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Goodness‐of‐fit tests of normality for the innovations in ARMA models

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  • Gilles R. Ducharme
  • Pierre Lafaye de Micheaux

Abstract

. In this paper, we propose a goodness‐of‐fit test of normality for the innovations of an ARMA(p, q) model with known mean or trend. The test is based on the data driven smooth test approach and is simple to perform. An extensive simulation study is conducted to study the behaviour of the test for moderate sample sizes. It is found that our approach is generally more powerful than existing tests while holding its level throughout most of the parameter space and, thus, can be recommended. This agrees with theoretical results showing the superiority of the data driven smooth test approach in related contexts.

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  • Gilles R. Ducharme & Pierre Lafaye de Micheaux, 2004. "Goodness‐of‐fit tests of normality for the innovations in ARMA models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 373-395, May.
    • Handle: RePEc:bla:jtsera:v:25:y:2004:i:3:p:373-395
    DOI: 10.1111/j.1467-9892.2004.01875.x
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    1. B. L. Shea, 1987. "Estimation Of Multivariate Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 95-109, January.
    2. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
    3. C. Granger, 1976. "Tendency towards normality of linear combinations of random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 23(1), pages 237-248, December.
    4. Z. Lomnicki, 1961. "Tests for departure from normality in the case of linear stochastic processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 4(1), pages 37-62, December.
    5. Norbert Henze, 1997. "Do components of smooth tests of fit have diagnostic properties?," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 121-130, January.
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    1. Gilles R. Ducharme & Bénédicte Fontez, 2004. "A Smooth Test of Goodness-of-Fit for Growth Curves and Monotonic Nonlinear Regression Models," Biometrics, The International Biometric Society, vol. 60(4), pages 977-986, December.

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