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## Durbin-Watson

### Definition

A measure of first-order autocorrelation, that is, of autocorrelation in time series where independent variables are not lagged. (Autocorrelation is sometimes referred to as serial correlation).

The Durbin-Watson statistic is defined as:

where T is the total number of periods and e is defined as in R Square.

The Durbin-Watson statistic lies in the range 0-4. A value of 2 or nearly 2 indicates that there is no first-order autocorrelation. An acceptable range is 1.50 - 2.50.

Where successive error differences are small, Durbin-Watson is low (less than 1.50); this indicates the presence of positive autocorrelation. Positive autocorrelation is very common. Where successive error differences are large, Durbin-Watson is high (more than 2.50); this indicates the presence of negative autocorrelation. Negative autocorrelation is not particularly common.

In time series with lagged variables, the Durbin-Watson statistic is unreliable as it tends toward a value of 2.0.

Autocorrelation occurs when the error terms of a regression model are not independent; that is, when the values of historical periods in the forecast model are influencing the values of current periods. Time series with a strong seasonal or cyclical pattern are often highly correlated. High autocorrelation means that MLR using the ordinary least squares method is not a suitable forecasting technique for this data.