Download and examine the data set linked below that contains the maximum daily temperatures (averaged monthly; abbreviated aMDT) in the city of Dallas, TX from January 2000 to December 2020. MeanDallasTemps.csv 4 For questions requiring 95% confidence bands, use 1.96 standard deviations on each side of the mean to determine the 95% span. a. Consider the task of modeling this data using a SARIMA model. Based on your knowledge of monthly variation in temperature, what value would be most appropriate for the seasonal lag term, 7 b. Using the seasonal lag selection in the previous subguestion, fit the SARIMA(p.d.q) = (P D), model to the full aMDT time series for all combinations of pyd,q, P, D, and Q in {0, 1} except the four cases where P =1, D = 0, = 1, and d = 0(Hint: this means you should be checking 60 different combinations). In answering this question, you should fit the various models to the full data set (do not split it into a training/test split) and assume that 4 = 0 (where is the constant term). Identify which of these models best fits the data and report the AlCc value for this model and the estimated values of the unknown parameters. (Mote: the following part c., d. and e. are asking very similar questions, with the main difference being the model to iit. Consider working on them altogether.) c. Consider the task of forecasting the aMDT twelve months in advance. For the last five vears of data (2016-2020), predict the value of aMDT using all of the data up until one year prior to the prediction (i.e. predict the aMDT for January 2016 using all of the data up to and including January 2015, then add in the observed aMDT for February 2015 and predict aMDT for February 2016, etc.). Use the values of p, d, , P, D, and Q) as determined to be best in part b, but update your coefficients at every time step using the new data. Create a plot of the one-year-in-advance predictions and 95% confidence bands superimposed on a time series plot of the observed aMDT values from January 2010 to December 2020. Report the one-year-in-advance prediction of aMDT for January 2018, along with the upper and lower bounds of the prediction interval. (Hint: Making one-year-in-advance predictions with newly added data at each time step may reguire a for loop) d. Now consider an alternative model for the the aMDT data that does not have a seasonal component. Report the AlCe value for an ARIMA(3.1.1) model fit to the full aMDT data set. Refit the model to make one-year-in-advance predictions of aMDT for the last five years of the observation window (2016-2020) as you did in the previous subguestion. Plot vour predictions and 95% confidence bounds, along with the true observed values shown. Set your x-axis to span January 2010 to December 2020. Additionally, report your one-year-in-advance prediction for the aMDT for January 2018, along with your upper and lower bounds of your prediction interval. Does the fitted model produce predictions that capture seasonal behavior? How do the predictions from the ARIMA(3,1,1) model that does not include a specific seasonal component compare to the predictions from the model fitted in part .? e. Now we work on the ARIMA model with a different set of parameters. Report the AICc value for an ARIMA(12.1,0) model fit to the full aMDT data set. Refit the model to make one-year-in-advance predictions of aMDT for the last five years of the observation window (2016-2020) as you did in the previous subquestion. Plot your predictions and 95% confidence bounds, along with the true observed values shown in. Set your x-axis to span January 2010 to December 2020. Additionally, report your one-year-in-advance prediction for the aMDT for January 2018, along with your upper and lower bounds of your prediction interval. Does the fitted model produce predictions that capture seasonal behavior? How do the predictions from the ARIMA(12,1,0) model compare to the predictions from the models fitted in parts c. and d