Plot the time series data. Forecast for the 21st period using simple exponential smoothing with alpha 0.2 and 0.9 and plot the actual 20 period values with forecasted values. Compare the two forecasts using MSE and RMSE. Also calculate the errors and plot the errors for the two forecasts. Comment on the plots (about stationarity). Do you see systematic underestimation? Now perform the forecast using Holt’s two parameter model with alpha = 0.2 and beta = 0.5. Plot the Holt’s forecast with actual values. Also calculate the MSE for Holt’s forecast. Is it better than the simple exponential smoothing forecasts?  Plot the errors for Holt’s model. Does it look nearly stationary.

Part (B)- 60 points
For the data below (Production = Y in million tons) plot the data and comment whether you see a seasonal pattern. Perform Holt-Winters’ seasonal forecast using alpha = 0.6, beta = 0.3 and gamma  = 0.9.  Make forecasts for 2007-q1 and 2007-q2 using Holt-Winters’ model. Calculate the errors and MSE and RMSE. Plot the errors and comment on the plot.