Recent Developments in Nonlinear Cointegration with Applications to Macroeconomics and Finance Book

	List of Figures
	List of Tables
	Preface
	Acknowledgments
1	Introduction	1
1	Combining the hypotheses of nonstationarity and nonlinearity	1
1.1	The economic arguments	1
1.2	The econometric arguments	3
1.3	Terminology and methodological aspects	6
1.4	An overview of the main topics of the book	8
2	A brief review of some nonlinear models	11
2.1	Bilinear models	11
2.2	Threshold autoregressive models	19
3	Unit root and stationarity tests	26
3.1	The Dickey-Fuller tests	26
3.2	The Phillips-Perron tests	31
3.3	The Schmidt-Phillips test	33
3.4	The Elliott, Rothenberg and Stock test	35
3.5	The KPSS test	38
2	Are the Unit-Root Tests Adequate for Nonlinear Models?	45
1	Introduction	45
2	Examples of nonlinear models with unit roots and long-memory	47
2.1	The squared transformation of a unit root process	47
2.2	SETAR(2,1,1) models with unit roots	48
2.3	SETAR models with interior regimes	49
2.4	Other nonlinear processes	51
2.5	Long-range dependent nonlinear models	52
2.6	Hermite expansion of nonlinearly transformed I(1) processes	54
3	Monte Carlo experiments: applying the classical tests to nonlinear models	58
3.1	Smooth transition models	59
3.2	Bilinear models	62
3.3	Other nonlinear time series models	68
3.4	Monte Carlo simulations on nonlinear transformations of unit roots	70
4	Extensions of traditional unit root tests based on ADF regressions	71
4.1	ADF tests based on the rank of the series	71
4.2	A modified ADF test based on Taylor expansions	72
5	Nonlinear stochastic and deterministic trends	75
5.1	Introducing hysteresis in random walks models	75
5.2	Detecting nonlinear stochastic trends in macroeconomic series	79
6	Data Analysis on macroeconomic and financial variables	80
6.1	Unit root test on bilinear models: the example of financial data	80
6.2	Applying MADF regressions on macroeconomic time series	86
6.3	Are there nonlinear stochastic trends in economic series?	89
3	Nonlinear measures of persistence in time series	117
1	Introduction	117
2	Short memory and extended memory variables	119
3	Mixing conditions	121
3.1	Definition	121
3.2	Geometric ergodicity	122
3.3	Near-epoch dependent processes	125
3.4	Testing the mixing conditions on nonlinear models	128
4	k[superscript th]-order dependence in time series	137
4.1	Mixing conditions and k[superscript th]-order cumulants and moments	137
4.2	Nonlinear autocorrelation and long-range memory	146
5	Correlation and entropy measures	154
5.1	Using the information theory	154
5.2	A simulation study and empirical applications	158
4	Nonlinear Equlibratioon, Cointegration and NEC Models	193
1	Introduction	193
2	Nonlinear equilibration	194
2.1	Attractors, transients and adiabatic approximation	194
2.2	Equilibration	198
2.3	Testing and modelling equilibration when the attractor is a fixed point
2.4	Application: modelling the relationship between the exchange rates and their fundamentals	203
3	Nonlinear cointegration	217
3.1	Preliminary definitions: co-mixing and cointegration	217
3.2	Single equations nonlinear error-correction models	220
3.3	Nonlinear cointegration analysis for vector systems	223
3.4	A NEC model of the price-wage loop in France	228
3.5	Bubbles or nonlinear dynamics?	242
4	Nonlinear co-trending between a set of variables	247
4.1	Nonlinear deterministic trends in univariate time series	247
4.2	Nonlinear co-trending	251
4.3	Application: testing the convergence of fiscal policies in Europe	254
5	Asymmetric and Threshold Nonlinear Error-Correction Models	267
1	Introduction	267
2	Asymmetries in partial adjustment models	268
3	Threshold autoregressive NEC models	271
3.1	Testing for threshold cointegration	272
3.2	A threshold NEC model of the French consumption function	274
3.3	Application to finance and possible extensions	280
	Index	291