Revisions of Trend-Cycle Estimators of Moving Average Seasonal Adjustment Methods

Abstract

One of the main purposes of the seasonal adjustment of economic time series is to provide information on current economic conditions, particularly to determine the state of the cycle at which the economy stands. Since seasonal adjustment means removing seasonal variations, thus leaving a seasonally adjusted series consisting of trend cycle together with the irregular fluctuations, it is often very difficult to detect cyclical turning points for series strongly contaminated with irregulars. In such cases, it may be preferable to smooth the seasonally adjusted series using trend-cycle filters, which suppress as much as possible the irregulars without affecting the cyclical component. It is inherent, however, in any moving average procedure that the first and last n points of an original series cannot be smoothed with the same symmetric filters applied to middle values. The current and most recent years of data are smoothed by asymmetric filters, which change for each point in time. Hence, as new information becomes available, revisions are made because of (a) the new innovations entering the series and (b) the changes in the weight system or frequency response function of the filters. The purpose of this study is to calculate the size of the revisions of the asymmetric trend-cycle filters of X-11 and X-11-ARIMA and to analyze the pattern of these revisions.

KEY WORDS:

• Smoothed seasonal adjustment
• Revisions
• X-11
• X-11-ARIMA