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Biometrika 1986 73(3):725-730; doi:10.1093/biomet/73.3.725
© 1986 by Biometrika Trust
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Diagnostic testing of univariate time series models

GRETA M. LJUNG

Department of Mathematics, Massachusetts Institute of Technology Cambridge, Massachusetts, 02139, U.S.A.

The portmanteau statistic for testing the adequacy of an autoregressive-moving average model is based on the first m autocorrelations of the residuals from the fitted model. This paper examines the properties of this test for various choices of m. A modification which allows the use of small values of m is shown to result in a more powerful test. The Lagrange multiplier statistic (Godfrey, 1979) and a test statistic examined by Newbold (1980) are also discussed.

Key Words: Autoregressive-moving average model • Lagrange multiplier test • Portmanteau test • Residual autocorrelation • Time series model checking


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