Nonparametric Identification of Nonlinear Time Series: Selecting Significant Lags

Abstract In this article we suggest a nonparametric procedure for selecting significant lags in the model description of a general nonlinear stationary time series. The procedure can be applied to both the conditional mean and the conditional variance and is valid for heteroscedastic series. The procedure is illustrated by simulations and sunspot data, lynx data, and blowfly data are analyzed. It is indicated that projectors can be used in conjunction with the procedure for selecting significant lags to check the adequacy of an additive time series model.

[1]  Dag Tjøstheim,et al.  Nonparametric Identification of Nonlinear Time Series: Projections , 1994 .

[2]  H. Akaike.  Statistical predictor identification , 1970 .

[3]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[4]  Howell Tong,et al.  Consistent nonparametric order determination and chaos, with discussion , 1992 .

[5]  C. Granger,et al.  USING THE MUTUAL INFORMATION COEFFICIENT TO IDENTIFY LAGS IN NONLINEAR MODELS , 1994 .

[6]  W. Härdle,et al.  How Far are Automatically Chosen Regression Smoothing Parameters from their Optimum , 1988 .

[7]  D. Tjøstheim,et al.  Identification of nonlinear time series: First order characterization and order determination , 1990 .

[8]  Richard A. Davis,et al.  Time Series: Theory and Methods , 2013 .

[9]  K. Yoshihara.  Limiting behavior of U-statistics for stationary, absolutely regular processes , 1976 .

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

[11]  P. Robinson.  NONPARAMETRIC ESTIMATORS FOR TIME SERIES , 1983 .

[12]  B. Y. Thanoon.  SUBSET THRESHOLD AUTOREGRESSION WITH APPLICATIONS , 1990 .

[13]  Ruey S. Tsay,et al.  NON‐LINEAR TIME SERIES ANALYSIS OF BLOWFLY POPULATION , 1988 .

[14]  H. Tong,et al.  On residual sums of squares in non-parametric autoregression , 1993 .

[15]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

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

[17]  Howell Tong,et al.  Some Comments on the Canadian Lynx Data , 1977 .

[18]  C. Z. Wei.  On Predictive Least Squares Principles , 1992 .

[19]  T. Rao,et al.  An Introduction to Bispectral Analysis and Bilinear Time Series Models , 1984 .

[20]  D. Tjøstheim,et al.  Functional Identification in Nonlinear Time Series , 1991 .

[21]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[22]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[23]  R. Shibata.  Selection of the order of an autoregressive model by Akaike's information criterion , 1976 .

[24]  H. Tong,et al.  On consistent nonparametric order determination and chaos , 1992 .

[25]  P. Lewis,et al.  Nonlinear Modeling of Time Series Using Multivariate Adaptive Regression Splines (MARS) , 1991 .