By Franses P.H., Dijk D.v., Opschoor A.
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Extra info for Time Series Models for Business and Economic Forecasting
The content of the present chapter merely reflects what should be a useful basis for modeling real-world time series, such as those discussed in the previous chapter. It is our experience that with the tools outlined in this chapter, it is possible to construct a time series model that is useful for forecasting and to understand how such models can be modified so that features such as seasonality and non-linearity, for example, can be incorporated. Preliminaries As before, the univariate time series of interest is denoted by yt , where yt can be log(wt ), with wt being the originally observed time series.
The fact that the lines for the different quarters are not clearly separated suggests that there is not much seasonal variation in this time series. On the other hand, closer inspection of the graph shows that before 1980, the time series for the second and fourth quarters were considerably above that for the third quarter, suggesting that indeed the seasonal pattern may have been more pronounced during the first half of the sample period, and has changed around 1980. 2), like yt − yt−1 = μ1 D1,t + μ2 D2,t + · · · + μ S D S,t + u t t = 2, 3, .
A second feature of many economic time series is that seasonality changes over time. 12, and sometimes such changes occur only slowly, as is the case for UK consumption. In Chapter 5, we will review methods to describe and forecast economic time series with changing seasonality. 12 indicates that time series features may change over time. For this series, the mean of the observations in the first part of the sample is smaller than that in the second part of the sample, and in the third part there even emerges a seasonal pattern that was previously absent.