A data set of $324$ measurements of an industrial robot's positions are in the robot object in the TSA package. Type library $($TSA$)$; data $($robot$)$; print $($robot$)$ in R to see the data set.

$($a$)$ Plot the time series. What basic pattern do you see from the plot? Might a stationary model be appropriate for this plot?

$($b$)$ Using tools such as the ACF, PACF, and$/$or EACF, tentatively specify the type of model $($AR$,$ MA$,$ or ARMA$)$ as well as the order$($s$)$ of the model.

$($c$)$ Use the best subsets ARMA approach to specify a model. Consider up to $8$AR terms and up to $8$MA terms. Does the "best" subset ARMA model agree with the model you specified in part$($b$)?$

$($d$)$ Repeat parts $($a$)-($c$)$ on the first difference of the robot time series. Does this analysis suggest a particular model for the original robot data? Briefly explain.