标题: Random Walk vs Unit Root [打印本页] 作者: maratikus 时间: 2011-7-11 19:43 标题: Random Walk vs Unit Root
I read that unit root is a time series that is not covariance stationary, and it's tested as
x= 0 + xt-1 +E. Is unit root a type of random walk?
Can someone please explain the difference between the two?作者: luda002 时间: 2011-7-11 19:43
A stock that follows a random walk has no mean reversion level, so you can't predict which direction it is likely to trend in the future. A unit root infers that the value of the lagged coefficient is = 1, and therefore follows a random walk making it not covariance stationary (since the mean reverting level is defined as b0/b1-1...if b1=1, then the denominator is 0 and this is undefined). So basically, a stock that follows a random walk is defined as having a unit root.
In the equation above, you have described a random walk with no drift since the intercept term = 0.作者: jacksparrow 时间: 2011-7-11 19:43
I believe a unit root refers specifically to the coefficient in a time series (b1). If the coefficient is not statistically significant from 1, then it has a unit root. Random walks describe the dependent variable, which is equal to the value of the dependent value in the previous period plus an error term. So basically, a random walk has a unit root because the coefficient's mean reverting level (bo/(1-b1)) is undefined.
