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Analysis of variance estimators for the seasonal adjustment of economic time series Diewart, Walter Erwin

Abstract

The purpose of this thesis is to develop a valid statistical procedure for the estimation of the seasonal component of an economic time series when the seasonal component is suspected to be partly additive and partly multiplicative to the trend. The proposed procedure is based on a three-way classification analysis of variance model, where the first classification is used to represent the long term trend of the series, the second classification is used to represent any regular trend or cycle within the long term trend, and the third classification is used to represent the seasonal. The interaction term between the long term trend and the seasonal may be used to represent any long term change in the nature of the seasonal. However, as the standard analysis of variance significance tests assume independently distributed residuals, it is necessary to develop a test for independence of residuals against the very likely alternative of first order (positive) serial correlation. This is done by calculating the mean and variance of the Durbin-Watson d statistic for the three-way classification analysis of variance model. A numerical example is given to illustrate the procedure.

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