ARIMA Models
INSTRUCTIONS: Use MINITAB 17 to complete the following questions. You are to work independently on this assignment. All data sets for this assignment have been provided. Please submit your completed assignment that includes relevant MINITAB output and comments (make sure to comment on your results when asked) as ONE WORD document .
1. Use the data set WeeklyRestaurantSales.MTW. These data are weekly sales at a small restaurant.
(a) Prepare a time series plot, ACF and PACF for these data. Is there evidence to suggest that the data should be differenced? Explain.
(b) Prepare the ACF and PACF for the first differenced data. Identify one plausible ARIMA model based on these plots. Justify your selection.
(c) Fit an ARIMA (1, 1, 0) to these data and show the ACF and PACF for the residuals. Is this model adequate based on the sampling statistics? Explain.
(d) Fit an ARIMA (0, 1, 1) to these data and show the ACF and PACF for the residuals. Is this model adequate based on the sampling statistics? Explain.
(e) Fit an ARIMA (1, 1, 1) to these data and show the ACF and PACF for the residuals. Is this model adequate based on the sampling statistics? Explain.
(f) Which of the three models fit above is the best? Justify your choice!
2. Use the data set BASIRONQ.MTWprovided with this assignment. These data show basic quarterly iron production in Australia (thousands tons) from March 1956 to September 1994. (Source: https://data.is/TSDLdemo).
(a) Prepare a time series plot, ACF and PACF for these data. Is there evidence to suggest that the data should be differenced? Explain.
(b) Prepare the ACF and PACF for the first differenced data. Explain why this appears to be more of an AR process than an MA process.
(c) Fit an ARIMA (1, 1, 0) to these data and show the ACF and PACF for the residuals. Is this model adequate based on the sampling statistics? Explain.
(d) Fit an ARIMA (2, 1, 0) to these data and show the ACF and PACF for the residuals. Is this model adequate based on the sampling statistics? Explain.
(e) Fit an ARIMA (3, 1, 0) to these data and show the ACF and PACF for the residuals. Is this model adequate based on the sampling statistics? Explain.
(f) Which of the three models fit above is the best? Justify your choice!
Attachment:- Minitab.rar