Problem I. Daily Minimum Temperature Continued We will again use the daily minimum temperatures.csv file from Canvas to complete this problem. The Daily Minimum Temperatures dataset describes the minimum daily temperatures over 10 years (1981-1990) in the city Melbourne, Australia. The units are in degrees Celsius and there are 3650 observations. The data were recorded by the Australian Bureau of Meteorology. Note on leap years, the day December 31st has been removed so that they still have 365 days. a. Recall in HW7 you fit an AR(1) model to this time series data. Did an AR(1) seem like a truly suitable model for the data? b. Choose a suitable order and lag of differencing for this time series. Make a time series plot of the differenced time series. Is the differenced time series stationary? Explain both your choice of order and lag, as well as your answer for whether it is stationary. c. Look at the acf and pacf of the differenced time series from part b. Does it seem like any particular AR or MA model will be suitable? Pick the model you think is most likely to be suitable and explain your answer. [Note don't use both AR and MA terms, just do one or the other.] d. Fit the model you selected in part c, and run diagnostics. Write down the fitted model. e. Now instead fit the model ARMA(2,2). Write down the fitted model. f. Forecast out the temperature for January 1st 1991 using the model selected in part c and the model from part e. Comment on if the two predictions are similar.