QUESTION 4 (10 MARKS) Use the following information to answer parts a and b below. Given below are Excel outputs for various estimated autoregressive models for the motor vehicle taxes collected by the federal government (in millions of dollars) from quarter 2 2012 through quarter 4 2018. You are also given that the tax collected for the state for quarter 2, quarter 3 and quarter 4 for 2018 are 2011, 2216 and 2259 millions of dollars respectively. First-Order Autoregressive (AR1) Model: Coefficients Standard Error Stat P-value Intercept 196.368 202.637 0.969 0.344 LAG 1 TAXES 0.910 0.110 8.262 0.000 P-value Second-Order Autoregressive (AR2) Model: Coefficients Standard Errort Stat Intercept 201.137 221.447 0.908 LAG 1 TAXES 0.921 0.220 4.198 0.375 0.000 LAG 2 TAXES -0.014 0.234 -0.062 0.951 Third-Order Autoregressive (AR3) Model: Coefficients Standard Error t Stat P-value Intercept 19.3862 134.8610 0.1437 0.8872 LAG 1 TAXES 0.8927 0.1305 6.8410 0.0000 -0.7499 0.1834 -4.0858 0.0006 LAG 2 TAXES LAG 3 TAXES 0.8745 0.1425 6.1366 0.0000 t Stat P-value Fourth-Order Autoregressive (AR4) Model: Coefficients Standard Error Intercept -45.7446 109.3043 LAG 1 TAXES 0.3585 0.1871 -0.4185 0.6805 1.9165 0.0713 LAG 2 TAXES -0.2276 0.2109 -1.0794 0.2947 LAG 3 TAXES 0.2353 0.2180 1.0793 0.2947 LAG 4 TAXES 0.7071 0.2057 3.4379 0.0029 a. Using a 5% level of significance, what is the appropriate autoregressive model for motor vehicle taxes collected by the federal government? Fully explain your answer. (5 marks) b. If one decides to use the Third-Order Autoregressive model, what will the predicted motor vehicle taxes collected by the federal government for quarter 1 2019? Show all workings