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Question 2 Using the quantmod Iibrary; download the stock prices of Microsolt Irom January Ist, 2000 (use the symbol "MSFT" within Ihe getSymbols ( ) func...

Question

Question 2 Using the quantmod Iibrary; download the stock prices of Microsolt Irom January Ist, 2000 (use the symbol "MSFT" within Ihe getSymbols ( ) function):Comment on the plot of the time series: does appear t0 be stationary? If not, suggest how to make stationary: To obtain the stock returns we need take first difference of the stock prices: does this time series appear t0 be stationary? Analyse the ACF and PACF plots of the returns: does there appear to be dependence? Analyse the

Question 2 Using the quantmod Iibrary; download the stock prices of Microsolt Irom January Ist, 2000 (use the symbol "MSFT" within Ihe getSymbols ( ) function): Comment on the plot of the time series: does appear t0 be stationary? If not, suggest how to make stationary: To obtain the stock returns we need take first difference of the stock prices: does this time series appear t0 be stationary? Analyse the ACF and PACF plots of the returns: does there appear to be dependence? Analyse the ACF and PACF plots of Ihe absolute value of the returns: does there appear to be dependence? Discuss Propose and estimale Ime series model for Ihe returns and Ior the absolute returns Justily the models.



Answers

Use the data in MINWAGE.DTA for sector 232 to answer the following questions.
(i) Confirm that lwage 232 , and lemp232, are best characterized as I(1) processes. Use the augmented DF test with one lag of gwage232 and gemp232, respectively, and a linear time trend. Is there any doubt that these series should be assumed to have unit roots?
(ii) Regress lemp232, on lwage $232,$ and test for cointegration, both with and without a time trend,
allowing for two lags in the augmented Engle-Granger test. What do you conclude?
(iii) Now regress lemp232, on log of the real wage rate, Irwage2 $32_{t}=\operatorname{lwage} 232_{t}-\operatorname{lcpi}_{t r}$ and a time trend. Do you find cointegration? Are they "closer" to being cointegrated when you use real wages rather than nominal wages?
(iv) What are some factors that might be missing from the cointegrating regression in part (iii)?

Yeah, Part one. The first order. Auto correlation. Issa. Correlation of a time series variable with its first bag. We have four Siri's to examine the first order auto relation here. The first one is the lock of I M V P C. It's row one. That's how we did. Note the first order auto correlation coefficient. It's about 0.6 39 for the same Siri's, but the trended row one hat become smaller. It is 0.485 mhm, or the log of price we get. Row one had equals 10.9 for nine. And after we d train this Siri's through one hat is still very high 0.8 to 2. So for the Siri's I M v p c, we can roll out Ah, unit root in this variable. But for the other variable price, we cannot confidently say that this this Siri's is not a unit route. And if you recall, you need root Refers to you a time Siri's that is highly persistent for a unit root. Siri's Row one hat is roughly one right here. This is our estimated equation. Okay, The coefficient on the first difference of lock price implies that a 1% point increased in the growth in price leads to you a 3.88 percent increase in housing investment and because we have a temp trend in the right hand side of the equation. So this increase is compared to the trend. This is an increase above the trend of housing investment Park pre. If we regress the de Trended Law I m. V p. C. On the first difference of law, price and the time trend, we wouldn't get an estimation result with our square of 0.303 This is much lower than what we got previously when we do not d train lock of I M v p. C. In this part, the first difference in law price or the growth in law price, explains Onley. About 30% of the variation in the log of I M v P C above its trend at four. This is the estimated equation. The coefficient on the difference of lock price has reduced substantially. It is no longer significant at the 5% level against a positive one sided alternative. The out square is also much smaller, indicating that the change in love price explains very little variation in the change of lock I M V P. C. Different thing eliminates linear time trends. That's why the estimate on the trend thanks one is very small and very statistically insignificant.

Part one. For the series lock of s and. p 500. The augmented dickey fuller statistic with our trend is T Equals -179. And the statistic with a train is minus 2.2. These are both above their respective 10 critical values and the estimated route close to one or the other series. The lock of industrial production index. The augmented dickey fuller statistics without a trend is -1.37 and with a trend it is -2.52. These again are not close to restricting even at the 10 level And the estimated roots are again very close to one part two. The simple regression of Lockett S&P 500 unlock of industrial production index is as follows. The T. Statistic for variable L. I. P. Is almost 70 and the R. Square is very close. 21 These are signs of a spurious regression or three Women. Is the residual U.T. had obtained from the model. In part two, we will run an augmented dickey fuller test and the statistic is -1.57. The estimated route is over fine 99 There's no evidence of co integration, March four Oops. This is part five. We should do part 4 1st We add a linear tantra into the regression from part two and again we run the augmented dickey fuller test. The T. Statistic from the test Is -1.88. And the estimated route Is again about .99. Yeah. So we come back to the conclusion in part three. There is no evidence of co integration. Even with a tam trinh R five, It seems that two series do not move together. Even if we allow them to have unrestricted timely near trends, linear time trends. The analysis that's not point is to a long run equilibrium relationship.

Part one. We get the old l s residuals u T hat. Then we run their regression with U T hat on its first leg. The coefficient on U T had minus one is row het and it is 0.281 with a standard error of 0.94 This produced a T statistic of 2.99 So there is evidence for serial correlation in the errors. Yeah. Yeah, this test required strict XO gen ity and we can make a case that all explanatory variables are strictly exhaustion is for the dummies such as, Ah, seasonal dummy and we can dummies. And also the time trend. They must be exogenous because they are determined by the calendar. Yeah, For statewide unemployment rate, it is safe to assume that unexplained changes in P R C F 80 the dependent variable today do not cause future changes. Instead, wide unemployment rate human makes Yeah, and lastly for the two policy variables speed limit law and sit Bell Law, it's reasonable. Thio assume these variables to be strictly exhaustion ists because over this period the policy changes were permanent once they occurred. Part two, we are still estimating the Betas by old L s. But we're computing different standard errors that have some raw business to serial correlation. The Beta head of speed law is 0.6 71 with a standard error of 0.267 and the Beta head of seat belt law is minus 0.2 95 and the standard error is 950.331 Compared to the old L as standard error and T statistic, you may find that the T statistic four speed law has fallen to about 2.5. But the variable is still significant. Yeah. For seat belt law, the T statistic is less than one in absolute value. So given the new computation of standard error, we find little evidence that sit Bella had an effect on the percent of, um, accidents, resulting in fatality for three. This is the estimates using P W method, and I skip the results for the Tan Trinh and the monthly Dummies. Row Hot is 0.289 You may find that there is no important changes. Both policy variable coefficients get closer to zero, and the standard heroines are bigger than the incorrect old l s standard errors, so the basic conclusion is the same. The increase in the speed limit appeared to increase PR cf 80 but the seat belt law, why it is estimated to decrease PR CF 80 does not have a statistically significant effect.

Problem. 21 question A like last limits is negative. 20. My understand negative. 10 minus zero zero. My understand, then 20 22 13 and 13 to 14. Eso the frequencies is one fine 15, one, three and 10 Eso The relative frequencies is 1/35 James opened or to nine and 35 inches community frequencies, and this is open for three. Open for 29 Opening toe 86 and, uh oh, point or 86 and all points or 29 Question scene. The two graphs here. This is the Taliban, and this is the old meal. It's community. Okay, Relative frequencies on the preaching is actually is asking about, on average poor industrials. So the same performance implied years period.


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