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周梅 · 2024年09月03日

Quantitative

  1. CFA II
  2. Quantitative

* 问题详情，请 查看题干

NO.PZ201709270100000502

问题如下：

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.

为什么不是random walk with a draft ,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

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1 个答案

袁园_品职助教 · 2024年09月04日

嗨，从没放弃的小努力你好：


这里需要区分协方差平整和随机游走两个式子和H0都是不同的。

  1. 随机游走的式子是 xt=b0+b1x(t-1)+εt

H0:g=0，当接受原假设时，才是单位根。说明：在一段时期内，某个时间序列的预测值（xt）的变化量等于残差项+b0。由于残差项是一个取值不确定的随机变量，这会导致预测值的变化毫无规律可言，完全随机生成。这种数据的特征就叫作带漂移项的随机游走（random walk with a drift）。

2.协方差平整的式子是yt=b0+b1y(t-1)+εt 这里的yt=Xt-X(t-1)

通常差分后的数据yt都是平稳的。如果差分后的数据仍然是非平稳的，那么我们可以对yt再做一次差分，以此类推直到数据平稳为止。

所以我们区别一下，单位根其实是对数据本身进行检验，而协方差平稳是对数据差分后进行检验。本质上是两个model，题干中regression1是单位根的方程，而regression2是协方差的AR(1)方程，题目中问的是模型2，所以是协方差平稳问题。

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