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Use the data in HSEINV for this exercise.(i) Test for a unit root in log( invpc), including a linear time trend and two lags of $\Delta \log ($invpct$)$ . Use a 5$\%$ significance level.(ii) Use the approach from part (i) to test for a unit root in log(price).(iii) Given the outcomes in parts (i) and (ii), does it make sense to test for cointegration between $\quad \log ($invpc$)$ and log(price)?

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(i) strongly reject unit root (ii) cannot reject unit root (iii) no

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Chapter 18

Advanced Time Series Topics

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Part one. This is our regression result. Mhm. We have the intercept of -188 and we have log of I. N. V. P. C. At Tam T -1. We have the time trend and we have their dependent variables with its first lack and second leg. We have 39 observations And that are square is .4. The dependent variable. G I N V p C. Is a lock growth rate of I N. V. P. C. Yes. Yes. Yeah. We then run a augmented dickey fuller. You need to retest. And the T statistic for the test is minus point minus four point 82 This is well below there. one critical value of -3 96 So we are able to reject the null hypothesis. What to you? We run a similar regression to the log of price. The lock growth rate of price is the dependent variable and the explanatory variables include the lower value of the first leg of price, the lock growth rate of price, first lack and second leg. We also include a temp train in this regression And we have 39 observations with our square of .2. Again we run the dickey fuller test and the T statistic for this test is minus 2.41 greater then minus three point one. To the critical value. Actually the 10 critical value. Oh so it means that we cannot reject the null of. You need root at a small significance level. R. Three. So the results from part one and 2. In short. Yeah we know that lock of I N. V. P. C. Does not contain a unit root. Meanwhile log a price may contain yeah A unit root. Yeah. Yeah. So it doesn't make sense if we Consider the co integration between the two. Yeah.

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