Question: The forecaster in given Exercise augments her AR(4) model for IP growth to include four lagged values of ?Rt where Rt is the interest rate on three-month U.S. Treasury bills (measured in percentage points at an annual rate).
Exercise: The index of industrial production (IP) is a monthly time series that measures the quantity of industrial commodities produced in a given month. This problem uses data on this index for the United States. All regressions are estimated over the sample period 1960:1 to 2000:12 (that is, January 1960 through December 2000). Let Yi = 1200 x In(IPt/IPt-1).
Use this AR(4) to forecast the value of Y, in January 2001 using the following values of IP for August 2000 through December 2000:
c. Worried about potential seasonal fluctuations in production, the fore-caster adds Xt-12 to the auto regression. The estimated coefficient on Xt-12 is -0.054 with a standard error of 0.053. Is this coefficient statistically significant?
d. Worried about a potential break, she computes a QLR test (with 15% trimming) on the constant and AR coefficients in the AR(4) model. The resulting QLR statistic was 3.45. Is there evidence of a break? Explain.
e. Worried that she might have included too few or too many lags in the model, the forecaster estimates AR(p) models for p = 1, , 6 over the same sample period. The sum of squared residuals from each of these estimated models is shown in the table. Use the BIC to estimate the number of lags that should be included in the auto regression. Do the results differ if you use the AIC?
