Example
The first order autoregressive model, has a unit root when . In this example, the characteristic equation is . The root of the equation is .
If the process has a unit root, then it is a non-stationary time series. That is, the moments of the stochastic process depend on . To illustrate the effect of a unit root, we can consider the first order case, starting from y0=0:
By repeated substitution, we can write . Then the variance of is given by:
The variance depends on t since, while . Note that the variance of the series is diverging to infinity with t.
Read more about this topic: Unit Root
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