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JillTian · 2024年03月15日

Dickey Fuller Test

NO.PZ2023040502000043

问题如下:

The analyst decides to do additional analysis by first-differencing the data and running anew regression: yt = b0 + b1yt–1 + εt, where yt = xt – xt–1.

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


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

选项:

A.

a random walk

B.

covariance stationarity

C.

a random walk with drift

解释:

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 differs significantly from zero. Also, the residual autocorrelations do not differ significantly from zero. As a result, Regression 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.

这里g是0.04,t statistic也很小,无法推翻H0,说明g=0,那怎么样都该属于random walk啊(with or w/out drift)

2 个答案

品职助教_七七 · 2024年10月04日

嗨,努力学习的PZer你好:


@费尔南多

表格中给出的t统计量,都是基于 假设该系数为0 的原假设计算出来的。

所以t统计量为正且很小(小于Critical value),就不能拒绝为0的原假设,也就是说明该系数为0。

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努力的时光都是限量版,加油!

品职助教_七七 · 2024年03月15日

嗨,努力学习的PZer你好:


这道题没有使用DF test,不涉及到g。

两个t statistics都很小,说明b0和b1都为0,所以yt = b0 + b1yt–1 + εt就相当于yt = 0 + 0*yt–1 + εt=εt。

此后的所有分析和结论都是针对上述的yt=εt进行的。这个序列是stationary的。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

费尔南多 · 2024年09月30日

“两个t statistics都很小,说明b0和b1都为0”。这句话我没理解,为什么能通过t统计量推断b0 b1都为0?

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NO.PZ2023040502000043问题如下 The analyst cis to aitionanalysis first-fferencing the ta anrunning anew regression:yt = + b1yt–1 + εt,where yt = xt – xt–1.Exhibit 1. First-fferenceExchange Rate AR(1)Mol: Month-EnObservations, Last 10 YearsBaseon the regression output in Exhibit 1, the first-fferenceeries useto run Regression is consistent with: A.a ranm walkB.covarianstationarityC.a ranm walk with ift The critict-statistic a 5% confinlevel is1.98. a result, neither the intercept nor the coefficient on the first lagof the first-fferenceexchange rate in Regression ffers significantly fromzero. Also, the resiautocorrelations not ffer significantly fromzero. a result, Regression creceto yt = εtwith 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 autocorrelateisconsistent with the covarianof the times series, with itself being constantanfinite fferent lags. Because the variananthe meof ytare constant anfinite in eaperio we calso conclu thytis covarianstationary. 两个t statistics都很小,说明b0和b1都为0,所以yt = + b1yt–1 + εt就相当于yt = 0 + 0*yt–1 + εt=εt。这为什么不是simple ranm walk呢?

2024-11-11 05:25 1 · 回答

NO.PZ2023040502000043 问题如下 The analyst cis to aitionanalysis first-fferencing the ta anrunning anew regression:yt = + b1yt–1 + εt,where yt = xt – xt–1.Exhibit 1. First-fferenceExchange Rate AR(1)Mol: Month-EnObservations, Last 10 YearsBaseon the regression output in Exhibit 1, the first-fferenceeries useto run Regression is consistent with: A.a ranm walk B.covarianstationarity C.a ranm walk with ift The critict-statistic a 5% confinlevel is1.98. a result, neither the intercept nor the coefficient on the first lagof the first-fferenceexchange rate in Regression ffers significantly fromzero. Also, the resiautocorrelations not ffer significantly fromzero. a result, Regression creceto yt = εtwith 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 autocorrelateisconsistent with the covarianof the times series, with itself being constantanfinite fferent lags. Because the variananthe meof ytare constant anfinite in eaperio we calso conclu thytis covarianstationary. 那不是reject了没有autocorrelation的null hypothesis,应该有autocorrelation?

2024-09-09 23:18 1 · 回答

NO.PZ2023040502000043 问题如下 The analyst cis to aitionanalysis first-fferencing the ta anrunning anew regression:yt = + b1yt–1 + εt,where yt = xt – xt–1.Exhibit 1. First-fferenceExchange Rate AR(1)Mol: Month-EnObservations, Last 10 YearsBaseon the regression output in Exhibit 1, the first-fferenceeries useto run Regression is consistent with: A.a ranm walk B.covarianstationarity C.a ranm walk with ift The critict-statistic a 5% confinlevel is1.98. a result, neither the intercept nor the coefficient on the first lagof the first-fferenceexchange rate in Regression ffers significantly fromzero. Also, the resiautocorrelations not ffer significantly fromzero. a result, Regression creceto yt = εtwith 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 autocorrelateisconsistent with the covarianof the times series, with itself being constantanfinite fferent lags. Because the variananthe meof ytare constant anfinite in eaperio we calso conclu thytis covarianstationary. 答案没看懂,可以讲解下吗

2023-08-23 10:54 1 · 回答