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This exercise also uses the data from VOLAT. Computer Exercise Cll studies the long-run relationship between stock prices and industrial production. Here, you will study the question of Granger causality using the percentage changes.(i) Estimate an $\mathrm{AR}(3)$ model for $p c i p_{r}$ , the percentage change in industrial production (reported atan annualized rate). Show that the second and third lags are jointly significant at the 2.5$\%$ level.(ii) Add one lag of $p c s p_{t}$ to the equation estimated in part (i). Is the lag statistically significant?What does this tell you about Granger causality between the growth in industrial production and the growth in stock prices?(iii) Redo part (ii) but obtain a heteroskedasticity-robustic. Does the robust test change yourconclusions from part (ii)?

(i) see video (ii) yes, thus Granger cause (iii) no

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Chapter 18

Advanced Time Series Topics

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Part one. The f statistic for the 2nd and 3rd legs with two and 550° of freedom is 3.76 And the p value is 0- four. So the 2nd and 3rd legs are jointly significant. Part two we at p c s p t minus one to the A. R three model in part one and estimate the model. We get. The coefficient for this new variable is point zero 31 And it's t statistic is 2.4, so this variable is significant and we can conclude that pc s p grandeur causes pc type In Part three. We win estimate the model with heterocyclic elasticity robust statistic. The T statistic now is 2.47, So our conclusion from part two remains the same.

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