Nonlinear Time Series Modelling: An Introduction

Recent developments in nonlinear time series modelling are reviewed. Three main types of nonlinear models are discussed: Markov Switching, Threshold Autoregression and Smooth Transition Autoregression. Classical and Bayesian estimation techniques are described for each model. Parametric tests for nonlinearity are reviewed with examples from the three types of models. Finally, forecasting and impulse response analysis is developed.

[1]  Gary Koop,et al.  Dynamic Asymmetries in U.S. Unemployment , 1999 .

[2]  S. Chib,et al.  Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts , 1993 .

[3]  K. Chan,et al.  Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model , 1993 .

[4]  René Garcia,et al.  Asymptotic null distribution of the likelihood ratio test in Markov switching models , 1998 .

[5]  D. Andrews,et al.  Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative , 1992 .

[6]  H. Tong,et al.  ON ESTIMATING THRESHOLDS IN AUTOREGRESSIVE MODELS , 1986 .

[7]  T. Teräsvirta.  Specification, Estimation, and Evaluation of Smooth Transition Autoregressive Models , 1994 .

[8]  Simon Potter,et al.  Nonlinear Impulse Response Functions , 1998 .

[9]  Gary Koop,et al.  Do recessions permanently change output , 1993 .

[10]  S. Satchell,et al.  Why do regime‐switching models forecast so badly? , 1999 .

[11]  S. Chib.  Marginal Likelihood from the Gibbs Output , 1995 .

[12]  M. Hashem Pesaran,et al.  A floor and ceiling model of US output , 1997 .

[13]  Simon M. Potter.  A Nonlinear Approach to US GNP , 1995 .

[14]  B. Hansen.  Sample Splitting and Threshold Estimation , 2000 .

[15]  Michel Lubrano,et al.  Bayesian Analysis of Nonlinear Time Series Models with Threshold , 1996 .

[16]  M. B. Priestley,et al.  Non-linear and non-stationary time series analysis , 1990 .

[17]  M. Pithon,et al.  Erratum , 1998 .

[18]  Peter E. Rossi,et al.  Nonlinear dynamic structures , 1993 .

[19]  Bruce E. Hansen,et al.  Erratum: The likelihood ratio test under nonstandard conditions: Testing the Markov switching model of GNP , 1996 .

[20]  William A. Brock,et al.  8 Nonlinear time series and macroeconometrics , 1993 .

[21]  C. Granger,et al.  Modelling Nonlinear Economic Relationships , 1995 .

[22]  Gary Koop,et al.  Parameter uncertainty and impulse response analysis , 1996 .

[23]  T. Teräsvirta,et al.  Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models , 1992 .

[24]  Chang‐Jin Kim,et al.  State-Space Models with Regime-Switching: Classical and Gibbs Sampling Approaches with Applications , 1999 .

[25]  James D. Hamilton.  A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle , 1989 .

[26]  Bruce E. Hansen,et al.  Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis , 1996 .

[27]  Clive W. J. Granger,et al.  Forecasting white noise , 2001 .

[28]  James D. Hamilton.  Analysis of time series subject to changes in regime , 1990 .

[29]  Andrew J. Filardo.  Business-Cycle Phases and Their Transitional Dynamics , 1994 .

[30]  M. Hashem Pesaran,et al.  Impulse response analysis in nonlinear multivariate models , 1996 .

[31]  Gary Koop,et al.  Bayes factors and nonlinearity: Evidence from economic time series , 1999 .

[32]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[33]  Hung Man Tong,et al.  Threshold models in non-linear time series analysis. Lecture notes in statistics, No.21 , 1983 .