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DURBIN WATSON STATISTICS
Durbin–Watson statistic is defined as a test statistic which is used to detect the presence of Autocorrelation which is a relationship between values separated from each other by a given time lag in the errors and residuals in statistics.
Durbin and Watson applied this statistic to the residuals from ordinary least squares regressions which are used to develop bounds tests for the null hypothesis. These are the errors which are serially uncorrelated against the alternative that they follow a first order autoregressive process.
Later there are several von Neumann–Durbin–Watson type test statistics for the null hypothesis that the errors on a regression model follow a process with a unit root against the alternative hypothesis that the errors follow a stationary first order autoregression.
Durbin Watson Statistics Homework Help
If et is the errors and residuals in statistics which is associated with the observation at time t, then the test statistic is given by
where T is the number of observations and d is approximately equal to 2(1 − r), where r is defined as the sample autocorrelation of the residuals and d = 2 indicates no autocorrelation. The value of d is between 0 and 4 and if the value of this statistic is substantially less than 2 then there is an evidence of positive serial correlation.
If the value is less than 1.0, there may be cause for alarm and small values of d indicate successive error terms are on average close in value to one another, or positively correlated. If d > 2, successive error terms are on average which is much different in value from one another which is negatively correlated.
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Positive autocorrelation can be tested at significance α where the test statistic d is compared to lower as well as the upper critical values and if d < dL,α, there is statistical evidence that the error terms are positively autocorrelated and if d > dU,α, there is no statistical evidence and if dL,α < d < dU,α, the test is inconclusive.
Negative autocorrelation can be tested at significance α where the test statistic (4 − d) is compared to lower and upper critical values and if (4 − d) < dL,α, there is statistical evidence that the error terms are negatively autocorrelated and if (4 − d) > dU,α, there is no statistical evidence and if dL,α < (4 − d) < dU,α, the test is inconclusive.
