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双 · 2023年02月17日

为什么b1=0，不是random walk

  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b1=0，不是random walk，毕竟x只跟随机量有关，那他也是随机的

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1 个答案

星星_品职助教 · 2023年02月18日

同学你好，

这是一个定义的问题。random walk被定义为了b1=1，不是b1=0.

即在random walk的定义下，下一期的值是和本期值有关的（Xt=Xt-1+ε），而不是完全的随机项（Xt=ε）。

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