Wallis Statistic

Definition: A Wallis statistic comes from a test for fourth-order in the residuals of a regression, from Wallis (1972) Econometrica 40:617-636. Fourth-order serial correlation comes up in the context of quarterly data; e.g., seasonality. Formally, the statistic is:

d₄=(sum from t=5 to t=T of:

(e_t-e_t-4)²/(sum from t=1 to t=T of:

e_t²)

where the series of e_t are the residuals from a regression.

Tables for interpreting the statistic are in Wallis (1972).

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