IStatistics.DurbinWatsonProbabilities

Syntax

DurbinWatsonProbabilities(DW: Double; N: Integer; K: Integer; Var pL: Double; Var pU: Double);

Parameters

DW. Durbin-Watson statistic.

N. Number of observations.

K. Number of model variables including constant.

pL. Probability value of the lower limit of the Durbin-Watson statistics range.

pU. Probability value of the upper limit of the Durbin-Watson statistics range.

Description

The DurbinWatsonProbabilities method calculates probability values of Durbin-Watson statistics range bounds.

Comments

After executing the method the pL and pU parameters take probability values of the lower and upper limits of the Durbin-Watson statistics range.

If the statistic DW > 2, probabilities are calculated for the value DW' = 4 - DW, and there is negative residuals autocorrelation.

If N ≤ 60, probabilities are calculated by the Pan’s algorithm, if N > 60, they are calculated by normal approximation.

Interpretation of results:

Let α is a set significance level (1, 2.5 or 5%):

If pl≤ α, zero hypothesis is rejected, there is residuals autocorrelation.
If pl > α, and pu ≤ α there is uncertainty.
If pl > α, zero hypothesis is not rejected, there is no autocorrelation.

Example

Add a link to the Stat system assembly.

Sub UserProc;
Var
    Stat: Statistics;
    N, K, alpha: Integer;
    DW, pU, pL: Double;
Begin
    Stat := New Statistics.Create;
    // Set number of observations
    N := 20;
    // Set number of model variables
    K := 5;
    // Set Durbin-Watson statistics value
    DW := 1.6;
    // Calculate probability values of the lower and upper bounds of the Durbin-Watson statistics range
    Stat.DurbinWatsonProbabilities(DW, N, K, pL, pU);
    // Output lower and upper range bounds
    Debug.WriteLine("Probability of the lower range bound: " + pL.ToString);
    Debug.WriteLine("Probability of the upper range bound: " + pU.ToString);
    //Check hypothesis on the significance level 5%
    alpha := 5;
    Debug.WriteLine("Check hypothesis:");
    If( pL <= alpha/100 )Then
        Debug.WriteLine("Zero hypothesis is rejected, autocorrelation coefficient p <> 0, there is residuals autocorrelation");
    End If;
    If(( pL > alpha/100 )And( pU <= alpha/100 ))Then
        Debug.WriteLine(" Uncertainty ");
    End If;
    If( pU > alpha/100 )Then
        Debug.WriteLine("Zero hypothesis is accepted, autocorrelation coefficient p = 0, there is not residuals autocorrelation");
    End If;
End Sub UserProc;

After executing the example the console window displays probability values of the lower and upper bounds of the Durbin-Watson statistics range, the hypothesis about residuals autocorrelation is checked.