Contents
How is the seasonal difference of a time series calculated?
Seasonal differencing. The seasonal difference of a time series is the series of changes from one season to the next. For monthly data, in which there are 12 periods in a season, the seasonal difference of Y at period t is Y(t)-Y(t-12).
Why does seasonal differencing remove gross features of seasonality?
Seasonal differencing therefore usually removes the gross features of seasonality from a series, as well as most of the trend. Here is a plot of the seasonal difference of AUTOSALE/CPI, the deflated auto sales series.
How is seasonal difference of Y expressed in Statgraphics?
In Statgraphics, the seasonal difference of Y with a seasonal period of 12 is expressed as SDIFF (Y,12), although you should not often need to use this expression: seasonal differencing, like nonseasonal differencing, can be performed as an analysis option within the time series procedures.
How to remove trend and seasonal effects from CO 2 2?
Let’s use diff () to remove the trend and seasonal signal from the CO 2 2 time series, beginning with the trend. Close inspection of Figure 4.1 would suggest that there is a nonlinear increase in CO 2 2 concentration over time, so we’ll set differences = 2 ):
Which is the first difference of seasonal difference?
First difference of seasonal difference. The seasonal difference of a time series is the series of changes from one season to the next. For monthly data, in which there are 12 periods in a season, the seasonal difference of Y at period t is Y(t)-Y(t-12).
Which is the first difference of a monthly time series Y?
The first difference of the seasonal difference of a monthly time series Y at period t is equal to (Y (t) – Y (t-12)) – (Y (t-1) – Y (t-13)). Equivalently, it is equal to (Y (t) – Y (t-1)) – (Y (t-12) – Y (t-13)).
When to use seasonal difference in forecasting model?
If the seasonal difference (i.e., the season-to-season change) of a time series looks like stationary noise, this suggests that the mean (constant) forecasting model should be applied to the seasonal difference. For monthly data, whose seasonal period is 12, the seasonal difference at period t is Y (t)-Y (t-12).