Assignment #5
Instructions. Please type your answer key before turning it in. Don't forget to include your name and to include every graph/output that is requested in this activity.
Go to https://fred.stlouisfed.org/ and search for Real Personal Consumption Expenditures (series pcecca). This series is available since 1929. Download the data in annual frequency as an EXCEL file. Import your files into Eviews. File should show the data to be available from 1929 to 2019.
a. Let it be the variable pieces in period t. Create the variable gc (annual consumption growth rate) with the formula gc = 100 yt—yt—1 . When creating the variable, make sure that you have not made a mistake inyt—1the formula. Show the time series for gc for the period 1929 - 2019 (paste the graph in your homework).
b. For the period 1980 - 2017 (NOTICE THE PERIOD) create the correlogram for the variable gc, use up to 12 lags.
c. The requested correlogram of the consumption growth (variable gc) could be consistent with processes in the AR family, as well as in the MA family (or ARMA processes). For the period 1980-2017, estimate an AR(1) process of the form yt = a + $yt—1 + ot. Use Maximum Likelihood estimation (under menu
Estimation, after inputting your equation gc c ar(1), select Options, then under Method select ML).1
Show your output.
d. For the same period as above, now estimate an MA(2) process of the form yt = µ+ot +81ot—1 +82ot—2. Use Maximum Likelihood estimation. The particular specification for your model is gc c ma(1) ma(2). Show your output.
e. Are your AR(1) and MA(2) models covariance-stationary and invertible? Explain each case separately and back up your answer. For each, explain why the answer is yes or no and why.
f. Are your residuals white noise? From your estimation exercises, paste your residuals of both of your estimation exercises here and explain why they appear to be white noise or not.
g. Report both the AIC and SIC of your models. Based on each of these criterions (AIC and SIC), which model should be preferred ?
h. From parts (e), (f) and g), there should be a model that should be statistically preferred to the other one. Under the assumption of quadratic loss (means you can use the conditional mean as the optimal forecast) use the best model to forecast gc for the years 2018 and 2019. Select a dynamic forecast (as done in the videos). Compare your forecast to the actual growth rates in consumption that were observed in 2018 and 2019. Paste your forecast diagram here and then type the forecasted values.
i. Refer to your forecast for 2018 (imagine you are in 2017 providing the forecast for year 2018). Let Y be the random variable consumption growth in year 2018 (gc2018). Given the conditional mean and standard deviation of your forecast, find the level of the growth rate y0 such that the following holds P [Y ≤ y0] = 10%and then explain the meaning of such a probabilistic statement. Assume that the innovation ot is distributed normally
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