The Index of Industrial Production (IPt) 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 1986:M1–2013:M12 (that is, January 1986 through December 2013). Let Yt = 1200 × ln(IPt/IPt−1). (a) A forecaster states that Yt shows the monthly percentage change in IP, measured in percentage points per annum. Is this correct? Why? (b) Suppose she estimates the following AR(4) model for Yt: Yˆ t = 0.787 + 0.052Yt−1 + 0.185Yt−2 + 0.234Yt−3 + 0.164Yt−4 Use this AR(4) to forecast the value of Yt in January 2014, using the following values of IP for July 2013 through December 2013: Table 1:
The Index of Industrial Production (IPt) 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 1986:M1–2013:M12 (that is, January 1986 through December
2013). Let Yt = 1200 × ln(IPt/IPt−1).
(a) A forecaster states that Yt shows the monthly percentage change in IP, measured in percentage points per
annum. Is this correct? Why?
(b) Suppose she estimates the following AR(4) model for Yt:
Yˆ
t = 0.787 + 0.052Yt−1 + 0.185Yt−2 + 0.234Yt−3 + 0.164Yt−4
Use this AR(4) to forecast the value of Yt in January 2014, using the following values of IP for July 2013 through
December 2013:
Table 1:
Date 2013 M:7 2013 M:8 2013 M:9 2013 M:10 2013 M:11 2013 M:12
IP 99.016 99.561 100.196 100.374 101.034 101.359
(c) Worried about potential seasonal fluctuations in production, she adds Yt−12 to the autoregression. The
estimated coefficient on Yt−12 is 0.061, with a standard error of 0.043. Is this coefficient statistically significant?
(e) Worried that she might have included too few or too many lags in the model, the forecaster estimates AR(p)
models for p = 0, 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
autoregression. Do the results differ if you use the AIC?
Table 2:
AR Order 0 1 2 3 4 5 6
SSR 19533 18643 17377 16285 15842 15824 15824
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
