A bivariate time series consisting of sales data and a leading indicator is listed as Series M in Part Five of this book. The series is also available as ‘‘BJsales’’ in the datasets package of R.

(a) Plot the two time series using R.

(b) Calculate and plot the autocorrelation and partial autocorrelation functions of the two series. Find a suitable model for the leading indicator series.

(c) Calculate and plot the cross-correlation function between the two variables.

(d) Calculate and plot the cross-correlation function after prewhitening the series using the time series model developed in part (b).

(e) Estimate the impulse response function ???????? for the two series.