Alternative Approaches to Length of Month Adjustment
William R. Bell
KEY WORDS: calendar effects, REGARIMA model, time series
We consider two approaches to adjustment for length of month variation in nonnegative flow time series observed monthly. One approach is to divide the observed series value in each month by the length of that month and then multiply all series values by the average length of month (30.4375). The other approach is to include length of month as an explanatory variable in a regression model with ARIMA time series errors (REGARIMA model), and then estimate and remove the length of month effect. For additive models we observe that the two approaches will be different, and that arguments can be made for either approach so that the choice between them may be a matter of personal preference. For multiplicative models (additive models for the logged series), we observe that the two approaches are approximately equivalent if and only if the estimated length of month coefficient is approximately .035. Since this is also the value that would be expected for the length of month coefficient in a model for the logged series, we argue that in multiplicative models one should adjust for the length of month by division and then rescaling, rather than by using an estimated term from a REGARIMA model.
Source: U.S. Census Bureau, Statistical Research Division
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