1. (20\%) (a) (4 points) The figure below shows the monthly log sales (LogSales). What time series patterns (two components) do you identify from the graph? (b) (2 points) Given the components that you identified above, which exponential smoothing model should you use for forecasting? (c) (6 points) A researcher uses the following regression model to forecast LogSales . t. Specify how you would modify the model so as to take into account the time series components that you identify in part (a). Make sure that you state clearly the definitions of your variables. LogSalet=?0+?1?DP??t+?t where GDPGr refers to the GDP growth. (d) (4 points) For the model that you specified in (b), state under what situation will you have the perfect multicollinerity problem. Explain clearly how the multicollinearity problem arises. (e) (4 points) If you would like to build an ARIMA(p,d,q) model for LogSales, what adjustments should you make to the data to handle the components that you identify above before estimating the ARIMA model? 1. (20\%) (a) (4 points) The figure below shows the monthly log sales (LogSales). What time series patterns (two components) do you identify from the graph? (b) (2 points) Given the components that you identified above, which exponential smoothing model should you use for forecasting? (c) (6 points) A researcher uses the following regression model to forecast LogSales . t. Specify how you would modify the model so as to take into account the time series components that you identify in part (a). Make sure that you state clearly the definitions of your variables. LogSalet=?0+?1?DP??t+?t where GDPGr refers to the GDP growth. (d) (4 points) For the model that you specified in (b), state under what situation will you have the perfect multicollinerity problem. Explain clearly how the multicollinearity problem arises. (e) (4 points) If you would like to build an ARIMA(p,d,q) model for LogSales, what adjustments should you make to the data to handle the components that you identify above before estimating the ARIMA model