In this chapter, we consider three case studies of linear time series analysis. Our goals are (i) to demonstrate applications of the methods discussed in Chapter 2; (b) to show the usefulness and limitations of linear time series models; and (c) to gain further experience in analyzing time series data with R. The three cases considered are (i) the monthly global temperature anomalies from January 1880 to August 2010, (ii) the monthly US unemployment rate with or without the weekly initial jobless claims, and (iii) the weekly US regular gasoline price from January 6, 1997, to September 27, 2010, and the crude oil price from January 3, 1997, to September 24, 2010. We chose these three cases because they are timely, have important implications to the US economy, and are informative in achieving the goals of the chapter.

A main difficulty for the beginners of time series analysis is finding an adequate model for a given series. This is particularly so when the dynamic dependence of the data is complex or when many models seem to fit the data well. In this chapter, we tackle this difficulty by working through real examples. Our goal is that the three case studies are helpful to the reader.

Let us start by accepting Professor George Box’s dictum concerning statistical models: All models are wrong, but some are useful (Box, 1976). Our goal then is to find an appropriate model that is ...

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