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magico · 2019年12月10日

问一道题：NO.PZ201709270100000502

  1. CFA II
  2. Quantitative

* 问题详情，请 查看题干

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.

方程最终不是Yt与残差项吗？ 为什么不是random walk？

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4 个答案

星星_品职助教 · 2021年03月21日

@Yan

根据Exhibit 1中最后一张表的t-test结果（都不能拒绝ρ=0的原假设），可以发现εt满足no autocorrelation。所以残差项之间彼此是不相关的。从而直接就可以得到COV(εt，εt+k)=0。

所以就是协方差不变且等于0.

星星_品职助教 · 2020年12月09日

@简ying_0214

1. 三条假设是“协方差平稳的那三条假设”

2. 具体指的是“协方差平稳的三个条件：均值不变（μ=0），方差不变（同方差），和协方差不变（协方差=0），所以属于协方差平稳”

Yan · 2021年03月21日

为什么说这里是协方差不变呢？就是为什么说这里是协方差为0呢？

星星_品职助教 · 2019年12月16日

同学你好，

回一下追问哈，随机游走是有明确定义的，就是只有“b1=1”这种情况下才是随机游走模型。

而b1=0虽然形式上很像，但并不构成随机游走。b1=0实质上构成的是协方差平稳的时间序列，因为满足了协方差平稳的那三条假设。

简ying · 2020年12月08日

为什么就满足了那三条假设？前面章节讲线性回归的那三条假设吗？这里不是自回归模型了吗？自回归模型里也对残差有这些假设吗？有点晕了

星星_品职助教 · 2019年12月11日

同学你好，


Random walk的定义是b1=1，也就是yt=b0+yt-1+εt 这种形式。


而yt=εt这种形式相当于是b1=0。此外，这个序列符合协方差平稳的三个条件：均值不变（μ=0），方差不变（同方差），和协方差不变（协方差=0），所以属于协方差平稳，B选项正确，加油。



magico · 2019年12月12日

是啊，形式上相当于random walk，为什么又不能选呢？

星星_品职助教 · 2019年12月12日

形式上不是random walk，random walk的定义是b1=1，而yt=εt这种形式相当于是b1=0

magico · 2019年12月14日

好像还是没有完全理解， 这个yt的方程，就是只有随机项， 那么从随机游走的本质来理解，这个方程的本质来看不是一个随机模型？

星星_品职助教 · 2019年12月16日

字数比较多，重新起了一条回复哈

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