问一道题：NO.PZ201709270100000503 第3小题

NO.PZ201709270100000503 问题如下 3.Baseon the regression results in Exhibit 1, the origintime series of exchange rates: A.ha unit root. B.exhibits stationarity. C.cmoleusing lineregression. A is correct. If the exchange rate series is a ranm walk, then the first-fferenceseries will yiel= 0 an= 0, anthe error terms will not serially correlate The ta in Exhibit 1 show ththis is the case: Neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero because the t-statistiof both coefficients are less ththe critict-statistic of 1.98. Also, the resiautocorrelations not ffer significantly from zero because the t-statistiof all autocorrelations are less ththe critict-statistic of 1.98. Therefore, because all ranm walks have unit roots, the exchange rate time series useto run Regression 1 ha unit root. 我觉得应该是差分过后的变量是随机游走

NO.PZ201709270100000503 问题如下 MBusse is analyst in the researpartment of a large hee fun He wrecently asketo velop a mol to prethe future exchange rate between two currencies. Busse gathers monthly exchange rate ta from the most recent 10-yeperioanruns a regression baseon the following AR(1) mol specification:Regression 1: xt = + b1xt–1 + εt, where xt is the exchange rate time t.Baseon his analysis of the time series anthe regression results, Busse reaches the following conclusions:Conclusion 1: The varianof xt increases over time.Conclusion 2: The mean-reverting level is unfineConclusion 3: es not appeto significantly fferent from 0.Busse cis to aitionanalysis first-fferencing the ta anrunning a new regression.Regression 2: yt = + b1yt–1 + εt, where yt = xt – xt–1.Exhibit 1 shows the regression results. Exhibit 1. First-fferenceExchange Rate AR(1) Mol: Month-EnObservations, Last 10 YearsNote: The critict-statistic the 5% significanlevel is 1.98.Busse cis thhe will neeto test the ta for nonstationarity using a ckey–Fuller test. To so, he knows he must mol a transformeversion of Regression 1. Busse’s next assignment is to velop a mol to prefuture quarterly sales for PowereP, Inc., a major electroniretailer. He begins running the following regression:Regression 3: ln Salest – ln Salest–1 = + b1(ln Salest–1 – ln Salest–2) + εt.Exhibit 2 presents the results of this regression. Exhibit 2. Log fferenceSales: AR(1) Mol PowereP, Inc., Last 10 Years of Quarterly SalesNote: The critict-statistic the 5% significanlevel is 2.02.Because the regression output from Exhibit 2 raises some concerns, Busse runs a fferent regression. These regression results, along with quarterly sales ta for the past five quarters, are presentein Exhibits 3 an4, respectively. Exhibit 3. Log fferenceSales: AR(1) Mol with SeasonLPowereP, Inc., Last 10 Years of Quarterly SalesNote: The critict-statistic the 5% significanlevel is 2.03. Exhibit 4. Most Recent Quarterly Sales ta (in billions)After completing his work on PowereP, Busse is asketo analyze the relationship of oil prices anthe stoprices of three transportation companies. His firm wants to know whether the stoprices cprectethe priof oil. Exhibit 5 shows selecteinformation from the results of his analysis. Exhibit 5. Analysis Summary of StoPrices for Three Transportation Stocks anthe Priof Oil To assess the relationship between oil prices anstoprices, Busse runs three regressions using the time series of eacompany’s stoprices the pennt variable anthe time series of oil prices the inpennt variable.3.Baseon the regression results in Exhibit 1, the origintime series of exchange rates: A.ha unit root. B.exhibits stationarity. C.cmoleusing lineregression. A is correct. If the exchange rate series is a ranm walk, then the first-fferenceseries will yiel= 0 an= 0, anthe error terms will not serially correlate The ta in Exhibit 1 show ththis is the case: Neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero because the t-statistiof both coefficients are less ththe critict-statistic of 1.98. Also, the resiautocorrelations not ffer significantly from zero because the t-statistiof all autocorrelations are less ththe critict-statistic of 1.98. Therefore, because all ranm walks have unit roots, the exchange rate time series useto run Regression 1 ha unit root. 你好老师，这道题和上一道题问的有什么区别啊。为什么都是exhibit1 得出的结论，一个是covarianstationary一个是unit root。谢谢

NO.PZ201709270100000503 问题如下 3.Baseon the regression results in Exhibit 1, the origintime series of exchange rates: A.ha unit root. B.exhibits stationarity. C.cmoleusing lineregression. A is correct. If the exchange rate series is a ranm walk, then the first-fferenceseries will yiel= 0 an= 0, anthe error terms will not serially correlate The ta in Exhibit 1 show ththis is the case: Neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero because the t-statistiof both coefficients are less ththe critict-statistic of 1.98. Also, the resiautocorrelations not ffer significantly from zero because the t-statistiof all autocorrelations are less ththe critict-statistic of 1.98. Therefore, because all ranm walks have unit roots, the exchange rate time series useto run Regression 1 ha unit root. 请老师指正

NO.PZ201709270100000503 问题如下 MBusse is analyst in the researpartment of a large hee fun He wrecently asketo velop a mol to prethe future exchange rate between two currencies. Busse gathers monthly exchange rate ta from the most recent 10-yeperioanruns a regression baseon the following AR(1) mol specification:Regression 1: xt = + b1xt–1 + εt, where xt is the exchange rate time t.Baseon his analysis of the time series anthe regression results, Busse reaches the following conclusions:Conclusion 1: The varianof xt increases over time.Conclusion 2: The mean-reverting level is unfineConclusion 3: es not appeto significantly fferent from 0.Busse cis to aitionanalysis first-fferencing the ta anrunning a new regression.Regression 2: yt = + b1yt–1 + εt, where yt = xt – xt–1.Exhibit 1 shows the regression results. Exhibit 1. First-fferenceExchange Rate AR(1) Mol: Month-EnObservations, Last 10 YearsNote: The critict-statistic the 5% significanlevel is 1.98.Busse cis thhe will neeto test the ta for nonstationarity using a ckey–Fuller test. To so, he knows he must mol a transformeversion of Regression 1. Busse’s next assignment is to velop a mol to prefuture quarterly sales for PowereP, Inc., a major electroniretailer. He begins running the following regression:Regression 3: ln Salest – ln Salest–1 = + b1(ln Salest–1 – ln Salest–2) + εt.Exhibit 2 presents the results of this regression. Exhibit 2. Log fferenceSales: AR(1) Mol PowereP, Inc., Last 10 Years of Quarterly SalesNote: The critict-statistic the 5% significanlevel is 2.02.Because the regression output from Exhibit 2 raises some concerns, Busse runs a fferent regression. These regression results, along with quarterly sales ta for the past five quarters, are presentein Exhibits 3 an4, respectively. Exhibit 3. Log fferenceSales: AR(1) Mol with SeasonLPowereP, Inc., Last 10 Years of Quarterly SalesNote: The critict-statistic the 5% significanlevel is 2.03. Exhibit 4. Most Recent Quarterly Sales ta (in billions)After completing his work on PowereP, Busse is asketo analyze the relationship of oil prices anthe stoprices of three transportation companies. His firm wants to know whether the stoprices cprectethe priof oil. Exhibit 5 shows selecteinformation from the results of his analysis. Exhibit 5. Analysis Summary of StoPrices for Three Transportation Stocks anthe Priof Oil To assess the relationship between oil prices anstoprices, Busse runs three regressions using the time series of eacompany’s stoprices the pennt variable anthe time series of oil prices the inpennt variable.3.Baseon the regression results in Exhibit 1, the origintime series of exchange rates: A.ha unit root. B.exhibits stationarity. C.cmoleusing lineregression. A is correct. If the exchange rate series is a ranm walk, then the first-fferenceseries will yiel= 0 an= 0, anthe error terms will not serially correlate The ta in Exhibit 1 show ththis is the case: Neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero because the t-statistiof both coefficients are less ththe critict-statistic of 1.98. Also, the resiautocorrelations not ffer significantly from zero because the t-statistiof all autocorrelations are less ththe critict-statistic of 1.98. Therefore, because all ranm walks have unit roots, the exchange rate time series useto run Regression 1 ha unit root. 因为t=0.4504，所以不能拒绝原假设，说明 xt−1​​ - xt−2​​ 的系数等于0，所以 x(t)=x(t-1)+ 残差所以他们有单位根，就是Unit root。我这个理解对不低？

NO.PZ201709270100000503 老师好， 我看这道题的图表看了半天没看明白。表的标题明明是说AR(1)但是表的内容里面又涉及Xt-1 - Xt-2,这不是AR2了么？谢谢老师