Random Walk

Summaries

Random Walk:

x__t = x__t-1 + error

Random Walk with a drift (b0)

x__t = b0 + x__t-1 + error

Random Walk is not covariance stationary because the mean-reverting level is not defined (b0/0)

This means the coefficient of the lag variable = 1 and AR(1) is not valid

This time series thus has unit root

First differencing (method to change random walk to covariance stationary)

y__t = x_t – x__t-1 = error

Then the men reverting level is = 0/(1-0) = 0