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Preface; Contents; Chapter 1 INTRODUCTION AND SOME BASIC CONCEPTS; 1.1 Linearity and Gaussianity; 1.2 Examples of Nonlinear Time Series; 1.3 Initial Data Analysis; 1.3.1 Skewness, kurtosis, and normality; 1.3.2 Kendall's (partial) tau; 1.3.3 Mutual information coefficient; 1.3.4 Recurrence plot; 1.3.5 Directed scatter plot; 1.4 Summary, Terms and Concepts; 1.5 Additional Bibliographical Notes; 1.6 Data and Software references; Exercises; Chapter 2 CLASSIC NONLINEAR MODELS; 2.1 The General Univariate Nonlinear Model; 2.1.1 Volterra series expansions; 2.1.2 State-dependent model formulation
2.2 Bilinear Models2.3 Exponential ARMA Model; 2.4 Random Coefficient AR Model; 2.5 Nonlinear MA Model; 2.6 Threshold Models; 2.6.1 General threshold ARMA (TARMA) model; 2.6.2 Self-exciting threshold ARMA model; 2.6.3 Continuous SETAR model; 2.6.4 Multivariate thresholds; 2.6.5 Asymmetric ARMA model; 2.6.6 Nested SETARMA model; 2.7 Smooth Transition Models; 2.8 Nonlinear non-Gaussian Models; 2.8.1 Newer exponential autoregressive models; 2.8.2 Product autoregressive model; 2.9 Artificial Neural Network Models; 2.9.1 AR neural network model; 2.9.2 ARMA neural network model
2.9.3 Local global neural network model2.9.4 Neuro-coefficient STAR model; 2.10 Markov Switching Models; 2.11 Application: An AR…NN model for EEG Recordings; 2.12 Summary, Terms and Concepts; 2.13 Additional Bibliographical Notes; 2.14 Data and Software references; Appendix; 2.A Impulse Response Functions; 2.B Acronyms in Threshold Modeling; Exercises; Chapter 3 PROBABILISTIC PROPERTIES; 3.1 Strict Stationarity; 3.2 Second-order Stationarity; 3.3 Application: Nonlinear AR…GARCH model; 3.4 Dependence and Geometric Ergodicity; 3.4.1 Mixing coefficients; 3.4.2 Geometric ergodicity
3.5 Invertibility3.5.1 Global; 3.5.2 Local; 3.6 Summary, Terms and Concepts; 3.7 Additional Bibliographical Notes; 3.8 Data and Software References; Appendix; 3.A Vector and Matrix Norms; 3.B Spectral Radius of a Matrix; Exercises; Chapter 4 FREQUENCY-DOMAIN TESTS; 4.1 Bispectrum; 4.2 The Subba Rao…Gabr Tests; 4.2.1 Testing for Gaussianity; 4.2.2 Testing for linearity; 4.2.3 Discussion; 4.3 Hinich's Tests; 4.3.1 Testing for linearity; 4.3.2 Testing for Gaussianity; 4.3.3 Discussion; 4.4 Related Tests; 4.4.1 Goodness-of-fit tests; 4.4.2 Maximal test statistics for linearity
4.4.3 Bootstrapped-based tests4.4.4 Discussion; 4.5 A MSFE-Based Linearity Test; 4.6 Which Test to Use?; 4.7 Application: A Comparison of Linearity Tests; 4.8 Summary, Terms and Concepts; 4.9 Additional Bibliographical Notes; 4.10 Software References; Exercises; Chapter 5 TIME-DOMAIN LINEARITY TESTS; 5.1 Lagrange Multiplier Tests; 5.2 Likelihood Ratio Tests; 5.3 Wald Test; 5.4 Tests Based on a Second-order Volterra Expansion; 5.5 Tests Based on Arranged Autoregressions; 5.6 Nonlinearity vs. Specific Nonlinear Alternatives; 5.7 Summary, Terms and Concepts; 5.8 Additional Bibliographical Notes
2.2 Bilinear Models2.3 Exponential ARMA Model; 2.4 Random Coefficient AR Model; 2.5 Nonlinear MA Model; 2.6 Threshold Models; 2.6.1 General threshold ARMA (TARMA) model; 2.6.2 Self-exciting threshold ARMA model; 2.6.3 Continuous SETAR model; 2.6.4 Multivariate thresholds; 2.6.5 Asymmetric ARMA model; 2.6.6 Nested SETARMA model; 2.7 Smooth Transition Models; 2.8 Nonlinear non-Gaussian Models; 2.8.1 Newer exponential autoregressive models; 2.8.2 Product autoregressive model; 2.9 Artificial Neural Network Models; 2.9.1 AR neural network model; 2.9.2 ARMA neural network model
2.9.3 Local global neural network model2.9.4 Neuro-coefficient STAR model; 2.10 Markov Switching Models; 2.11 Application: An AR…NN model for EEG Recordings; 2.12 Summary, Terms and Concepts; 2.13 Additional Bibliographical Notes; 2.14 Data and Software references; Appendix; 2.A Impulse Response Functions; 2.B Acronyms in Threshold Modeling; Exercises; Chapter 3 PROBABILISTIC PROPERTIES; 3.1 Strict Stationarity; 3.2 Second-order Stationarity; 3.3 Application: Nonlinear AR…GARCH model; 3.4 Dependence and Geometric Ergodicity; 3.4.1 Mixing coefficients; 3.4.2 Geometric ergodicity
3.5 Invertibility3.5.1 Global; 3.5.2 Local; 3.6 Summary, Terms and Concepts; 3.7 Additional Bibliographical Notes; 3.8 Data and Software References; Appendix; 3.A Vector and Matrix Norms; 3.B Spectral Radius of a Matrix; Exercises; Chapter 4 FREQUENCY-DOMAIN TESTS; 4.1 Bispectrum; 4.2 The Subba Rao…Gabr Tests; 4.2.1 Testing for Gaussianity; 4.2.2 Testing for linearity; 4.2.3 Discussion; 4.3 Hinich's Tests; 4.3.1 Testing for linearity; 4.3.2 Testing for Gaussianity; 4.3.3 Discussion; 4.4 Related Tests; 4.4.1 Goodness-of-fit tests; 4.4.2 Maximal test statistics for linearity
4.4.3 Bootstrapped-based tests4.4.4 Discussion; 4.5 A MSFE-Based Linearity Test; 4.6 Which Test to Use?; 4.7 Application: A Comparison of Linearity Tests; 4.8 Summary, Terms and Concepts; 4.9 Additional Bibliographical Notes; 4.10 Software References; Exercises; Chapter 5 TIME-DOMAIN LINEARITY TESTS; 5.1 Lagrange Multiplier Tests; 5.2 Likelihood Ratio Tests; 5.3 Wald Test; 5.4 Tests Based on a Second-order Volterra Expansion; 5.5 Tests Based on Arranged Autoregressions; 5.6 Nonlinearity vs. Specific Nonlinear Alternatives; 5.7 Summary, Terms and Concepts; 5.8 Additional Bibliographical Notes