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izzyli · 2023年10月18日

帮忙解释详细一下这道题。谢谢。

NO.PZ2023040502000051

问题如下:

Charlent regresses monthly total returns of theBangkok SET Index on one-month Libor (for a US dollar–denominated contract).The period of the study is from July 2006 to December 2013. To improve thestatistical validity of the variables, for both the SET Index and Libor,Charlent uses the natural logarithms of one plus the monthly returns in theregression calculation.

REGRESSION OF SET INDEX ON LIBOR: ln(1 + SET) = α + β × ln(1+ Libor) + ε

Charlent suspects that his regression equation might not be wellspecified. In particular, he is concerned with the possibility that one or bothof the time series in the regression exhibit a unit root. Using theEngle–Granger approach, he tests the residuals from the regression and rejectsthe null hypothesis that the error term has a unit root.

The most appropriateconclusion that follows from the result of the Engle–Granger test is that thetwo time series are:

选项:

A.

cointegrated and tests of the estimates of theintercept and slope are thus valid.

B.

Not cointegrated and tests of the estimates of theintercept and slope are thus valid.

C.

cointegrated and tests of the estimates of theintercept and slope are thus not valid.

解释:

If the (Engle–Granger) Dickey–Fuller test rejects thenull hypothesis that the error term has a unit root (as Charlent’s test did),then the conclusion is that the error term in the regression is covariancestationary. Therefore, the two time series are cointegrated. The parameters andstandard errors from linear regression will be consistent and will allowtesting of the hypotheses about the long-term relationship between the twoseries.

帮忙解释详细一下这道题。谢谢。

1 个答案

星星_品职助教 · 2023年10月19日

同学你好,

如果构成模型的两组时间序列数据经过DF-EG test检验后,发现有unit root,则说明这两组数据是incointegrated的,这种情况下,截距和斜率的估计都是有问题的。

本题题干说明DF-EG test拒绝了 有unit root的原假设,则说明两个时间序列没有unit root,即是cointegrated的,系数估计也不会因为incointegated而出问题了。

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本题为经典题,课程已经提供详细的讲解。此后请基于讲解中不理解的地方进行提问。

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