Durbin-Watson

DURBINWATSONTEST(DataRange,ConfidenceLevel,NewTableFlag))

• $DataRange$ is the array of x and y values.
• $ConfidenceLevel$ is the value of alpha from 0 to 1.
• $NewTableFlag$ is either TRUE or FALSE. TRUE for getting results in a new cube. FALSE will display results in the same cube

Description

• This function gives the test statistic of the Durbin-Watson test.
• The test is used to detect the presence of autocorrelation in the residuals.
• Autocorrelation means that adjacent observations are correlated.
• If they are correlated, then least-squares regression underestimates the standard error of the coefficients.

Assumptions

The error terms are independent of each other.

• The Durbin-Watson test uses the following statistic:

$d={\frac {\sum _{i=2}^{n}(e_{i}-e_{i-1})^{2})}{\sum _{i=1}^{n}(e_{i})^{2}}}$

• where the $e_{i}=y_{i}-{\bar {y_{i}}}$ are the residuals.
• n is the number of elements in the sample.
• k is the number of independent variables.

• d takes the values between 0 and 4.
• d = 2 means there is no autocorrelation.
• A value substantially below 2 means that the data is positively autocorrelated.
• A value of d substantially above 2 means that the data is negatively autocorrelated.