TRADING-DAY VARIATIONS MULTIPLE-REGRESSION MODELS WITH RANDOM PARAMETERS

A large class of flows and stocks series related to production, shipments, sales and inventories are affected by trading-day or calendar variations. Trading-day variations represent the 'within-month variations' due to the number of times a particular day or days of the week occur in a calendar month. These variations are systematic and may strongly influence month-to-month comparisons. A simple trading-day regression model, developed by Young (1965), is currently used by the X-11-ARIMA (Dagum, 1980) and the Census Method II-X-11 variant (Shiskin, Young & Musgrave, 1967) to estimate trading-day variations. This simple model assumes that the trading-day coefficients are fixed and estimated by ordinary least squares. As long as the relative weight of daily activities is constant throughout the length of the chosen span of the series, this deterministic model produces reasonable estimates. However, that is not always a realistic assumption. The purpose of this paper is to introduce a multiple regression model that allows for stochastic changes of the trading-day coefficients used to calculate trading-day variations. Estimation and statistical inference for the trading-day regression are thoroughly discussed. Examples of the stochastic and deterministic models are given for real data.