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CONTENTS
INTRODUCTION
1. THE NATURE OF TIME SERIES
1.1 DESCRIPTION OF TIME SERIES
1.3 STATIONARITY
1.4 TRANSFORMATIONS OF TIME SERIES
1.5 TREND, SEASONAL, AND IRREGULAR PATTERNS
1.6 ARMA MODELS OF TIME SERIES
1.7 STYLIZED FACTS ABOUT TIME SERIES
2.1 LINEAR DIFFERENCE EQUATIONS
2.2 LAG OPERATOR
2.3 THE SOLUTION OF DIFFERENCE EQUATIONS
2.3.1 PARTICULAR SOLUTION AND LAG OPERATORS
2.3.2 SOLUTION BY ITERATION
2.3.3 HOMOGENOUS SOLUTION
2.3.4 PARTICULAR SOLUTION
2.4 STABILITY CONDITIONS
2.5 STABILITY AND STATIONARITY
3.1 ESTIMATION OF AN ARMA MODEL
3.1.1 AUTOCORRELATION FUNCTION – ACF
3.1.2 PARTIAL AUTOCORRELATION FUNCTION – PACF
3.1.3 Q-TESTS
3.1.5 INFORMATION CRITERIA
3.1.6 BOX-JENKINS METHODOLOGY
3.2.1 DETERMINISTIC TREND
3.2.2 STOCHASTIC TREND
3.2.3 STOCHASTIC PLUS DETERMINISTIC TREND
3.2.4 ADDITIONAL NOTES ON TRENDS IN TIME SERIES
3.3 SEASONALITY IN TIME SERIES
3.3.1 REMOVING SEASONAL PATTERNS
3.3.2 ESTIMATING SEASONAL PATTERNS
3.3.4 HODRICK-PRESCOTT FILTER
3.4 UNIT ROOTS
3.4.1 DICKEY-FULLER TEST
3.4.2 AUGMENTED DICKEY-FULLER TEST
3.4.3 PHILLIPS-PERRON TEST
3.4.4 SHORTCOMINGS OF THE STANDARD UNIT ROOT TESTS
3.4.5 KPSS TEST
3.5 UNIT ROOTS AND STRUCTURAL CHANGE
3.5.1 PERRON’S TEST
3.5.2 ZIVOT AND ANDREWS’ TEST
3.6 DETECTING A STRUCTURAL CHANGE
3.6.1 SINGLE STRUCTURAL CHANGE
3.6.2 MULTIPLE STRUCTURAL CHANGE
3.7 NON-LINEAR STRUCTURE AND CONDITIONAL HETEROSKEDASTICITY
3.7.1 CONDITIONAL AND UNCONDITIONAL EXPECTATIONS
3.7.2 ARCH MODEL
3.7.3 GARCH MODEL
3.7.4 DETECTING CONDITIONAL HETEROSKEDASTICITY
3.7.5 THE BDS TEST
3.7.6 AN ALTERNATIVE TO THE BDS TEST: INTEGRATION ACROSS THE CORRELATION INTEGRAL
3.7.7 IDENTIFICATION AND ESTIMATION OF A GARCH MODEL
3.7.8 EXTENSIONS OF ARCH-TYPE MODELS
3.7.9 MULTIVARIATE (G)ARCH MODELS
3.7.10 STRUCTURAL BREAKS IN VOLATILITY
4. MULTIPLE TIME SERIES
4.1 VAR MODELS
4.1.1 STRUCTURAL FORM, REDUCED FORM, AND IDENTIFICATION
4.1.2 STABILITY AND STATIONARITY OF VAR MODELS
4.1.3 ESTIMATION OF A VAR MODEL
4.2 GRANGER CAUSALITY
4.3 COINTEGRATION AND ERROR CORRECTION MODELS
4.3.1 DEFINITION OF COINTEGRATION
4.3.2 THE ENGLE-GRANGER METHODOLOGY
4.3.3 EXTENSIONS TO THE ENGLE-GRANGER METHODOLOGY
4.3.4 THE JOHANSEN METHODOLOGY
5. PANEL DATA AND UNIT ROOT TESTS
5.1 LEVIN, LIN, AND CHU PANEL UNIT-ROOT TEST WITH A NULL OF UNIT ROOT AND LIMITED COEFFICIENTS HETEROGENEITY
5.2. IM, PESARAN, AND SHIN UNIT-ROOT TEST WITH A NULL OF UNIT ROOT AND HETEROGENEOUS COEFFICIENTS
5.3 HADRI UNIT-ROOT TESTS WITHA NULL OF STATIONARITY
5.4 BREUER, MCNOWN, AND WALLACETEST FOR CONVERGENCE
5.5 VOGELSANG TEST FOR β-CONVERGENCE
APPENDIX A – MONTE CARLO SIMULATIONS
APPENDIX B – STATISTICAL TABLES
REFERENCES
INDEX