We use a computer program called X-12-ARIMA to derive our seasonal adjustment and produce seasonal factors.
It is difficult to estimate seasonal effects when the underlying level of the series changes over time. For this reason, the program starts by detrending the series with a crude estimate of the trend-cycle. It then derives crude seasonal factors from the detrended series. It uses these to obtain a better trend-cycle and detrended series from which a more refined seasonal component is obtained. This iterative procedure, involving successive improvements, is used because seasonal effects make it difficult to determine the underlying level of the series required for the first step. Crude and more refined irregular components are used to identify and compensate for data that are so extreme that they can distort the estimates of trend-cycle and seasonal factors.
The seasonal factors are divided into the original series to get the seasonally adjusted series. For example, suppose for a particular January, a series has a value of 100,000 and a seasonal factor of 0.80. The seasonally adjusted value for this January is 100,000/0.80=125,000.
If trading day or moving holiday effects are detected, their estimated factors are divided out of the series before seasonal factor estimation begins. The resulting seasonally adjusted series is therefore the result of dividing by the product of the trading day, holiday, and seasonal factors. The product factors are usually called the combined factors, although some tables refer to them as the seasonal factors for simplicity.
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