A statistic proposed by Durbin and Geoffrey Watson in 1950. Suppose the sequence of observations y₁, y₂,…, y_t forms a time series. Suppose also that there are k explanatory variables (see regression) taking values x_1t , x_2t,…, x_kt at time point t. It is proposed that the variation over time in the value of y_t, at time t, may be explained by the multiple regression model,where ε_t is the random error and β₀, β₁,…, β_k are unknown parameters.

The Durbin–Watson statistic, d, given bywhere ε̂_m is the ordinary least squares (see method of least squares) estimate of ε_m, tests whether the sequence ε₁, ε₂,…, ε_t consists of independent values (in which case d has expected value 2), or forms a Markov process in which each random error is related to its predecessor.