Stationarity, what it means and why models demand it

Question

Define weak and strict stationarity. Classify these processes: white noise, an AR(1) with \phi \lt 1, a random walk, and a price series versus its return series. Why does statistical inference need stationarity in the first place?

Accepted Answer

Definitions. A process is strictly stationary if the joint distribution of (X{t1}, \dots, X{tk}) is invariant to shifting all times by any h, the full probabilistic structure is time-invariant. It is weakly (covariance) stationary if just the first two moments are time-invariant: \mathbb{E}[Xt] = \mu and \operatorname{Cov}(Xt, X{t+k}) = \gammak for all t (finite variance, autocovariance depending only on the lag). Strict + finite variance ⟹ weak; for Gaussian processes the two coincide. Classification. - White noise (\varepsilont i.i.d., mean 0, variance \sigma^2): stationary, the benchmark c…

Stationarity, what it means and why models demand it

Your answer

More Statistics questions