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Use INTQRT for this exercise.(i) In Example $18.7,$ we estimated an error correction model for the holding yield on six-monthT-bills, where one lag of the holding yield on three-month T-bills is the explanatory variable. Weassumed that the cointegration parameter was one in the equation $h y 6_{t}=\alpha+\beta h y 3_{t-1}+u_{r}$ Now, add the lead change, $\Delta h y 3_{t}$ , the contemporaneous change, $\Delta h y 3_{t-1},$ and the lagged change, $\Delta h y 3_{t-2},$ of $h y 3_{t-1} .$ That is, estimate the equation$h y 6_{t}=\alpha+\beta h y 3_{t-1}+\phi_{0} \Delta h y 3_{t}+\phi_{1} \Delta h y 3_{t-1}+\rho_{1} \Delta h y 3_{t-2}+e_{t}$and report the results in equation form. Test $\mathrm{H}_{0} : \beta=1$ against a two-sided alternative. Assume that the lead and lag are sufficient so that $\left\{\mathrm{hy} 3_{t-1}\right\}$ is strictly exogenous in this equation and do not worry about serial correlation.(ii) To the error correction model in $(18.39),$ add $\Delta h y 3_{t-2}$ and $\left(h y 6_{t-2}-h y 3_{t-3}\right)$ . Are these terms jointly significant? What do you conclude about the appropriate error correction model?

(i) reject at 10% (ii) no. Use (18.39) model

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Chapter 18

Advanced Time Series Topics

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Part one. This is the estimated equation. A bit of you can tell that the first explanatory variable is significant seem to the second one, the third one very likely And the last one is also significant. These variables have estimated coefficients much larger in absolute her too. The standard error of the estimate We have 121 observations and elsewhere of 0.9. And this is there standard barrel of their error terms. Mhm. We test the null hypothesis, Beta equals one and beta is the coefficient of the first explanatory variable. H white three sub t minus one. Yeah. The T 36 for this test is calculated as 1.027 -1 altogether divided by .016 and you will get 1.69. We cannot reject the null hypothesis at the five level. Yeah But we can retract it at the 10 level racist. Okay, Part two. This is the estimated errol Kerr election correction model. So you can tell that neither of the added terms is individually significant. If we test for the joint significance, we get an f statistic of one point 35 With the P value of .264. So these variables are neither jointly nor individually significant. We should admit these terms from the regression and stay with the model in equation 18 39.

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