic

Objectives. Overlaps between different functional gastrointestinal disorders (FGIDs) are common. However, little is known about the impact of this overlap on patients’ health status. This study is aimed at analyzing the differences between patients with multiple as compared to one single FGID. Methods. A retrospective, cross-sectional study was conducted with patients presenting to a tertiary care FGID specialty clinic between 06/2012 and 01/2015 (n=294). They were characterized primarily according to their GI symptom severity (IBS-SSS) and secondarily to their physical as well as psychosocial symptom burden, quality of life, health care utilization, and work-related impairment. Differences between patients with >1 vs. 1 FGID were analyzed. Results. Of the 294 patients, 92.2% fulfilled the Rome III criteria for any FGID, and 48.0% had >1 FGIDs. FGID patients had a median age of 38 [23.0] years; 72.0% were female. Median GI symptom severity (IBS-SSS) scores were 339 [126] and 232 [163] in patients with >1 and 1 FGID, respectively (p1 FGIDs had higher general somatic symptom severity, higher illness anxiety, lower quality of life, and more work-related impairment. Almost no differences were found regarding their somatic as well as mental comorbidities. Conclusions. Multiple FGIDs are associated with an increased risk for complicated courses of illness as reflected in higher GI and somatic symptom severity, as well as stronger psychosocial and diet- and work-related impairment. Stepped and interdisciplinary models of care including psychosocial expertise and dietary advice are needed, especially for patients with multiple FGIDs

Emotional Intolerance and Core Features of Anorexia Nervosa: A Dynamic Interaction during Inpatient Treatment? Results from a Longitudinal Diary Study.

OBJECTIVE:The role of emotion dysregulation with regard to the psychopathology of anorexia nervosa (AN) is increasingly discussed. It is both assumed that AN symptoms have an impact on difficulties in tolerating aversive emotions and that-conversely-emotion dysregulation influences AN. To date, such conclusions are drawn on the basis of cross-sectional data not allowing for inferences on the temporal dynamics. The current study investigates the longitudinal interaction between emotional intolerance and core AN symptoms over the course of inpatient treatment by comparing patients with high (BMI<15 kg/m2) vs. low symptom severity (HSS vs. LSS). METHOD:The study adopted a longitudinal, process-oriented design with N = 16 analysed electronic diaries. Throughout the course of their inpatient treatment, the patients answered questions daily about emotional intolerance and their AN-specific cognitions and behaviours. The temporal dynamics between emotional intolerance and these variables were analysed using a multivariate time series approach. RESULTS:The time series of the processes under investigation adequately reflected the individual treatment courses. The majority of significant linear time trends was found for HSS patients. Most importantly, analysis revealed significant temporal interactions between emotional intolerance and AN symptoms in almost 70% of HSS patients. Thereby, up to 37% of variance in eating restraint and up to 23% in weight concern could be attributed to changes in emotional intolerance. CONCLUSIONS:The findings support the notion that intolerable unpleasant emotions in severely affected AN patients influence their psychopathology. Additionally, time series analysis outlined the inter-individual heterogeneity of psychosomatic treatment courses of AN patients

Time Course of Leptin in Patients with Anorexia Nervosa during Inpatient Treatment: Longitudinal Relationships to BMI and Psychological Factors

<div><p>Background</p><p>Leptin, a hormone secreted by adipose tissue, appears to play a major role in the homeostasis of body weight and psychobiological processes associated with anorexia nervosa (AN). However, there is scarce data on its exact influence on this disorder, in particular data over time.</p><p>Objective</p><p>The present study addresses whether leptin changes during inpatient treatment play a role for treatment outcome and psychological factors in underweight AN patients.</p><p>Methods</p><p>In order to understand whether leptin’s role differs in relation to AN severity, data were assessed from 11 patients with a very low BMI and a higher chronicity (high severity group; HSS; mean BMI at the beginning of the study = 13.6; mean duration of illness = 5.1 years) vs. nine with less severe symptoms (LSS; mean BMI = 16.2; mean duration of illness = 3.7 years). During the course of treatment, serum leptin concentrations were assessed weekly while weight (BMI) was assessed twice per week. Concomitantly, psychological variables were obtained by means of electronic diaries. Unconditional linear growth models were calculated to evaluate the temporal course of leptin in relation to BMI. For HSS patients, two phases of treatment (BMI < 16 and BMI ≥ 16 kg/m²) were investigated.</p><p>Results</p><p>Leptin increased significantly with BMI in both groups of patients. For HSS patients, the increase of leptin in the first treatment phase did not predict later increases in BMI. Furthermore, the relationship of leptin and psychological factors was modulated by symptom severity. In HSS patients, higher leptin levels were associated with greater feelings of depression, anxiety, and stress whereas in LSS patients a higher leptin level showed the trend to be associated with lower psychological symptom burden.</p><p>Conclusions</p><p>Our results suggest that leptin changes are differently associated with weight gain and psychological symptoms depending on the severity of starvation.</p></div

Plots of significant Granger causal relations combined with information from the electronic diaries as well as corresponding impulse response functions.

<p>Analysed time windows are shadowed in grey; family therapy sessions are marked with a black triangle; special notes from the diary are marked with *. Impulse response function (IRF) / orthogonalised IRF (OIRF): responses are considered significant if their error bands do not include 0. Confidence bounds are computed employing Hall bootstrap method. For a detailed description of IRF / OIRF see explanations in the text.</p

Lagged dependencies between emotional intolerance and AN symptom variables.

<p>Lagged dependencies between emotional intolerance and AN symptom variables.</p

Significant linear time trends of longitudinal regressions during inpatient treatment

<p>Significant linear time trends of longitudinal regressions during inpatient treatment</p

Characteristics of the analyzed sample

<p>Characteristics of the analyzed sample</p