Stationarity, Autocorrelation, White Noise, and Linear Time Series

This tutorial introduces basic concepts about stationarity, autocorrelation, white noise, and linear time series.

1  Stationarity

1.1  Strict stationarity

A time series {\(r_t\)} is said to be strictly stationary if the joint distribution of \((t_{t_1},\cdots,r_{t_k})\,\) is identical to  \((t_{t_1+l},\cdots,r_{t_k+l})\,\) for all t, where k is an arbitrary positive integer and (\(t_1,\cdots,r_k\)) is a collection of k positive integers.

In other words, strict stationarity requires that the joint distribution of (\(r_{t_1},\cdots,r_{t_k}\)) is invariant under time shift. This is a very hard condition that is hard to verify empirically. Read more Stationarity, Autocorrelation, White Noise, and Linear Time Series