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2) Forecasting ARMA models (40 points) In an attachment to this assignment, you find the file dat aset2 xlsx

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2) Forecasting ARMA models (40 points) In an attachment to this assignment, you find the file dat aset2 xlsx. It contains quarterly data from 1953-Q4 to 2019-Q4 on: 
• the variable "cyclical consumption" (cc) calculated according to Priestley] (12020; 
]Atanasov, Moller, and] 
• the market excess return (ret) calculated as the difference between the return on the S&P500 index (our proxy for the market return) and the return on U.S. Treasury bills (our proxy for the risk-free rate). Import the two time series into R without modifying the Excel file. Restrict the sample in such a way that you have observations for the market excess return and the cyclical consumption variable. For exercise parts (a) to (d), use data from the beginning of the sample to 2005-Q4. (a) Find the best ARMA (p, q) representation for market excess returns according to the Akaike information criterion. Consider all possible combinations with p = {Om and q = {0,1}. Explain how you find the best model. (10 points) (b) Link your results from exercise part (a) to the efficient market hypothesis. (5 points) (c) For the best model you identified in exercise part (a), plot the autocorrelation function of the estimated residuals for up to 20 lags. Explain the pattern you observe. What do you conclude from this plot? (5 points) (d) Next, estimate the following regression model: ret,+1 = )31 + 32 cc, + th+1• (4) Use standard errors that are robust to heteroscedasticity. Comment on the statistical significance of 02. What does this imply? (5 points) (e) Next, compare the best ARMA (p, q) model from exercise part (a) with the model given in Equation (1§ by performing an out-of-sample forecasting exercise. The data from the beginning of the sample to 2005-Q4 is the (in-sample) estimation period, while you use the data from 2006-Q1 to 2019-Q4 as your (out-of-sample) forecast evaluation period. When conducting this forecasting exercise use a recursive expanding estimation window for both models. Compute the Root Mean Square (Forecast) Error (RMSE) for both models. (/ 0 points) (f) Calculate the ratio of RMSE between the two models as a measure of comparison in forecast accuracy and comment on the results. (5 points) 
References 
Atanasov, V., S. V. Moller, and R. Priestley. 2020. Consumption fluctuations and expected returns. The Journal of Finance 75:1677-1713. doi:10.1111/jofi.12870