A model for a time series having no trend (see moving average; the constant mean is taken as 0). Let X₁, X₂,…, be successive instances of the random variable X, measured at regular intervals of time. Let ε_j be the random variable denoting the random error at time j. A pth-order model relates the value at time j to the preceding p values bywhere α₁, α₂,…, α_p are constants. Such a model is written in brief as AR(p). The AR(1) process is a Markov chain (see Markov process). Autoregressive models can also be expressed as moving average models. Models combining both type of process include ARMA models and ARIMA models.

The Yule–Walker equations, introduced by Yule in 1927 and Walker in 1931, relate α₁, α₂,…, α_p to the population autocorrelation values ρ₁, ρ₂,…, ρ_p by the p equations:with ρ_−a = ρ_a for all a, and with ρ₀ = 1.