Durbin–Watson Test

HISTORY

Durbin, J. and Watson, G.S. invented this test in 1950.

MATHEMATICAL ASPECTS

Consider the case of a multiple linear regression model containing ${ p-1 }$ independent variables. The model is written:

$$ Y_t = \beta_0 + \sum_{j=1}^{p-1} \beta_j X_{jt} + \varepsilon_t\:,\quad t = 1,\ldots, T\:, $$

where

Y _t :

is the dependent variable,

X _jt ,:

with ${ j=1, \ldots, p-1 }$ are the independent variables

β _j ,:

with ${ j=1, \ldots, p-1 }$ are the parameters to be estimated,

ε _t :

with ${ t=1, \ldots, T }$ is an unobservable random error term.

In the matrix form, the model is written as:

$$...