Post sample parameter stability tests under linear aggregation of economic relationships

Rugaimukamu, Deogratias Matayo Bengesi (1981) Post sample parameter stability tests under linear aggregation of economic relationships. University of Southampton, Doctoral Thesis.

Abstract

The distributions of the F, or Chow, and X2 test statistics for parameter stability are examined when the estimation is subject to aggregation bias. In standard regression with non-stochastic regressors and Ordinary least squares estimation, the F or Chow test is found to have a doubly non-central F distribution under the alternative hypothesis of presence of aggregation bias. Tables of the cumulative doubly non-central F are given for some selected values. The results seem to indicate that the F test retains some sensitivity in the presence of aggregation bias though careful interpretation is required. The exact distribution of the X2 test, where the numerator of the F test is replaced by the sum of squared forecast errors, is obtained by invoking the theory of mixtures. Comparison of the two tests is made by deriving bounds for the X2 test for fixed 6 1 and determinant of Cih + Xf(xexe)-1Xf], where 61 is the numerator non-centrality parameter of the doubly non-central F, Xe and Xf are matrices of observations on regressors in the estimation and forecast periods respectively. The bounds do riot turn out to be too wide but they indicate that the X2 test was not be deemed trustworthy. An example in a dynamic model context also seems to suggest that the X2 test cannot be relied upon bacause it gives a far bigger than nominal size of the test. The problems of extending the analysis to dynamic and simultaneous models are also discussed.

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