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A cubic spline extension of the Durbin-Watson test. (English) Zbl 0664.62068
We propose a new test for model misspecification in linear regression, based on a measure of ‘smoothness’ of the regression residuals. This ‘curvature statistic’ is related to a property of cubic splines and leads to a convenient, powerful test for patterns. The distribution of the curvature statistic may be derived from assumptions of normality. For equally spaced data, the calculations are simplified and a table of significance points of the distribution is given. Smoothness considerations also lead to a natural generalization of the Durbin-Watson or mean-square successive differences statistic for unequally spaced observations. This generalized mean-squared successive differences statistic arises when linear splines are substituted for cubic splines in the development of the curvature statistic.

62J05 Linear regression; mixed models
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F03 Parametric hypothesis testing
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