时间序列第6讲.ppt

Applied Time Series Analysis Instructor: 郭惠英 Email: Guo_hy606@126.com Phone: 7666606 X11:Seasonal Adjustment Methods Filter based methods of seasonal adjustment are often known as X11 style methods. These are based on the ‘ratio to moving average’ procedure described in 1931 by Fredrick R. Macaulay, of the National Bureau of Economic Research in the US. The procedure consists of the following steps: X11 1)???? Estimate the trend by a moving average 2)???? Remove the trend leaving the seasonal and irregular components 3)???? Estimate the seasonal component using moving averages to smooth out the irregulars. Step 1: Initial estimate of the trend A symmetric 13 term (2x12) moving average is applied to an original monthly time series, Ot, to produce an initial estimate of the trend Tt. The trend is then removed from the original series, to give an estimate of the seasonal and irregular components. Step 1: Initial estimate of the trend Six values at each end of the series are lost as a result of the end point problem - only symmetric filters are used. Step 2: Preliminary estimate of the seasonal component A preliminary estimate of the seasonal component can then be found by applying a weighted 5 term moving average (S3x3) to the St.It series for each month separately. Step 2: Preliminary estimate of the seasonal component Although this filter is the default within X11, the ABS uses 7 term moving averages (S3x5) instead. The seasonal components are adjusted to add to 12 approximately over a 12 month period, so that they average to 1 in order to ensure Step 2: Preliminary estimate of the seasonal component that the seasonal component does not change the level of the series (does not affect the trend). The missing values at the ends of the seasonal component are replaced by repeating the value from the previous year. Step 3:Preliminary estimate of the adjusted data An approximation of the seasonally adjusted series is found by dividing the estimate of the se