On Concurrent Seasonal Adjustment

原文摘要

Concurrent seasonal adjustment uses all information up to and including the current month's figure and thus should provide more accurate estimates of final seasonally adjusted data than the prevalent official method where the current month's component is forecasted from data through the preceding December. This article evaluates the expected gain from employing concurrent seasonal adjustment, including the case in which the data contain both nonseasonal and seasonal revisions. The theoretical results are then applied to a linearized X-11-ARIMA procedure, using a group of common seasonal autoregressive integrated moving average (ARIMA) models, and to an analysis of actual series containing preliminary-data error. Concurrent adjustment is consistently found to afford greater accuracy, though to a smaller degree when not seasonally adjusted (NSA) data are also preliminary. The problem of how best to seasonally adjust current data arises because both the usual (X-11) and the optimal (in a signal extraction framework) adjustment procedures involve the as-yet unobserved future as well as the available past of the series. But the intuitively plausible idea of using all available information, which is possible only with concurrent adjustment, is counterbalanced by several factors, including (a) the difficulty of computing, and the awkwardness of publishing, an entire revised series every month, and (b) the necessity for avoiding the semblance of “fudging” the data. Thus there is a need to measure the degree of gain from concurrent adjustment, to weigh against these drawbacks. Measures of the gain from concurrent adjustment depend on both the series' behavior (model) and the seasonal adjustment procedure employed. As an example of each, the article examines series whose behavior is well characterized by the “airline model” of Box and Jenkins (1970) and that are seasonally adjusted by a linearized X-11-ARIMA procedure. The ratio of the root mean squared (RMS) revisions under concurrent and year-ahead adjustment, for such series, is graphed in Figure 4 of the article. RMS ratios below unity indicate the superiority of the concurrent estimate; the smaller these ratios, the greater the gain from concurrent adjustment. Thus, as Figure 4 shows, there is a greater gain from concurrent adjustment in later months, where more information is lost in the year-ahead method, and a greater gain for series' changes or growth rates than for levels. The effect of error in preliminary NSA data is to enlarge both the numerator and the denominator of the RMS ratios (both concurrent and year-ahead adjustments are more error-prone), with a tendency toward lowering, but not eliminating, the gain from concurrent adjustment. The extent of this effect depends on the size of the NSA data's revision variance relative to the final NSA series' innovation variance, as can be seen from Figure 6 of the article. As all models are but approximations to the truth, and as “linearized X-11-ARIMA” is an approximation to actual seasonal adjustment procedures employed, an example is included of an industrial production series published by the Federal Reserve Board. As expected, and as shown in Table 4, concurrent seasonal adjustment of the series is more accurate than year-ahead adjustment, but to a smaller degree because of the preliminary-data error in the NSA series.

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