Minimum Variance, Linear, Unbiased Seasonal Adjustment of Economic Time Series

Abstract A statistical theory based on the general linear statistical model is developed for seasonal adjustment of economic (and other) time series. A method for seasonal adjustment may be represented as taking place in two steps. The first step is to estimate the unknown parameters of the seasonal component of the series; the second step is to remove the estimated seasonal component from the set of observations. For the unique minimum variance, linear, unbiased method for seasonal adjustment, estimation is carried out through the unique, minimum variance, linear unbiased estimator. Sampling theory for statistical inference about a method for seasonal adjustment may be derived from normal sampling theory for the general linear statistical model. The properties of minimum variance, linearity, and unbiasedness provide a complete basis for the selection of a method for seasonal adjustment.

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