Weekly Seasonal Adjustment ‐ A Locally‐weighted Regression Approach

William P. Cleveland, Thomas D. Evans, and Stuart Scott


Weekly series have characteristics which make seasonal adjustment inaccessible or unsatisfactory with most available software. These series are typically compiled for weeks ending on a given day of the week, Saturday in the application presented here. The number of Saturday’s within a year can be either 52 or 53 and their position varies from year to year. These features violate the basic periodic time series structure assumed by X-12-ARIMA (soon to be X-13ARIMA-SEATS), TRAMO/SEATS, and STAMP. A locally-weighted least squares procedure is suggested here, which can be used with a weekly design matrix having 52 or 53 observations in a year. The procedure starts from the regression method in Pierce, Grupe, and Cleveland (1984), which assumes a deterministic seasonal component. The method is currently being applied at the Bureau of Labor Statistics, the Federal Reserve, and the Bank of Canada.