3. (Moving Average Forecast) In the file "PS3Sale.txt", there is a time series of sales data from 83.IV to 93.III. Let's hold-out the last four observations, that is not using them in estimation. (a) In the exponential moving average, determine the optimal (one decimal points) (use the first 36 observation to estimate). Forecast the last four periods and compare them to the actual last four observations to compute your average forecasting error (the square root of the average squared prediction error). (b) Set to what you find in (a), we now introduce a time trend, t. What is the optimal 1 ? (one decimal point) What is your average forecasting error for the last four observations (the square root of the average squared prediction error)? (c) Set and 1 to what you find in (a) and (b), we include an additional seasonality Ft. What is the optimal 2 ? (one decimal point) What is your average forecasting error for the last four observations (the square root of the average squared prediction error)? (d) Comparing your forecasting errors in the previous cases, what can you say? 3. (Moving Average Forecast) In the file "PS3Sale.txt", there is a time series of sales data from 83.IV to 93.III. Let's hold-out the last four observations, that is not using them in estimation. (a) In the exponential moving average, determine the optimal (one decimal points) (use the first 36 observation to estimate). Forecast the last four periods and compare them to the actual last four observations to compute your average forecasting error (the square root of the average squared prediction error). (b) Set to what you find in (a), we now introduce a time trend, t. What is the optimal 1 ? (one decimal point) What is your average forecasting error for the last four observations (the square root of the average squared prediction error)? (c) Set and 1 to what you find in (a) and (b), we include an additional seasonality Ft. What is the optimal 2 ? (one decimal point) What is your average forecasting error for the last four observations (the square root of the average squared prediction error)? (d) Comparing your forecasting errors in the previous cases, what can you say