IStatistics.DurbinWatsonStats

Fore Syntax

DurbinWatsonStats(N: Integer; K: Integer; Alpha: Double; Var dL: Double; Var dU: Double);

Fore.NET Syntax

DurbinWatsonStats(N: integer; K: integer; Alpha: double; var dL: double; var dU: double);

Parameters

N. Number of observations.

K. Number of model variables including constant.

Alpha. Significance level. It may take values 1, 2.5 and 5.

dL. Lower bound of the Durbin-Watson statistics.

dU. Upper bound of the Durbin-Watson statistics.

Description

The DurbinWatsonStats method returns approximated values of Durbin-Watson statistics range bounds taken from tables.

Comments

After executing the method the dL and dU parameters take values of the lower and upper bounds of the Durbin-Watson statistics range.

Interpretation of results:

If DW ≤ 2, positive autocorrelation is checked:

If du < DW, zero hypothesis is not rejected, there is no autocorrelation.
If dl < DW and DW < du, there is uncertainty.
If 0 < DW and DW < dl, zero hypothesis is rejected, there is positive residuals autocorrelation.

If DW > 2, negative autocorrelation is checked, it is required to recalculate the statistics DW = 4 - DW and check as in the first case.

Fore Example

Add a link to the Stat system assembly.

Sub UserProc;
Var
    Stat: Statistics;
    N, K: Integer;
    Alpha, dU, dL, DW: Double;
Begin
    Stat := New Statistics.Create;
    // Set number of observations
    N := 20;
    // Set number of model variables
    K := 5;
    // Set significance level
    Alpha := 5;
    // Calculate bounds of the Durbin-Watson statistics range
    Stat.DurbinWatsonStats(N, K, Alpha, dL, dU);
    // Output lower and upper range bounds
    Debug.WriteLine("Lower range bound: " + dL.ToString);
    Debug.WriteLine("Upper range bound: " + dU.ToString);
    //Check hypothesis
    DW := 1.98;
    Debug.WriteLine("Check hypothesis:");
    If (DW <= 2) Then
        If (dU < DW) Then
            Debug.WriteLine("Zero hypothesis is accepted, " +
            "correlation coefficient p = 0, no residual autocorrelation" );
        End If;
        If ((dL < DW) And (DW < dU)) Then
            Debug.WriteLine("Uncertainty");
        End If;
        If ((0 < DW) And (DW < dL)) Then
            Debug.WriteLine("Zero hypothesis is rejected, " +
            "autocorrelation coefficient p <> 0, there is residual autocorrelation" );
        End If;
    Else
        DW := 4 - DW;
        If (dU < DW) Then
            Debug.WriteLine("Zero hypothesis is accepted, " +
            "correlation coefficient p = 0, no residual autocorrelation" );
        End If;
        If ((dL < DW) And (DW < dU)) Then
            Debug.WriteLine("Uncertainty");
        End If;
        If ((0 < DW) And (DW < dL)) Then
            Debug.WriteLine("Zero hypothesis is rejected," +
            "autocorrelation coefficient p <> 0, there is negative residual autocorrelation" );
        End If;
    End If;
End Sub UserProc;

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

Fore.NET Example

The requirements and result of the Fore.NET example execution match with those in the Fore example.

Imports Prognoz.Platform.Interop.Stat;
…
Public Shared Sub Main(Params: StartParams);
Var
    Stat: Statistics;
    N, K: Integer;
    Alpha, dU, dL, DW: Double;
Begin
    Stat := New Statistics.Create();
    // Set number of observations
    N := 20;
    // Set number of model variables
    K := 5;
    // Set significance level
    Alpha := 5;
    // Calculate bounds of the Durbin-Watson statistics range
    Stat.DurbinWatsonStats(N, K, Alpha, Var dL, Var dU);
    // Output lower and upper range bounds
    System.Diagnostics.Debug.WriteLine("Lower range bound: " + dL);
    System.Diagnostics.Debug.WriteLine("Upper range bound: " + dU);
    //Check hypothesis
    DW := 1.98;
    System.Diagnostics.Debug.WriteLine("Check hypothesis:");
    If (DW <= 2) Then
        If (dU < DW) Then
            System.Diagnostics.Debug.WriteLine("Zero hypothesis is accepted, " +
            "correlation coefficient p = 0, no residual autocorrelation" );
        End If;
        If ((dL < DW) And (DW < dU)) Then
            System.Diagnostics.Debug.WriteLine("Uncertainty");
        End If;
        If ((0 < DW) And (DW < dL)) Then
            System.Diagnostics.Debug.WriteLine("Zero hypothesis is rejected, " +
            "autocorrelation coefficient p <> 0, there is residual autocorrelation" );
        End If;
    Else
        DW := 4 - DW;
        If (dU < DW) Then
            System.Diagnostics.Debug.WriteLine("Zero hypothesis is accepted, " +
            "correlation coefficient p = 0, no residual autocorrelation" );
        End If;
        If ((dL < DW) And (DW < dU)) Then
            System.Diagnostics.Debug.WriteLine("Uncertainty");
        End If;
        If ((0 < DW) And (DW < dL)) Then
            System.Diagnostics.Debug.WriteLine("Zero hypothesis is rejected, " +
            "autocorrelation coefficient p <> 0, there is negative residual autocorrelation" );
        End If;
    End If;
End Sub;