Track 12 · Time Series and Forecasting · Lesson 10 of 11
Stationarity and autoregressive models
Judge whether a series is stationary, make it stationary by differencing, and fit, interpret and forecast with autoregressive AR(p) models; describe ARIMA models conceptually.
A model that says “tomorrow looks a bit like today” works only if the rules of the series stay the same over time. Stationarity is that stability; differencing creates it; autoregressive models exploit it — and the same ideas underlie the ARIMA models built into most forecasting software.
A series is (weakly) stationary if its mean and variance do not change over time and the autocorrelation between two values depends only on how far apart they are, not on when. Stationary series fluctuate around a fixed level with a stable spread.
Things that break stationarity: a trend (the mean changes), seasonality (the mean depends on the month), a random walk (the level wanders with no pull back), a structural break, and a changing variance.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Judge stationarity from plots and ACFs
- Apply first, seasonal and second differences, and spot over-differencing
- Fit an AR(1) by Yule–Walker and forecast with mean reversion
- Relate AR(1) to its ACF φ^k and to the random walk
- Read ARIMA(p, d, q) orders conceptually