SingleExpForecast Routines

Summary

Single exponential forecast.

Declaration

Procedure SingleExpForecast(Y: TVec; YHat: TVec; const Alpha: TSample; T: Integer; InitMethod: Integer = 0);

Parameter	Description
Y	Time series data set.
YHat	Time series forecasts. Size of the YHat vector are adjusted automatically.
Alpha	Overal smoothing parameter used for forecast.
T	Forecast values up to T period.
InitMethod	Defines how the initial values for S[0] are calculated.

Description

Forecasts time series values by using single exponential smoothing equations. For single exponential smoothing, the h period ahead forecast is given by:

See Also
SingleExpSmooth

Example 1

Load data, assume Alpha is 0.33, forecast 20 points past the last value.

  Uses MtxExpr, StatTimeSerAnalysis, Math387;
  procedure Example;
  var Data,YHat: Vector;
      T: Integer;
      NumPoints: Integer;
      Residuals: TVec;
  begin
    NumPoints := 20;
    Data.LoadFromFile('aerosol_particles.vec');
    // last point period = Data.Length-1 + NumPoints
    T := Data.Length-1+NumPoints;
    SingleExpForecast(Data,YHat,0.33,T,0);
    // YHat now stores estimates for YHat[1,...Length-1]
    // so, if we need residuals, we have to subtract
    // these values from y[1,...,Length-1)
    Residuals.Size(YHat);
    Residuals.Sub(Y,YHat,1,0,YHat.Length);
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "StatTimeSerAnalysis.hpp"
  void __fastcall Example();
  {
    Vector Data,YHat, Residuals;
    int NumPoints = 20;
    Data->LoadFromFile("aerosol_particles.vec");
    // last point period = Data.Length-1 + NumPoints
    int T = Data->Length-1+NumPoints;
    SingleExpForecast(Data,YHat,0.33,T,0);
    // YHat now stores estimates for YHat[1,...Length-1]
    // so, if we need residuals, we have to subtract
    // these values from y[1,...,Length-1)
    Residuals->Size(YHat);
    Residuals->Sub(Y,YHat,1,0,YHat->Length);
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector Data = new Vector(0);
      Vector YHat = new Vector(0);
      Vector Residuals = new Vector(0);
      int NumPoints = 20;
      Data.LoadFromFile("aerosol_particles.vec");
      // last point period = Data.Length-1 + NumPoints
      int T = Data.Length-1+NumPoints;
      SingleExpForecast(Data,YHat,0.33,T,0);
      // YHat now stores estimates for YHat[1,...Length-1]
      // so, if we need residuals, we have to subtract
      // these values from y[1,...,Length-1)
      Residuals.Size(YHat);
      Residuals->Sub(Y,YHat,1,0,YHat.Length);
    }
  }

Declaration

Procedure SingleExpForecast(Y: TVec; YHat: TVec; var Alpha: TSample; T: Integer; out MSE: TSample; InitMethod: Integer = 0);

Parameter	Description
MSE	MSE, evaluated at minimum.

Description

First estimate Alpha parameters by single smoothing and then use returned value to forecast up to T periods. Use this routine if you don't know the best estimates for Alpha.

Example 1

Do estimation and forecasting in single routine call.

  Uses MtxExpr, StatTimeSerAnalysis, Math387;
  procedure Example;
  var Data,YHat: Vector;
      Alpha: TSample;
      T, NumPoints: Integer;
  begin
    NumPoints := 20;
    Data.LoadFromFile('aerosol_particles.vec');
    // last point period = Data.Length-1 + NumPoints
    T := Data.Length-1+NumPoints;
    // initial Alpha estimate = 0.6
    Alpha := 0.6;
    SingleExpForecast(Data,YHat,Alpha,T,MSE,0);
    // returs MSE and estimated Alpha (from MLE)
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "StatTimeSerAnalysis.hpp"
  void __fastcall Example();
  {
    Vector Data,YHat;
    int NumPoints = 20;
    Data->LoadFromFile("aerosol_particles.vec");
    // last point period = Data.Length-1 + NumPoints
    int T = Data.Length-1+NumPoints;
    // initial alpha estimate = 0.6
    double alpha := 0.6;
    double mse;
    SingleExpForecast(Data,YHat,alpha,T,mse,0);
    // returs mse and estimated Alpha (from MLE)
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector Data = new Vector(0);
      Vector YHat = new Vector(0);
      int NumPoints = 20;
      Data.LoadFromFile("aerosol_particles.vec");
      // last point period = Data.Length-1 + NumPoints
      int T = Data.Length-1+NumPoints;
      // initial alpha estimate = 0.6
      double alpha := 0.6;
      double mse;
      StatTimeSerAnalysis.SingleExpForecast(Data,YHat,ref alpha,T,out mse,0);
      // returs mse and estimated Alpha (from MLE)
    }
  }