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Yan · 2021年03月21日

怎么看出是满足covariance-stationary的第三个假设?

* 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.

1“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)”

“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.”为什么从这句话能看出满足第三个条件“协方差不变?


2强化班的PPT上提到了covariance-stationary的第三个假设的表述如下”constant and finite covariance with leading or lagged values",在这题是怎么体现的呢?

1 个答案

星星_品职助教 · 2021年03月21日

同学你好,

第一个问题:“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.”这句话的意思就是εt满足了covariance-stationary的三个条件。

这里面着重强调的是εt满足了no autocorrelation(根据Exhibit 1中最后一张表的t-test可以得到这个结论)。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,即你在第二个问题里提到的“constant and finite covariance”


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