Testing for Smooth Transition Nonlinearity in the Presence of Outliers

Regime-switching models, like the smooth transition autoregressive [STAR] model, are typically applied to time series of moderate length. Hence, the nonlinear features that these models intend to describe may be reflected in only a few observations. Conversely, neglected outliers in a linear time series of moderate length may incorrectly suggest STAR (or other) type(s of) nonlinearity. In this article we propose outlier robust tests for STAR-type nonlinearity. These tests are designed such that they have a better level and power behavior than standard nonrobust tests in situations with outliers. We formally derive local and global robustness properties of the new tests. Extensive Monte Carlo simulations show the practical usefulness of the robust tests. An application to several quarterly industrial production indexes illustrates that apparent nonlinearity in time series sometimes seems due to only a few outliers.

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

[2]  Laurie Davies,et al.  The identification of multiple outliers , 1993 .

[3]  F. Peracchi,et al.  Robust M-Tests , 1991, Econometric Theory.

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

[5]  Howell Tong,et al.  Non-Linear Time Series , 1990 .

[6]  E. Handschin,et al.  Bad data analysis for power system state estimation , 1975, IEEE Transactions on Power Apparatus and Systems.

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

[8]  Andre Lucas,et al.  Outlier Robust Gmm Estimation of Leverage Determinants in Linear Dynamic Panel Data Models , 1997 .

[9]  V. Yohai,et al.  Influence Functionals for Time Series , 1986 .

[10]  D. G. Simpson,et al.  On One-Step GM Estimates and Stability of Inferences in Linear Regression , 1992 .

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

[12]  James G. MacKinnon,et al.  Graphical Methods for Investigating the Size and Power of Hypothesis Tests , 1998 .

[13]  Ruey S. Tsay,et al.  Testing and Modeling Threshold Autoregressive Processes , 1989 .

[14]  Simon M. Potter.  A Nonlinear Approach to U.S. GNP , 1993 .

[15]  Timo Teräsvirta,et al.  Aspects of modelling nonlinear time series , 1986 .

[16]  G. C. Tiao,et al.  Some advances in non‐linear and adaptive modelling in time‐series , 1994 .

[17]  H. White.  A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity , 1980 .

[18]  Timo Teräsvirta,et al.  Testing linearity against smooth transition autoregressive models , 1988 .

[19]  P. Rousseeuw.  Multivariate estimation with high breakdown point , 1985 .

[20]  Philip Hans Franses,et al.  Modeling Multiple Regimes in the Business Cycle , 1999, Macroeconomic Dynamics.

[21]  P. Rousseeuw,et al.  Unmasking Multivariate Outliers and Leverage Points , 1990 .

[22]  C. W. Coakley,et al.  A Bounded Influence, High Breakdown, Efficient Regression Estimator , 1993 .

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

[24]  Werner A. Stahel,et al.  Robust Statistics: The Approach Based on Influence Functions , 1987 .

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

[26]  Philip Hans Franses,et al.  The effects of additive outliers on tests for unit roots and cointegration , 1994 .

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

[28]  R. Tsay.  Nonlinearity tests for time series , 1986 .

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

[30]  R. Tsay.  Time Series Model Specification in the Presence of Outliers , 1986 .

[31]  G. C. Tiao,et al.  Estimation of time series parameters in the presence of outliers , 1988 .

[32]  Herman K. van Dijk,et al.  Classical and Bayesian aspects of robust unit root inference , 1995 .

[33]  R. Davies.  Hypothesis Testing when a Nuisance Parameter is Present Only Under the Alternatives , 1987 .

[34]  P. Rousseeuw.  Least Median of Squares Regression , 1984 .

[35]  R. Douglas Martin,et al.  ROBUST METHODS FOR TIME SERIES , 1981 .

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

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

[38]  R. Luukkonen,et al.  Lagrange multiplier tests for testing non-linearities in time series models , 1988 .

[39]  Timo Teräsvirta,et al.  Modelling Economic Relationships with Smooth Transition Regressions , 1996 .

[40]  R. Davies.  Hypothesis testing when a nuisance parameter is present only under the alternative , 1977 .

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

[42]  Andre Lucas,et al.  Unit Root Tests Based on M Estimators , 1995, Econometric Theory.

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