The index of industrial production (IPt ) is a monthly time

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The index of industrial production (IPt ) is a monthly time series that measures the quantity of industrial commodities

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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 to 2013:M12 (that is, January 1986 through December 2013). Let Yt = 1200 * ln(IPt>IPt - 1). a. The forecaster states that Yt shows the monthly percentage change in IP, measured in percentage points per annum. Is this correct? Why? b. Suppose that a forecaster estimates the following AR(4) model for Yt : Yn t = 0.787 + 0.052Yt - 1 + 0.185Yt - 2 + 0.234Yt - 3 + 0.164Yt - 4 . (0.539) (0.093) (0.053) (0.078) (0.066) 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: c. Worried about potential seasonal fluctuations in production, the forecaster adds Yt - 12 to the autoregression. The estimated coefficient on Yt - 12 is ?0.063 with a standard error of 0.045. 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 3.94. 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 = 0, 1, c, 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?

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