The software JMulTi: concept, development, and application in VAR analysis [Elektronische Ressource] : with a detailed discussion of bootstrap confidence intervals for impulse responses / von Alexander Benkwitz

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The Software JMulTi: Concept, Development,and Application in VAR Analysis.With a detailed discussion of bootstrap confidence intervalsfor impulse responses.D I S S E R T A T I O Nzur Erlangung des akademischen Gradesdoctor rerum politicarum(Doktor der Wirtschaftswissenschaft)¨im Fach Okonometrieeingereicht an derWirtschaftswissenschaftliche Fakult¨atder Humboldt-Universit¨at zu BerlinvonHerrn Dipl.-Kfm. Alexander Benkwitzgeboren am 27.01.1971 in Neu DelhiPr¨asident der Humboldt-Universit¨at zu Berlin:Prof. Dr. Jurgen¨ MlynekDekan der Wirtschaftswissenschaftliche Fakult¨at:Prof. Michael C. Burda, Ph.D.Gutachter:1. Prof. Dr. Helmut Lutk¨ epohl2. Prof. Harald Uhlig, Ph.D.eingereicht am: 30. April 2002Tag des Kolloquiums: 3. Juli 2002AbstractThe thesis develops and examines tools for the analysis of dynamic multi–equation models (VAR models). First, a general concept for the integration ofstatisticproceduresintoamenucontrolledsoftwareisdeveloped. TheresultingJava–library consists of configurable graphical user interface components andfunctions,whichallowcommunicationtothestatisticsoftwarepackageGauss.This library is the basis for the software JMulTi, a menu-driven program foranalyzing univariate and multivariate time series.The use of JMulTi for analyzing VAR models is documented next.

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The Software JMulTi: Concept, Development,
and Application in VAR Analysis.
With a detailed discussion of bootstrap confidence intervals
for impulse responses.
D I S S E R T A T I O N
zur Erlangung des akademischen Grades
doctor rerum politicarum
(Doktor der Wirtschaftswissenschaft)
¨im Fach Okonometrie
eingereicht an der
Wirtschaftswissenschaftliche Fakult¨at
der Humboldt-Universit¨at zu Berlin
von
Herrn Dipl.-Kfm. Alexander Benkwitz
geboren am 27.01.1971 in Neu Delhi
Pr¨asident der Humboldt-Universit¨at zu Berlin:
Prof. Dr. Jurgen¨ Mlynek
Dekan der Wirtschaftswissenschaftliche Fakult¨at:
Prof. Michael C. Burda, Ph.D.
Gutachter:
1. Prof. Dr. Helmut Lutk¨ epohl
2. Prof. Harald Uhlig, Ph.D.
eingereicht am: 30. April 2002
Tag des Kolloquiums: 3. Juli 2002Abstract
The thesis develops and examines tools for the analysis of dynamic multi–
equation models (VAR models). First, a general concept for the integration of
statisticproceduresintoamenucontrolledsoftwareisdeveloped. Theresulting
Java–library consists of configurable graphical user interface components and
functions,whichallowcommunicationtothestatisticsoftwarepackageGauss.
This library is the basis for the software JMulTi, a menu-driven program for
analyzing univariate and multivariate time series.
The use of JMulTi for analyzing VAR models is documented next. Unre-
stricted and restricted VAR models for the monetary sector of Germany are
estimatedanddifferentbootstrapconfidenceintervalsforimpulseresponsesare
computed and compared. These intervals are subject of a concluding and de-
tailed analysis. It is examined whether the bootstrap methods used in JMulTi
(and further suggestions, e.g. the subsampling) are able to overcome the pos-
sible inconsistency of the standard asymptotic method when computing con-
fidence intervals for impulse responses. A Monte–Carlo–study illustrates the
performance of the examined methods.
Keywords:
VAR Analysis, Bootstrap, JMulTi, JavaZusammenfassung
Die Dissertation entwickelt und untersucht Methoden fur¨ die Analyse dy-
namischerMehrgleichungsmodelle(VARModelle).Zuerstwirdeinallgemeines
Konzept fur die Einbindung statistischer Prozeduren in eine menugesteuerte¨ ¨
Software entwickelt. Die resultierende Java–Bibliothek besteht aus konfigu-
rierbaren Oberflac¨ henkomponenten und Funktionen, die die Kommunikation
zum statistischen Softwarepaket Gauss ermoglichen. Diese Bibliothek ist die¨
Grundlagefur¨ dieSoftwareJMulTi,einemmenugef¨ uhrten¨ ProgrammzurAna-
lyse univariater und multivariater Zeitreihen.
Der Einsatz von JMulTi bei der Analyse von VAR Modellen wird anschlie-
ßend dokumentiert. Dazu werden fur¨ den monet¨aren Sektor in Deutschland
unrestringierte und restringierte VAR Modelle geschat¨ zt und unterschiedliche
Bootstrapkonfidenzintervallen fur Impulsantworten berechnet und verglichen.¨
Diese Intervalle sind Gegenstand einer abschließenden und detaillierten Ana-
lyse. Es wird untersucht, ob die in JMulTi verwendeten Bootstrapverfahren
(und weitergehende Vorschlage wie z.B. das Subsampling) in der Lage sind,¨
die mog¨ liche Inkonsistenz des standardasymptotischen Verfahrens bei der Be-
rechnung von Konfidenzintervallen fur¨ Impulsantworten zu ub¨ erwinden. Eine
Monte–Carlo–StudieillustriertdieLeistungsfahigkeitderuntersuchtenMetho-¨
den.
Schlagworter:¨
VAR Analyse, Bootstrap, JMulTi, JavaAcknowledgments
The research was carried out within the Sonderforschungsbereich 373 (SFB
373) at Humboldt University Berlin. The author is grateful for financial sup-
port by the Deutsche Forschungsgemeinschaft. The author also enjoyed his
stay at the PhD program “Graduiertenkolleg Angewandte Mikrook¨ onomik” of
Humboldt University and Free University Berlin in the very early stage of his
work.
IwouldliketothankProf.Dr.HelmutLut¨ kepohlforsupervisingmythesis.
Hisvaluablecommentsandsuggestionswereanimportantsourceforimproving
my work and for the progress of the project JMulTi.
Also, I would like to thank the members of the SFB 373 and their speaker
Prof. Dr. Wolfgang H¨ardle for the productive and frank working environment.
Furthermore, I would like to thank Prof. Michael H. Neumann for giving me
an introduction to the mathematical view of the bootstrap methodology. I
also enjoyed many discussions with Dr. Holger Bartel about this subject.
The work on a software that could execute procedures of statistical soft-
ware packages was driven by the simple idea of having at least two instead
of one statistical programs running on the computer. When it became clear
that this idea could be realized, more effort was put into that project and
Markus Kr¨atzig joint the development. He also contributed the final name:
JMulTi. The graphical user interface of the currentversion was written bythe
Alexander Benkwitz and Markus Kr¨atzig. The econometrics of JMulTi and
iiiii
the thereby used Gauss procedures had been the work of many people (in
alphabetical order): Alexander Benkwitz, Ralf Brug¨ gemann, Markus Kr¨atzig,
Prof. Lutk¨ epohl, Prof. Ter¨asvirta, and Prof. Tschernig. In addition, many col-
leagues and students who commented on earlier versions of JMulTi helped to
improve this software a lot.
Finally, I am indebted to the people and companies who provided soft-
ware resources free of charge in the world wide web: Figures 2.1 and 2.12
were created using the free Tkpaint 1.6 from Samy Zafrany (http://www.
netanya.ac.il/~samy/tkpaint.html). The screen shots were made with
the 20 days free trial version of ImageForge by Cursor Arts (http://www.
cursorarts.com/). Image format conversion was done with ImageForge and
the conversion tool jpeg2ps.exe from Thomas Merz (i.e. search for “jpeg2ps”
at http://www.dante.de/). And last but not least, JMulTi was created
by using the free program Visual Age for Java, Entry Edition from IBM
(http://www7.software.ibm.com/vad.nsf).Contents
Acknowledgments i
Contents iv
List of Figures x
List of Tables xii
Abbreviations xii
1 Introduction 1
2 A graphical user interface for statistical procedures 4
2.1 Preliminary considerations . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Choice of programming language . . . . . . . . . . . . . 8
2.1.2 Choice of statistical software package . . . . . . . . . . . 15
2.2 Concept specification . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1 Two basic models . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Sub tasks derived from basic models . . . . . . . . . . . 18
2.2.3 Implementation in Java . . . . . . . . . . . . . . . . . . 20
2.2.4 Run Gauss as a statistical engine . . . . . . . . . . . . . 28
2.2.5 Error handling . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 How to create single step GUI applications for Gauss . . . . . . 34
ivCONTENTS v
2.3.1 The container class . . . . . . . . . . . . . . . . . . . . . 34
2.3.2 Execute Gauss-code . . . . . . . . . . . . . . . . . . . . 35
2.4 How to create and extend multiple step GUI applications for
Gauss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Available data . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.2 Program flow . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.3 Menus as knots for program flow . . . . . . . . . . . . . 39
2.4.4 Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.5 The use of an integrated development environment . . . . . . . 41
2.5.1 Use and advantage . . . . . . . . . . . . . . . . . . . . . 42
2.5.2 Visual programming . . . . . . . . . . . . . . . . . . . . 42
2.6 The anatomy of a JStatCom-based program . . . . . . . . . . . 45
2.6.1 Problem description . . . . . . . . . . . . . . . . . . . . 45
2.6.2 Definition of input and output variables . . . . . . . . . 46
2.6.3 GUI components . . . . . . . . . . . . . . . . . . . . . . 47
2.6.4 The containment hierarchy . . . . . . . . . . . . . . . . . 48
2.6.5 Event handling . . . . . . . . . . . . . . . . . . . . . . . 49
2.6.6 Visual programming . . . . . . . . . . . . . . . . . . . . 50
2.7 Summary and perspectives . . . . . . . . . . . . . . . . . . . . . 52
3 Analyzing VAR models with JMulTi 55
3.1 Introduction to JMulTi . . . . . . . . . . . . . . . . . . . . . . . 57
3.1.1 Program structure . . . . . . . . . . . . . . . . . . . . . 57
3.1.2 Installation . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.1.3 Starting JMulTi . . . . . . . . . . . . . . . . . . . . . . . 58
3.1.4 General program handling . . . . . . . . . . . . . . . . . 60
3.1.5 Loading data sets . . . . . . . . . . . . . . . . . . . . . . 61
3.2 Analysis of VAR models . . . . . . . . . . . . . . . . . . . . . . 64
3.2.1 Determining statistical properties of time series . . . . . 65CONTENTS vi
3.2.2 The VAR model . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.3 The VEC model. . . . . . . . . . . . . . . . . . . . . . . 67
3.2.4 Model specification . . . . . . . . . . . . . . . . . . . . . 70
3.2.5 Parameter constraints . . . . . . . . . . . . . . . . . . . 73
3.2.6 Model reduction procedures . . . . . . . . . . . . . . . . 75
3.2.7 VAR Model estimation . . . . . . . . . . . . . . . . . . . 76
3.2.8 VEC Model estimation . . . . . . . . . . . . . . . . . . . 78
3.2.9 Structural analysis . . . . . . . . . . . . . . . . . . . . . 80
3.3 Analyzing a German monetary system
with JMulTi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.1 Loading data set . . . . . . . . . . . . . . . . . . . . . . 89
3.3.2 Initial analysis. . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.3 Model specification . . . . . . . . . . . . . . . . . . . . . 91
3.3.4 VAR(5) model . . . . . . . . . . . . . . . . . . . . . . . . 93
3.3.5 The full VEC model . . . . . . . . . . . . . . . . . . . . 94
3.3.6 The subset VEC model . . . . . . . . . . . . . . . . . . . 95
3.3.7 Comparison of bootstrap confidence intervals . . . . . . . 98
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4 Bootstrap confidence intervals for impulse responses 100
4.1 Inference on estimated impulse responses . . . . . . . . . . . . . 102
4.1.1 Standard asymptotic inference . . . . . . . . . . . . . . . 103
4.1.2 Bootstrap inference . . . . . . . . . . . . . . . . . . . . . 105
4.2 Confidence intervals for impulse responses from an AR(1) . . . . 106
4.2.1 Confidence intervals based on standard asymptotics . . . 106
4.2.2 Confidence intervals based on the standard bootstrap . . 108
4.2.3 Hall’s percentile method . . . . . . . . . . . . . . . . . . 111
4.2.4 Confidence intervals based on a superefficient estimator . 112
4.2.5 Subsampling . . . . . . . . . . . . . . . . . . . . . . . . . 114CONTENTS vii
4.2.6 Subsampling with estimated rate of convergence . . . . . 116
4.2.7 Indirect confidence intervals . . . . . . . . . . . . . . . . 117
4.3 A Monte-Carlo experiment . . . . . . . . . . . . . . . . . . . . . 119
4.3.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.4 Summary and recommendations . . . . . . . . . . . . . . . . . . 128
Bibliography 130
A License agreement 137
B Documentation of Java library JStatCom 139
B.1 The Java library JStatCom . . . . . . . . . . . . . . . . . . . . 139
B.2 A simple GUI example . . . . . . . . . . . . . . . . . . . . . . . 140
B.3 Package util . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
B.3.1 Package Contents . . . . . . . . . . . . . . . . . . . . . . 144
B.3.2 Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B.3.3 Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
B.4 Package gauss.control . . . . . . . . . . . . . . . . . . . . . . 156
B.4.1 Package Contents . . . . . . . . . . . . . . . . . . . . . . 156
B.4.2 Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
B.5 Package gauss . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
B.5.1 Package Contents . . . . . . . . . . . . . . . . . . . . . . 163
B.5.2 Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 165
B.5.3 Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
B.6 Package util.component . . . . . . . . . . . . . . . . . . . . . 211
B.6.1 Package Contents . . . . . . . . . . . . . . . . . . . . . . 211
B.6.2 Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 213
B.6.3 Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214CONTENTS viii
C Gauss Control: A software which connects to Gauss for Win-
dows 235
C.1 Set up and configuration . . . . . . . . . . . . . . . . . . . . . . 236
C.1.1 File structure . . . . . . . . . . . . . . . . . . . . . . . . 236
C.1.2 Configuration . . . . . . . . . . . . . . . . . . . . . . . . 236
C.1.3 Temporary files . . . . . . . . . . . . . . . . . . . . . . . 238
C.2 The mother process . . . . . . . . . . . . . . . . . . . . . . . . . 239
C.3 The Gauss side . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
C.4 Example and test software . . . . . . . . . . . . . . . . . . . . . 242
C.5 Application with JMulTi . . . . . . . . . . . . . . . . . . . . . . 242
C.6 Documentation of exported functions in xlm.dll . . . . . . . . 243
C.6.1 Data structure . . . . . . . . . . . . . . . . . . . . . . . 243
C.6.2 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 243
C.7 Documentation of Gauss-library xlm . . . . . . . . . . . . . . . 261
C.7.1 Global variables . . . . . . . . . . . . . . . . . . . . . . . 261
C.7.2 Procedures. . . . . . . . . . . . . . . . . . . . . . . . . . 261
C.8 Suggestions for future extensions . . . . . . . . . . . . . . . . . 273
D Documentation of the Gauss library var 274
D.1 Implementation in Gauss . . . . . . . . . . . . . . . . . . . . . 275
D.2 Analyzing VAR Models . . . . . . . . . . . . . . . . . . . . . . . 276
D.2.1 Reduced form model . . . . . . . . . . . . . . . . . . . . 277
D.2.2 Structural form model . . . . . . . . . . . . . . . . . . . 278
D.2.3 Defining mixed variables . . . . . . . . . . . . . . . . . . 278
D.2.4 Linear restrictions. . . . . . . . . . . . . . . . . . . . . . 279
D.2.5 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 280
D.2.6 Impulse response analysis . . . . . . . . . . . . . . . . . 282
D.3 Analyzing VECMs . . . . . . . . . . . . . . . . . . . . . . . . . 284
D.3.1 Reduced form model . . . . . . . . . . . . . . . . . . . . 285