Question

The index of industrial production (IP_t) 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 Y_t =1200*ln(IP_t/IP_t-1)

Suppose that a forecaster estimates the following AR(4) model for Y_t:

= 0.787 0.052Y,-1 + 0.185Y,-2 + 0.234 Y,_3 + 0.164Y,-4. (0.053) (0.078) (0.539) (0.093) (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: 2013:M8 2013:M9 Date 2013:M10 2013:M11 2013:M12 2013:M7 IP 99.016 99.561 100.196 100.374 101.034 101.359

Worried about a potential break, the forecaster 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?

The 5% critical value is 3.55

The 1% critical value is 4.53

Based on this information, is there evidence of a break at the 5% level of significance? (Type Yes or No) Yes

Based on this information, is there evidence of a break at the 1% level of significance? (Type Yes or No) NO

The forecaster augments the AR(4) model for IP growth from Question 6 to include four lagged values of ΔR_t, where R_t is the interest rate on 3-month U.S. Treasury bills (measured in percentage points at an annual rate).

The Granger-causality F-statistic on the four lags of ΔR_t is 4.16. Do interest rates help predict IP growth?

The 1% critical value is ?

Based on this information, do interest rates help predict IP growth? (Type Yes or No)

Answer 1

Yes, there is an evidence of a break at the 5% level of significance as the resulting QLR statistic was 3.94 > critical value
No, there is not an evidence of a break at the 5% level of significance as the resulting QLR statistic was 3.94 < critical value

critical value of F:
degrees of freedom for the numerator = 4-1 =3
degrees of freedom for the denominator = 5*12-3 =57

The critical value corresponding to F_3,57 = 4.145
Yes, interest rates help predict IP growth as the Granger-causality F-statistic > critical value

1% significance level \ V1 4 6 7 1 2 3 5 V2 4052.19 4999.52 5403.34 5624.62 5763.65 5858.97 5928.33 98.502 2 99.000 99.166 99.24999.300 99.333 99.356 34.116 30.816 29.457 28.710 28.237 27.911 27.672 21.198 4 18.000 16.694 15.977 15.522 15.207 14.976 5 16.258 13.274 12.060 11.392 10.967 10.672 10.456 3.681 55 7.119 5.013 4.159 3.370 3.149 2.983 7.110 5.006 4.152 56 3.674 3.363 3.143 2.977 7.102 4.145 57 4.998 3.667 3.357 3.136 2.971 58 7.093 4.991 4.138 3.661 3.351 3.130 2.965 59 7.085 4.984 4.132 3.655 3.345 3.124 2.959 7.077 3.649 60 4.977 4.126 3.339 3.119 2.953 Ln