A portmanteau test for self-exciting threshold autoregressive-type nonlinearity in time series

A portmanteau test to detect self-exciting threshold autoregressive-type nonlinearity in time series data is proposed. The test is based on cumulative sums of standardized residuals from autoregressive fits to the data. Significance levels for the test under the hypothesis of linearity are obtain fr...

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Bibliographic Details
Published in:Biometrika 1986-12, Vol.73 (3), p.687-694
Main Authors: PETRUCCELLI, JOSEPH, DAVIES, NEVILLE
Format: Article
Language:English
Subjects:
Autoregressive models
Exact sciences and technology
Forecasting standards
Inference from stochastic processes
time series analysis
Mathematics
Modeling
Nonlinear time series
Nonlinearity
Portmanteau test
Power lines
Probability and statistics
Sciences and techniques of general use
Self-exciting threshold autoregressive model
Significance level
Statistics
Time series
Time series analysis
Time series forecasting
Time series models
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Summary:A portmanteau test to detect self-exciting threshold autoregressive-type nonlinearity in time series data is proposed. The test is based on cumulative sums of standardized residuals from autoregressive fits to the data. Significance levels for the test under the hypothesis of linearity are obtain from the asymptotic distribution of the cumulative sums as Brownian motion. The performance of the test is evaluated for simulated data from linear, bilinear and self-exciting threshold autoregressive models. It is also compared with another test which has been suggested for detecting general nonlinearity. Features of the proposed test, which make it useful in identifying the autoregressive order and the lag in threshold models, are discussed.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/73.3.687