Question: Find yearly data on a business or economic time series of interest to you for at least 20 continuous years. (This project requires access to computer software that can estimate ARIMA models.)
a. Graph this time series and comment on the structure you see.
b. Does the series appear to be stationary or no stationary? If it is extremely no stationary (ending up far away from where it started, for example), graph the differences to see if they appear to be stationary.
c. Fit a first-order autoregressive process to your series (or to the differences, if the series was no stationary). Based on the t statistic, is the autoregressive coefficient significant?
d. Fit a first-order moving-average process to your series (or to the differences, if the series was no stationary). Based on the t statistic, is the moving average coefficient significant?
e. Fit a first-order ARMA process to your series (or to the differences, if the series was no stationary). Based on the t statistics, which coefficients are significant?
f. Based on the results for these three models, which one do you select? You may want to exclude components that are not significant.
g. Now work with the original series (even if you have been using differences). Estimate your chosen model, including an integrated (I) component if you have been differencing, and find forecasts and forecast limits.
h. Graph the forecasts and forecast limits along with the original data and comment.
i. Comment on the model selection procedure. (Keep in mind that the selection procedure is much more complicated when higher-order processes are used.)