Calendar Effects in Monthly Time Series: Modeling and Adjustment

Abstract Most monthly time series that represent a total of some variable for each month contain calendar effects due to changing month length, day-of-the-week effects, and holidays. It is important to remove the calendar variation to allow an effective assessment of the variation due to important factors. New procedures for calendar adjustment are presented in this article. A plausible model for the daily data is used to derive a model for the monthly data in which the power transformed, month-length corrected data are equal to trend plus seasonal plus calendar plus irregular. The procedure for fitting the calendar component in the monthly model is (a) divide the aggregated monthly data by month length and multiply by 30.4375, the average month length; (b) choose a power transformation; (c) remove trend and seasonal components; (d) estimate the calendar parameters by robust regression. Since the model is only a hypothesis it is important to check its validity. This can be done by various residual plots in the regression analysis and by using spectrum analysis and time-domain graphical methods to detect residual calendar effects in the adjusted series. This approach is compared to the X-11 calendar estimation procedures. Key Words: Trading day adjustmentSeasonal adjustmentSpectrum analysisGraphics