Using these data, conduct the following analyses:(a) Plot and inspect the data. Summarize the dynamics with relevant ACF and PACF plots thataccount for the large drop in public drunkness arrests that occurs after June 1971. Discuss yourinitial models based on these diagnostics.(b) Fit an appropriate ARIMA model to the data from January 1966 to June 1971. Make sure youcheck the diagnostics to make sure there is no residual seasonal serial correlation.(c) Now include a permanent intervention variable that allows the constant in your model to changestarting in June 1971. Add this variable as a regressor in your ARIMA model and fit it to the fullsample. What do you conclude from this model. Hint: you can make the intervention variable using this intervene(d) Check and report the residual diagnostics for this model. What modifications need to be madeto the ARIMA specification after including the intervention?(e) Why is this procedure optimal? That is, why not just fit an ARIMA model to the full samplerather than use the part of the sample prior to the intervention like you did above?

Use the method of your choice to evaluate the following integral by hand. Show all work and state the method you are using