DoubleExpSmooth Routines

Summary

Double exponential smoothing.

Declaration

Function DoubleExpSmooth(Y: TVec; S, B: TVec; var Alpha, Gamma: TSample; InitMethod: Integer = 0): TSample;

Parameter	Description
Y	Time series data set.
S	Smoothed values (see above equation). Size and complex properties of S are set automatically.
b	Trend values (see above equation). Size and complex properties of b are set automatically.
Alpha	Defines initial estimate for Alpha, returns Alpha which minimizes MSE.
Gamma	Defines initial estimate for Gamma, returns Gamma which minimizes MSE.
InitMethod	Defines how the initial values for b[0] are calculated.

Result

MSE, evaluated at minimum.

Description

Performs double exponential smoothing using the following equations:

Smoothing scheme begins by setting S[0] to Y[0] and b[0] to pne of the following choices:

Different initialization methods are controlled by the InitMethod parameter. Default value (0) uses first equation, setting it to (1) means the second equation will be used and setting it to (2) means the third equation will be used to initialize b[0].

The first smoothing equation adjusts S[i] directly for the trend of the previous period, b[i-1], by adding it to the last smoothed value, S[i-1]. This helps to eliminate the lag and brings S[i] to the appropriate base of the current value. The second smoothing equation then updates the trend, which is expressed as the difference between the last two values. The equation is similar to the basic form of single smoothing, but here applied to the updating of the trend.

See Also
DoubleExpForecast

Example 1

Load data, perform smoothing and read Alpha,Gamma + MSE.

  Uses MtxExpr, StatTimeSerAnalysis, Math387;
  procedure Example;
  var Data,S,b: Vector
      Alpha,Gamma,MSE: TSample;
  begin
    Data.LoadFromFile('aerosol_particles.vec');
    // smooth data, initial alpha = 0.1, gamma = 0.3
    Alpha := 0.1;
    Gamma := 0.3;
    MSE := DoubleExpSmooth(Data,S,Alpha,Gamma,1);
    // results: MSE and MLE estimate for Alpha,Gamma
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "StatTimeSerAnalysis.hpp"
  void __fastcall Example();
  {
    Vector Data, S, b;
    Data->LoadFromFile("aerosol_particles.vec");
    // smooth data, initial alpha = 0.1, gamma = 0.3
    double alpha = 0.1;
    double gamma = 0.3;
    double MSE = DoubleExpSmooth(Data,S,alpha,gamma,1);
    // results: MSE and MLE estimate for alpha,gamma
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector Data = new Vector(0);
      Vector S = new Vector(0);
      Vector b = new Vector(0);
      Data.LoadFromFile("aerosol_particles.vec");
      // smooth data, initial alpha = 0.1, gamma = 0.3
      double alpha = 0.1;
      double gamma = 0.3;
      double MSE = DoubleExpSmooth(Data,S,ref alpha,ref gamma,1);
      // results: MSE and MLE estimate for alpha,gamma
    }
  }

Declaration

Procedure DoubleExpSmooth(Y: TVec; S, B: TVec; const Alpha, Gamma: TSample; out MSE: TSample; InitMethod: Integer = 0);

Parameter	Description
MSE	Returns MSE, evaluated for constant Alpha and Gamma.

Description

In this case a fixed smoothing constants Alpha, Gamma are used in smoothing equations (no minimization is performed).

Example 1

Load data, perform smoothing with Alpha = 0.2, Gamma = 0.18

  Uses MtxExpr, StatTimeSerAnalysis, Math387;
  procedure Example;
  var Data,S,b: Vector;
      MSE: TSample;
  begin
    Data.LoadFromFile('aerosol_particles.vec');
    // smooth data with Alpha=0.2, Gamma=0.18
    DoubleExpSmooth(Data,S,0.2,0.18,MSE,1);
    // results: MSE
  end;

  #include "MtxVecCpp.h"
  #include "Math387.hpp"
  #include "StatTimeSerAnalysis.hpp"
  void __fastcall Example();
  {
    Vector Data, S, b;
    double MSE;
    Data->LoadFromFile("aerosol_particles.vec");
    // smooth data with Alpha=0.2, Gamma=0.18
    DoubleExpSmooth(Data,S,0.2,0.18,MSE,1);
    // results: MSE
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector Data = new Vector(0);
      Vector S = new Vector(0);
      Vector b = new Vector(0);
      Data.LoadFromFile("aerosol_particles.vec");
      // smooth data with Alpha=0.2, Gamma=0.18
      double MSE;
      StatTimeSerAnalysis.DoubleExpSmooth(Data,S,0.2,0.18,out MSE,1);
    }
  }