问题如下:
After building a AR(1) model which is xt=b0+b1xt-1+εt, Steven does additional analysis by first-differencing the data and runs a new regression which is yt= b0+b1yt-1+εt, where yt= xt- xt-1.Then he gets a result that in the new regression,b0=b1=0. So variable xt:
选项:
A.is nonstationary.
B.doesn’t have a unit root.
C.is stationary.
解释:
A is correct.
考点: Random walk and unit roots.
解析:已知Steven做了一阶差分之后得到yt= b0+b1yt-1+εt中的b0=b1=0,即yt=εt= xt- xt-1,通过移项我们可以得到xt= xt-1+εt,不难发现此时b0=0,b1=1,这是很典型的simple random walk,同时也就意味着xt是不平稳的。A选项正确。
在unit root里面,不是b1=1才是non stationary吗?为什么这里是b0 = b1 =0就non stationary了呢?