1/The first data set contains 52 observations about the weekly closing price of AT&T common shares for year 1979. The data can be found on Blackboard with "AT&T" as a title. Use the observation 1 to 47 for model building and assessing model goodness of fit for estimation purposes. Use the observation 48 to 52 for assessing model goodness of fit for forecasting purposes.
a. Plot the original data and fit a White Noise model to the original data and based on the results of Residuals ACF and Residuals PACF, select an initial model. Estimate the model parameters. Check the stationarity and invertibility conditions. Are the parameter estimates significant? Are the model assumptions satisfied? In efforts to approach White Noise series, improve your initial model by fitting another model based on the initial model results of Residuals ACF and Residuals PACF. Estimate the model parameters. Check the stationarity and invertibility conditions. Are the parameter estimates significant? Are the model assumptions satisfied?
b. Select an alternative model (one that is different from your initial model) fit a White Noise model to the original data and based on the results of Residuals ACF and Residuals PACF. Estimate the model parameters. Check the stationarity and invertibility conditions. Are the parameter estimates significant? Are the model assumptions satisfied? In efforts to approach White Noise series, improve your alternative model by fitting another model based on the alternative model results of Residuals ACF and Residuals PACF. Estimate the model parameters. Check the stationarity and invertibility conditions. Are the parameter estimates significant? Are the model assumptions satisfied?
c. Based on the results obtained from parts a and b, fill in the tables below to evaluate the potential models. Which model do you prefer for estimation purposes? Which model do you prefer for forecasting purposes?
|
Checking Model Assumptions (Residuals)
|
|
Model/ Measure
|
|
|
|
|
|
Normality
|
|
|
|
|
|
Constant Variance
|
|
|
|
|
|
Independence
|
|
|
|
|
|
White noise
|
|
|
|
|
|
Model Stationarity
|
|
|
|
|
|
Model Invertibility
|
|
|
|
|
|
Goodness of fit for (Estimation)
|
|
Model/ Measure
|
|
|
|
|
|
RMSE
|
|
|
|
|
|
MAE
|
|
|
|
|
|
MAPE
|
|
|
|
|
|
Number of Parameters (Complexity)
|
|
|
|
|
|
Number of Significant Parameters
|
|
|
|
|
|
Goodness of fit for (Forecasting)
|
|
Model/ Measure
|
|
|
|
|
|
RMSE
|
|
|
|
|
|
MAE
|
|
|
|
|
|
MAPE
|
|
|
|
|
d. Use the entire data set and based on your best model for forecasting, forecast the observations: 53, 54, 55, 56, and 57. Provide both a point estimate and a confidence interval for each forecasted observation.
2/The second data set contains monthly Australian sales of fortified wine in thousands of litres from January of 1980 until July of 1995. There are a total of 187 observations. The data can be found on Blackboard with "fortifiedwine" as a title. Use the observation 1 to 180 (i.e., through the December of 1994) for model building and assessing model goodness of fit for estimation purposes. Use the observation 181 to 187 for assessing model goodness of fit for forecasting purposes.
a. Plot the original data and run a several models aiming to reach White Noise series. Examine each model Residuals ACF and Residuals PACF.
b. Select one of the best models you have from part (a) as initial model. For further diagnosis, estimate the model parameters. Check the stationarity and invertibility conditions. Are the parameter estimates significant? Are the model assumptions satisfied? Then selectanother good model you have from part (a) as alternative model. For further diagnosis, estimate the model parameters. Check the stationarity and invertibility conditions. Are the parameter estimates significant? Are the model assumptions satisfied?
c. Based on the results obtained from parts (a and b), fill in the tables below to evaluate the potential models. Which model do you prefer for estimation purposes? Which model do you prefer for forecasting purposes?
|
Checking Model Assumptions (Residuals)
|
|
Model/ Measure
|
|
|
|
Normality
|
|
|
|
Constant Variance
|
|
|
|
Independence
|
|
|
|
White noise
|
|
|
|
Model Stationarity
|
|
|
|
Model Invertibility
|
|
|
|
Goodness of fit for (Estimation)
|
|
Model/ Measure
|
|
|
|
RMSE
|
|
|
|
MAE
|
|
|
|
MAPE
|
|
|
|
Number of Parameters (Complexity)
|
|
|
|
Number of Significant Parameters
|
|
|
|
Goodness of fit for (Forecasting)
|
|
Model/ Measure
|
|
|
|
RMSE
|
|
|
|
MAE
|
|
|
|
MAPE
|
|
|
d. Use the entire data set and based on your best model for forecasting, forecast the observations: 188, 189, 190, 191, 192. Provide both a point estimate and a confidence interval for each forecasted observation.
Attachment:- Arima model.rar