StatTimeSerAnalysis.TripleExpSmooth Method ([In] TVec, [In] TVec, [In] TVec, [In] TVec, double, double, double, [In] int)

Triple exponential smoothing.

Syntax

Visual Basic

public static double TripleExpSmooth([In] TVec Y, [In] TVec S, [In] TVec B, [In] TVec L, ref double Alpha, ref double Beta, ref double Gamma, [In] int Period);

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.
[In] TVec L	Seasonal indices (see above equation). Size and complex properties of L are set automatically.
ref double Alpha	Defines initial estimate for Alpha, returns Alpha which minimizes MSE.
ref double Beta	Defines initial estimate for Beta, returns Beta which minimizes MSE.
ref double Gamma	Defines initial estimate for Gamma, returns Gamma which minimizes MSE.
[In] int Period	Period length. An exception is raised if Y.Length mod Period is not 0.

Returns

MSE, evaluated at minimum.

Remarks

Performs triple exponential smoothing (also known as Holt-Winters smoothing) using the following equations:

where Y are the observations, S are the smoothed observations, b trend factors, L the seasonal indices and P is the period length. To initialize triple exponential smoothing method we need at least one complete season's data to determine initial estimates of the seasonal indices L[0]..L[P-1]. Again, there are several ways to initialize L values. The algorithm uses approach, described at www.itl.nist.gov/div898/handbook/pmc/section4/pmc435.htmpage. For initial estimate for S and b, the following equations are being used:

Note There are no S[0]..S[P-2] values; the smoothed series starts with the smoothed version of the Y[P] observation. Also note that the internal algorithm automatically accounts for this by resizing S,b vector to Y.Length-Period.

See Also

TripleExpForecast

Example

Generate 24 random values representing 4 quarters x 6 years = 24, perform smoothing and read Alpha,Beta,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); Vector L = new Vector(0); Data.Size(24,false); Data.RandGauss(); // smooth data, initial alpha = 0.1, beta=0.1, gamma = 0.3 double alpha = 0.1; double beta = 0.1; double gamma = 0.3; // Period = 4 double MSE = StatTimeSerAnalysis.TripleExpSmooth(Data,S, b, L, ref alpha,ref beta, ref gamma,4); // results: MSE and MLE estimate for Alpha,Beta,Gamma } }

Group

TripleExpSmooth Method

Links

StatTimeSerAnalysis Class, StatTimeSerAnalysis Members, Dew.Stats.Units Namespace, TripleExpSmooth Method, Example, See Also

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