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Biometrika 1986 73(3):687-694; doi:10.1093/biomet/73.3.687
© 1986 by Biometrika Trust
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A portmanteau test for self-exciting threshold autoregressive-type nonlinearity in time series

JOSEPH PETRUCCELLI and NEVILLE DAVIES

Department of Mathematical Sciences, Worcester Polytechnic Institute Massachusetts 01609, U.S.A.
Department of Mathematics, Statistics and Operational Research, Trent Polytechnic Nottingham NG1 4BU, U.K.

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.

Key Words: Nonlinear time series • Portmanteau test • Self-exciting threshold autoregressive model


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