开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

Serena1998 · 2021年11月28日

这里的b难道不是DF检验中的g吗

* 问题详情,请 查看题干

NO.PZ201709270100000502

问题如下:

Max Busse is an analyst in the research department of a large hedge fund. He was recently asked to develop a model to predict the future exchange rate between two currencies. Busse gathers monthly exchange rate data from the most recent 10-year period and runs a regression based on the following AR(1) model specification:

Regression 1: xt = b0 + b1xt–1 + εt, where xt is the exchange rate at time t.

Based on his analysis of the time series and the regression results, Busse reaches the following conclusions:

Conclusion 1: The variance of xt increases over time.

Conclusion 2: The mean-reverting level is undefined.

Conclusion 3: b0 does not appear to be significantly different from 0.

Busse decides to do additional analysis by first-differencing the data and running a new regression.

Regression 2: yt = b0 + b1yt–1 + εt, where yt = xt – xt–1.

Exhibit 1 shows the regression results.

Exhibit 1. First-Differenced Exchange Rate AR(1) Model: Month-End Observations, Last 10 Years

Note: The critical t-statistic at the 5% significance level is 1.98.

Busse decides that he will need to test the data for nonstationarity using a Dickey–Fuller test. To do so, he knows he must model a transformed version of Regression 1. Busse’s next assignment is to develop a model to predict future quarterly sales for PoweredUP, Inc., a major electronics retailer. He begins by running the following regression:

Regression 3: ln Salest – ln Salest–1 = b0 + b1(ln Salest–1 – ln Salest–2) + εt.

Exhibit 2 presents the results of this regression.

Exhibit 2. Log Differenced Sales: AR(1) Model PoweredUP, Inc., Last 10 Years of Quarterly Sales

Note: The critical t-statistic at the 5% significance level is 2.02.

Because the regression output from Exhibit 2 raises some concerns, Busse runs a different regression. These regression results, along with quarterly sales data for the past five quarters, are presented in Exhibits 3 and 4, respectively.

Exhibit 3. Log Differenced Sales: AR(1) Model with Seasonal Lag PoweredUP, Inc., Last 10 Years of Quarterly Sales

Note: The critical t-statistic at the 5% significance level is 2.03.

Exhibit 4. Most Recent Quarterly Sales Data (in billions)

After completing his work on PoweredUP, Busse is asked to analyze the relationship of oil prices and the stock prices of three transportation companies. His firm wants to know whether the stock prices can be predicted by the price of oil. Exhibit 5 shows selected information from the results of his analysis.

Exhibit 5. Analysis Summary of Stock Prices for Three Transportation Stocks and the Price of Oil

To assess the relationship between oil prices and stock prices, Busse runs three regressions using the time series of each company’s stock prices as the dependent variable and the time series of oil prices as the independent variable.


2. Based on the regression output in Exhibit 1, the first-differenced series used to run Regression 2 is consistent with:

选项:

A.

a random walk.

B.

covariance stationarity.

C.

a random walk with drift.

解释:

B is correct. The critical t-statistic at a 5% confidence level is 1.98. As a result, neither the intercept nor the coefficient on the first lag of the first-differenced exchange rate in Regression 2 differs significantly from zero. Also, the residual autocorrelations do not differ significantly from zero. As a result, Regression 2 can be reduced to yt = εt with a mean-reverting level of b0/(1 b1) = 0/1 = 0.

Therefore, the variance of yt in each period is Var(εt) = σ2. The fact that the residuals are not autocorrelated is consistent with the covariance of the times series, with itself being constant and finite at different lags. Because the variance and the mean of yt are constant and finite in each period, we can also conclude that yt is covariance stationary.

因为因变量是yt-yt-1,这里验证的应该是g=0,也就是covaraince non stationary?

1 个答案

星星_品职助教 · 2021年11月29日

同学你好,

这道题是从covariance stationary的定义出发的。如即果时间序列满足三个条件,就是covariance stationary。

整道题不涉及到DF检验的问题。

  • 1

    回答
  • 0

    关注
  • 806

    浏览
相关问题

NO.PZ201709270100000502 问题如下 2. Baseon the regression output in Exhibit 1, the first-fferenceseries useto run Regression 2 is consistent with: A.a ranm walk. B.covarianstationarity. C.a ranm walk with ift. B is correct. The critict-statistic a 5% confinlevel is 1.98. a result, neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero. Also, the resiautocorrelations not ffer significantly from zero. a result, Regression 2 creceto yt = εt with a mean-reverting level of b0/(1 – b1) = 0/1 = 0.Therefore, the varianof yt in eaperiois Var(εt) = σ2. The faththe resials are not autocorrelateis consistent with the covarianof the times series, with itself being constant anfinite fferent lags. Because the variananthe meof yt are constant anfinite in eaperio we calso conclu thyt is covarianstationary. 为什么不是ranm walk with a aft ,题目中t统计值为0.4504 ,接受H0:G=0,存在单位根,请助教讲解答疑

2024-09-03 16:29 1 · 回答

NO.PZ201709270100000502 问题如下 2. Baseon the regression output in Exhibit 1, the first-fferenceseries useto run Regression 2 is consistent with: A.a ranm walk. B.covarianstationarity. C.a ranm walk with ift. B is correct. The critict-statistic a 5% confinlevel is 1.98. a result, neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero. Also, the resiautocorrelations not ffer significantly from zero. a result, Regression 2 creceto yt = εt with a mean-reverting level of b0/(1 – b1) = 0/1 = 0.Therefore, the varianof yt in eaperiois Var(εt) = σ2. The faththe resials are not autocorrelateis consistent with the covarianof the times series, with itself being constant anfinite fferent lags. Because the variananthe meof yt are constant anfinite in eaperio we calso conclu thyt is covarianstationary. 具体的视频讲解在哪里可以找到

2024-08-25 11:28 1 · 回答

NO.PZ201709270100000502 问题如下 2. Baseon the regression output in Exhibit 1, the first-fferenceseries useto run Regression 2 is consistent with: A.a ranm walk. B.covarianstationarity. C.a ranm walk with ift. B is correct. The critict-statistic a 5% confinlevel is 1.98. a result, neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero. Also, the resiautocorrelations not ffer significantly from zero. a result, Regression 2 creceto yt = εt with a mean-reverting level of b0/(1 – b1) = 0/1 = 0.Therefore, the varianof yt in eaperiois Var(εt) = σ2. The faththe resials are not autocorrelateis consistent with the covarianof the times series, with itself being constant anfinite fferent lags. Because the variananthe meof yt are constant anfinite in eaperio we calso conclu thyt is covarianstationary. yt = εt 为什么不是随机游走

2024-08-09 22:28 1 · 回答

NO.PZ201709270100000502 问题如下 2. Baseon the regression output in Exhibit 1, the first-fferenceseries useto run Regression 2 is consistent with: A.a ranm walk. B.covarianstationarity. C.a ranm walk with ift. B is correct. The critict-statistic a 5% confinlevel is 1.98. a result, neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero. Also, the resiautocorrelations not ffer significantly from zero. a result, Regression 2 creceto yt = εt with a mean-reverting level of b0/(1 – b1) = 0/1 = 0.Therefore, the varianof yt in eaperiois Var(εt) = σ2. The faththe resials are not autocorrelateis consistent with the covarianof the times series, with itself being constant anfinite fferent lags. Because the variananthe meof yt are constant anfinite in eaperio we calso conclu thyt is covarianstationary. 老师,还是不太明白,题目中“Conclusion 1: The varianof xt increases over time.”,不是说明Xt方差不稳定吗,为什么会选B呢?

2023-07-28 17:18 1 · 回答

NO.PZ201709270100000502 问题如下 2. Baseon the regression output in Exhibit 1, the first-fferenceseries useto run Regression 2 is consistent with: A.a ranm walk. B.covarianstationarity. C.a ranm walk with ift. B is correct. The critict-statistic a 5% confinlevel is 1.98. a result, neither the intercept nor the coefficient on the first lof the first-fferenceexchange rate in Regression 2 ffers significantly from zero. Also, the resiautocorrelations not ffer significantly from zero. a result, Regression 2 creceto yt = εt with a mean-reverting level of b0/(1 – b1) = 0/1 = 0.Therefore, the varianof yt in eaperiois Var(εt) = σ2. The faththe resials are not autocorrelateis consistent with the covarianof the times series, with itself being constant anfinite fferent lags. Because the variananthe meof yt are constant anfinite in eaperio we calso conclu thyt is covarianstationary. 请问本题是否直接可以从b1判断,即因为题目中b1给了不等于1,所以不是unit root或者说是 covariance-stationary?

2023-04-12 09:41 1 · 回答