Model validity tests for non-linear signal processing applications

Abstract Time series model validity tests based on general correlations are presented in this paper. It is shown that the tests Φxi xi(τ), Φ xi xi 2(τ) and Φ xi xi xi(τ1, t2) can only detect a subset of any possible unmodelled terms in the residuals, whereas Φ xi 2 xi 2(τ) detects all possible terms. These basic results are then extended to include functions of process or residual terms as entries in the correlation. Simulation studies are included to demonstrate the effectiveness of the tests when applied to estimated models of both simulated and real data sequences.

[1]  G. Box,et al.  Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models , 1970 .

[2]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[3]  C. Granger,et al.  An introduction to bilinear time series models , 1979 .

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

[5]  Sheng Chen,et al.  Modelling and analysis of non-linear time series , 1989 .

[6]  Torsten Bohlin,et al.  Maximum-power validation of models without higher-order fitting , 1978, Autom..

[7]  M. Priestley.  STATE‐DEPENDENT MODELS: A GENERAL APPROACH TO NON‐LINEAR TIME SERIES ANALYSIS , 1980 .

[8]  T. Ozaki.  2 Non-linear time series models and dynamical systems , 1985 .

[9]  S. Billings,et al.  Correlation based model validity tests for non-linear models , 1986 .

[10]  G. Box,et al.  On a measure of lack of fit in time series models , 1978 .

[11]  Kuldeep Kumar.  ON THE IDENTIFICATION OF SOME BILINEAR TIME SERIES MODELS , 1986 .

[12]  S. Billings,et al.  A prediction-error and stepwise-regression estimation algorithm for non-linear systems , 1986 .

[13]  A. J. Lawrance,et al.  Modelling and Residual Analysis of Nonlinear Autoregressive Time Series in Exponential Variables , 1985 .

[14]  N. Davies,et al.  Significance levels of the Box-Pierce portmanteau statistic in finite samples , 1977 .

[15]  A. I. McLeod,et al.  DIAGNOSTIC CHECKING ARMA TIME SERIES MODELS USING SQUARED‐RESIDUAL AUTOCORRELATIONS , 1983 .