A Unified Approach to Nonlinearity, Structural Change, and Outliers

This paper demonstrates that the class of conditionally linear and Gaussian state-space models offers a general and convenient framework for simultaneously handling nonlinearity, structural change and outliers in time series. Many popular nonlinear time series models, including threshold, smooth transition and Markov-Switching models, can be written in state-space form. It is then straightforward to add components that capture parameter instability and intervention effects. We advocate a Bayesian approach to estimation and inference, using an efficient implementation of Markov Chain Monte Carlo sampling schemes for such linear dynamic mixture models. The general modelling framework and the Bayesian methodology are illustrated by means of several examples. An application to quarterly industrial production growth rates for the G7 countries demonstrates the empirical usefulness of the approach.

[1]  D. Hendry,et al.  Nonlinear Econometric Modeling in Time Series , 2006 .

[2]  Paolo Giordani,et al.  A cautionary note on outlier robust estimation of threshold models , 2006 .

[3]  James Morley,et al.  The Importance of Nonlinearity in Reproducing Business Cycle Features , 2005 .

[4]  Chin Nam Low,et al.  Random Walk Smooth Transition Autoregressive Models , 2006 .

[5]  J. Geweke,et al.  Contemporary Bayesian Econometrics and Statistics , 2005 .

[6]  Francesco Battaglia,et al.  Outlier Detection And Estimation In NonLinear Time Series , 2005 .

[7]  The Importance of Nonlinearity in Reproducing Business Cycle Features , 2005 .

[8]  Have output growth rates stabilised? evidence from the g‐7 economies , 2003 .

[9]  Adrian Pagan,et al.  A comparison of two business cycle dating methods , 2003 .

[10]  T. Teräsvirta,et al.  Time-Varying Smooth Transition Autoregressive Models , 2003 .

[11]  James H. Stock,et al.  Has the Business Cycle Changed? Evidence and Explanations , 2003 .

[12]  Ana Beatriz Galvão,et al.  Can non-linear time series models generate US business cycle asymmetric shape? , 2002 .

[13]  James D. Hamilton,et al.  New directions in business cycle research and financial analysis , 2002 .

[14]  Michael P. Clements,et al.  Can oil shocks explain asymmetries in the US Business Cycle? , 2002 .

[15]  T. Mills,et al.  Plucking models of business cycle fluctuations: Evidence from the G-7 countries , 2002 .

[16]  Chang-Jin Kim,et al.  Nonlinearity and the permanent effects of recessions , 2002 .

[17]  Siem Jan Koopman,et al.  A simple and efficient simulation smoother for state space time series analysis , 2002 .

[18]  Siem Jan Koopman,et al.  Time Series Analysis by State Space Methods , 2001 .

[19]  Olivier J. Blanchard,et al.  The Long and Large Decline in U.S. Output Volatility , 2001 .

[20]  Adrian Pagan,et al.  Dissecting the cycle: a methodological investigation , 2002 .

[21]  R. Kohn,et al.  Efficient Bayesian Inference for Dynamic Mixture Models , 2000 .

[22]  Chang-Jin Kim,et al.  Common Stochastic Trends, Common Cycles, and Asymmetry in Economic Fluctuations , 2000 .

[23]  Timo Teräsvirta,et al.  Smooth transition autoregressive models - A survey of recent developments , 2000 .

[24]  Luc Bauwens,et al.  Bayesian Inference in Dynamic Econometric Models , 2000 .

[25]  C. Nelson.  Output fluctuations in the United States: what has changed since the early 1980s? comments , 2000 .

[26]  Gary Koop,et al.  Nonlinearity, Structural Breaks Or Outliers In Economic Time Series? , 2000 .

[27]  Gary Koop,et al.  Are Apparent Findings of Nonlinearity Due to Structural Instability in Economic Time Series , 2001 .

[28]  Chang‐Jin Kim,et al.  Has the U.S. Economy Become More Stable? A Bayesian Approach Based on a Markov-Switching Model of the Business Cycle , 1999, Review of Economics and Statistics.

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

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

[31]  R. Kohn,et al.  Diagnostics for Time Series Analysis , 1999 .

[32]  B. Raj,et al.  The U.S. Productivity Slowdown: A Peak through the Structural Break Window , 1999 .

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

[34]  Simon M. Potter,et al.  Dynamic asymmetries in US unemployment , 1999 .

[35]  Chang-Jin Kim,et al.  Business Cycle Turning Points, A New Coincident Index, and Tests of Duration Dependence Based on a Dynamic Factor Model With Regime Switching , 1998, Review of Economics and Statistics.

[36]  Mahmoud M. Gabr,et al.  Robust estimation of bilinear time series models , 1998 .

[37]  Margaret Mary McConnell,et al.  Output Fluctuations in the United States: What Has Changed Since the Early 1980s? , 1998 .

[38]  Gregory D. Hess,et al.  Measuring and Comparing Business-Cycle Features , 1997 .

[39]  K. R. Kadiyala,et al.  Numerical Methods for Estimation and Inference in Bayesian VAR-models , 1997 .

[40]  Elvezio Ronchetti,et al.  Robustness Aspects of Model Choice , 1997 .

[41]  Christopher A. Sims,et al.  Advances in Econometrics , 1996 .

[42]  Philip Hans Franses,et al.  Testing for Smooth Transition Nonlinearity in the Presence of Outliers , 1996 .

[43]  Unit Roots and Infrequent Large Shocks: New International Evidence on Output Growth , 1995 .

[44]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

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

[46]  Siu Hung Cheung,et al.  On robust estimation of threshold autoregressions , 1994 .

[47]  James D. Hamilton.  State-space models , 1994 .

[48]  Lon-Mu Liu,et al.  Joint Estimation of Model Parameters and Outlier Effects in Time Series , 1993 .

[49]  T. Fomby,et al.  Large Shocks, Small Shocks, and Economic Fluctuations: Outliers in Macroeconomic Time Series , 1994 .

[50]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

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

[52]  R. Tsay.  Outliers, Level Shifts, and Variance Changes in Time Series , 1988 .

[53]  Oscar H. Bustos,et al.  Robust Estimates for ARMA Models , 1986 .

[54]  L. Denby,et al.  Robust Estimation of the First-Order Autoregressive Parameter , 1979 .

[55]  M. Otto,et al.  Outliers in Time Series , 1972 .