Time series plot

Home sales are often considered an important determinant of the future health of the economy. Thus, there is widespread interest in being able to forecast total houses sold (THS). Quarterly data for THS are shown in the following table in thousands of units:

 

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a. Prepare a time-series plot of THS. Describe what you see in this plot in terms of trend and seasonality.

 

b. Calculate and plot the first twelve autocorrelation coefficients for PHS. What does this autocorrelation structure suggest about the trend?

 

c. De-trend the data by calculating first differences: DTHSt  THSt  THSt1 Calculate and plot the first eight autocorrelation coefficients for DTHS. Is there a trend in DTHS?