The variable PCEP is the price index for personal consumption expenditures from the U.S. National Income and Product Accounts (NIPA).
In this hands-on exercise you will construct forecasting models for the rate of inflation, based on PCEP.
For this analysis, use the sample period 1963:Q1â€“2012:Q4 (where data before 1963 may be used, as necessary, as initial values for lags in regressions).
- Use the QLR test with 15% trimming to test the stability of the coefficients in the AR(2) model for â€œthe change in inflationâ€ . Is the AR(2) model stable? Explain.
- Compute the (annualized) inflation rate,
- Plot the value of Infl from 1963:Q1 through 2012:Q4. Based on the plot, do you think that Infl has a stochastic trend? Explain.
Double click in the table below to access to the excel table.
Yes, Itâ€™s going upward before 1980 and going down afterwards. Its randomly determined.
- Compute the first four autocorrelations of
- Plot the value of Infl from 1963:Q1 through 2012:Q4. The plot should look â€œchoppyâ€ or â€œjagged.â€Explain why this behavior is consistent with the first autocorrelation that you computed in part (i) for .
- Compute Run an OLS regression of on . Does knowing the change in inflation this quarter help predict the change in inflation next quarter? Explain.
- Estimate an AR(2) model for ÂInfl. Is the AR(2) model better than an AR(1) model? Explain.
- Estimate an AR(p) model for . What lag length is chosen by BIC? What lag length is chosen by AIC?
- Use the AR(2) model to predict â€œthe change in inflation from 2012:Q4 to 2013:Q1â€-that is, predict the value of Â
- Use the AR(2) model to predict â€œthe level of the inflation rateâ€ in 2013:Q1â€”that is, Â.
- Use the ADF test for the regression in Equation (14.31) with two lags of to test for a stochastic trend in .
- Is the ADF test based on Equation (14.31) preferred to the test based on Equation (14.32) for testing for stochastic trend in ? Explain.
- In (i) you used two lags of . Should you use more lags? Fewer lags? Explain.
- Based on the test you carried out in (i), does the AR model for contain a unit root? Explain carefully. (Hint: Does the failure to reject a null hypothesis mean that the null hypothesis is true?)
- Using the AR(2) model for with a sample period that begins in 1963:Q1, compute pseudo out-of-sample forecasts for the change in inflation beginning in 2003:Q1 and going through 2012:Q4. That is, compute:
- Are the pseudo out-of-sample forecasts biased?That is, do the forecast errors have a nonzero mean?
- How large is the RMSFE of the pseudo out-of-sample forecasts? Is this consistent with the AR(2) model for estimated over the 1963:Q1â€“2002:Q4 sample period?
- There is a large outlier in 2008:Q4. Why did inflation fall so much in 2008:Q4? (Hint: Collect some data on oil prices. What happened to oil prices during 2008?)