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

.  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...

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Bibliographic Details
Published in:Journal of time series analysis 2004-05, Vol.25 (3), p.373-395
Main Authors: Ducharme, Gilles R., Lafaye de Micheaux, Pierre
Format: Article
Language:English
Subjects:
ARMA process
Econometrics
Gaussian white noise
goodness-of-fit test
Mathematical analysis
Mathematical models
Mathematics
normality of residuals
Simulation
smooth test
Statistical methods
Statistics
Studies
Time series
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Summary:.  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.
ISSN:0143-9782
1467-9892
DOI:10.1111/j.1467-9892.2004.01875.x