Calculating Method with Specifying Seasonal Autoregression and Moving Average

This example uses method of estimating model coefficientsdescribed in the Library Of Methods And Models section. Seasonal autoregression order and moving average order are to be specified for this method. Such settings are used by the ARIMA model in modeling container.

To execute the example, add a link to the Stat system assembly.

Sub UserProc;
Var
    lr: ISmLinearRegress;
    Y, X: array[43] Of double;
    ARMA: ISlARMA;
    Inits: Array[2] Of Double;
    res: Integer;
    CoefficientsAR, CoefficientsMA, CoefficientsX: ICoefficients;
    ModelCoefficients: IModelCoefficients;

    Sub Print(Arr: array Of Double);
    Var
        i: Integer;
    Begin
        For i := 0 To Arr.Length - 1 Do
            Debug.WriteLine("    " + Arr[i].ToString);
        End For;
    End Sub Print;
Begin
    lr := New SmLinearRegress.Create;
// explained series values
    Y[00] := 6209; Y[15] := 8516; Y[30] := 14242;
    Y[01] := 6385; Y[16] := 8941; Y[31] := 14704;
    Y[02] := 6752; Y[17] := 9064; Y[32] := 13802;
    Y[03] := 6837; Y[18] := 9380; Y[33] := 14197;
    Y[04] := 6495; Y[19] := 9746; Y[34] := 15010;
    Y[05] := 6907; Y[20] := 9907; Y[35] := 15589;
    Y[06] := 7349; Y[21] := 10333; Y[36] := 15932;
    Y[07] := 7213; Y[22] := 10863; Y[37] := 16631;
    Y[08] := 7061; Y[23] := 11693; Y[38] := 17394;
    Y[09] := 7180; Y[24] := 12242; Y[39] := 17758;
    Y[10] := 7132; Y[25] := 12227; Y[40] := 17308;
    Y[11] := 7137; Y[26] := 12910; Y[41] := 16444;
    Y[12] := 7473; Y[27] := 13049; Y[42] := 16413;
    Y[13] := 7722; Y[28] := 13384;
    Y[14] := 8088; Y[29] := 14036;
// explanatory series values
    X[00] := 4110; X[15] := 7486; X[30] := 11781;
    X[01] := 4280; X[16] := 7832; X[31] := 11681;
    X[02] := 4459; X[17] := 8153; X[32] := 11903;
    X[03] := 4545; X[18] := 8468; X[33] := 11900;
    X[04] := 4664; X[19] := 9054; X[34] := 11986;
    X[05] := 4861; X[20] := 9499; X[35] := 12206;
    X[06] := 5195; X[21] := 9866; X[36] := 12734;
    X[07] := 5389; X[22] := 10217; X[37] := 12990;
    X[08] := 5463; X[23] := 10763; X[38] := 13516;
    X[09] := 5610; X[24] := 10683; X[39] := 13866;
    X[10] := 5948; X[25] := 10494; X[40] := 14141;
    X[11] := 6218; X[26] := 10938; X[41] := 14141;
    X[12] := 6521; X[27] := 11198; X[42] := 14237;
    X[13] := 6788; X[28] := 11546;
    X[14] := 7222; X[29] := 11865;
// Sample period
    lr.ModelPeriod.FirstPoint := 1;
    lr.ModelPeriod.LastPoint := 20;
    lr.Forecast.LastPoint := 40;
    lr.MissingData.Method := MissingDataMethod.Casewise;
    lr.Explained.Value := Y;

// exogenous variable is to be used in the model
    lr.Explanatories.Clear;
    lr.Explanatories.Add.Value := X;
    ModelCoefficients := lr.ModelCoefficients;
// a constant is used in the model
    ModelCoefficients.Intercept.Mode := InterceptMode.AutoEstimate;
    ARMA := lr.ARMA;
// seasonal autoregression order
    ARMA.ParseARSeas("3");
// seasonal moving average order

    ARMA.ParseMASeas("1");
// Method of determining initial approximations
    ARMA.CalcInitMode := ARMAInitType.Auto;
// initial approximations of seasonal autoregression
// seasonal/non-seasonal autoregression and seasonal/non-seasonal moving
    Inits[0] := 0.0025;
    Inits[1] := 0.0025;
    ARMA.InitAR := Inits;
    ARMA.InitMA := Inits;
    ARMA.InitARSeas := Inits;
    ARMA.InitMASeas := Inits;
// seasonal/non-seasonal difference
    ARMA.DiffSeas := 0;
    ARMA.Diff := 2;
// seasonality period
    ARMA.PeriodSeas := 4;
// optimization method
    ARMA.EstimationMethod := ARMAEstimationMethodType.GaussNewton;
//number of iterations for optimization method
    ARMA.MaxIteration := 50;
// model calculation
    res := lr.Execute;
    Debug.WriteLine(lr.Errors);
    If (res = 0) Then
    // autoregression coefficients
        Debug.WriteLine("----Seasonal autoregression coefficients' estimation----");
        CoefficientsAR := ARMA.CoefficientsARSeas;
        Debug.WriteLine(" Value:");
        Print(CoefficientsAR.Estimate);
        Debug.WriteLine("Standard error:");
        Print(CoefficientsAR.StandardError);
        Debug.WriteLine(" t-statistic:");
        Print(CoefficientsAR.TStatistic);
        Debug.WriteLine(" Probability:");
        Print(CoefficientsAR.Probability);
    //Moving average coefficients' estimates
        Debug.WriteLine("----Seasonal moving average coefficients' estimation----");
        CoefficientsMA := ARMA.CoefficientsMASeas;
        Debug.WriteLine(" Value:");
        Print(CoefficientsMA.Estimate);
        Debug.WriteLine("Standard error:");
        Print(CoefficientsMA.StandardError);
        Debug.WriteLine(" t-statistic:");
        Print(CoefficientsMA.TStatistic);
        Debug.WriteLine(" Probability:");
        Print(CoefficientsMA.Probability);
    // exogenous variable coefficients
        Debug.WriteLine("----Coefficient estimates X----");
        CoefficientsX := ModelCoefficients.Coefficients;
        Debug.WriteLine(" Value:");
        Print(CoefficientsX.Estimate);
        Debug.WriteLine("Standard error:");
        Print(CoefficientsX.StandardError);
        Debug.WriteLine(" t-statistic:");
        Print(CoefficientsX.TStatistic);
        Debug.WriteLine(" Probability:");
        Print(CoefficientsX.Probability);
    // explained series values
        Debug.WriteLine("----Explained series----");
        Print(lr.Explained.Value);
    // Model series values
        Debug.WriteLine("----Modeling series----");
        Print(lr.Fitted);
    // forecast series values
        Debug.WriteLine("----Forecast series----");
        Print(lr.Forecast.Value);
    End If;
End Sub UserProc;

After executing the example a linear regression model with the following parameters is created:

Explained and explanatory variables;
Orders of seasonal autoregression and seasonal moving average;
Initial approximations of seasonal or non-seasonal autoregresion and seasonal or non-seasonal moving average;
Difference, seasonal difference, seasonality period;
The Quasi-Newton method is used as an optimization method.

The console window displays values of coefficients for seasonal autoregression, seasonal moving average, explanatory variable and values of explained, model and forecasting series:
No errors
----Seasonal autoregression coefficients' estimation----
Value:
    0.43490707409749907
Standard error:
    0.2734980430624076
t-statistic:
    1.5901652137169431
Probability:
    0.14010396559499899
----Estimates for seasonal moving average coefficients----
Value:
    0.18484173929552522
Standard error:
    0.34372507506364647
t-statistic:
    0.53776041582447442
Probability:
    0.60145259222766068
----Coefficients' estimates X----
Value:
    -0.085392355517884433
Standard error:
    0.11621187624989106
t-statistic:
    -0.73479887145324774
Probability:
    0.47783497431661037
----Explained series----
    6209
    6385
    6752
    6837
    6495
    6907
    7349
    7213
    7061
    7180
    7132
    7137
    7473
    7722
    8088
    8516
    8941
    9064
    9380
    9746
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----Model series----
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    6387.2302929023381
    6378.7277682049989
    6285.405571028482
    6543.5292131985507
    6861.3182832802295
    7059.6741634377986
    7314.8511042611171
    7739.3388404068264
    8162.9940757614158
    8608.6490097510541
    9219.4043335455754
    9757.2216352950072
    10331.513511943327
    10825.774150882695
    11287.576127818098
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----Forecast series----
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    11657.541261930295
    11865.3597446065
    11923.511224107375
    11776.073777507245
    11412.930110495705
    10868.682212136939
    10101.372242464256
    9081.4270870175988
    7787.15982313526
    6189.5716843245982
    4292.6298840343716
    2108.3657950774118
    -382.94251526214703
    -3182.4330708414723
    -6295.9308590365545
    -9742.5548279478699
    -13567.998489133301
    -17793.461768225756
    -22464.005707318353
    -27609.781335809264