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StatTimeSerAnalysis.DoubleExpSmooth Method ([In] TVec, [In] TVec, [In] TVec, double, double, [In] int)
StatTimeSerAnalysis Class  StatTimeSerAnalysis Members  Dew.Stats.Units Namespace  DoubleExpSmooth Method  Example  See Also
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Double exponential smoothing.

Syntax
C#
Visual Basic
public static double DoubleExpSmooth([In] TVec Y, [In] TVec S, [In] TVec B, ref double Alpha, ref double Gamma, [In] int InitMethod);
Parameters
Parameters 
Description 
[In] TVec Y 
Time series data set. 
[In] TVec S 
Smoothed values (see above equation). Size and complex properties of S are set automatically. 
[In] TVec B 
Trend values (see above equation). Size and complex properties of b are set automatically. 
ref double Alpha 
Defines initial estimate for Alpha, returns Alpha which minimizes MSE. 
ref double Gamma 
Defines initial estimate for Gamma, returns Gamma which minimizes MSE. 
[In] int InitMethod 
Defines how the initial values for b[0] are calculated. 
Returns

MSE,evaluated at minimum.

Remarks

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
Example

Load data, perform smoothing and read Alpha,Gamma + 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, initial alpha = 0.1, gamma = 0.3 double alpha = 0.1; double gamma = 0.3; double MSE = StatTimeSerAnalysis.DoubleExpSmooth(Data,S,b,ref alpha,ref gamma,1); // results: MSE and MLE estimate for alpha,gamma } }
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