StatTimeSerAnalysis::DoubleExpSmooth Function

StatTimeSerAnalysis Namespace

Overload List

#SignatureDescription
1double DoubleExpSmooth(TVec *Y, TVec *S, TVec *B, double &Alpha, double &Gamma, const int InitMethod = 0);Double exponential smoothing.
2void DoubleExpSmooth(TVec *Y, TVec *S, TVec *B, const double Alpha, const double Gamma, double &MSE, const int InitMethod = 0);In this case a fixed smoothing constants Alpha, Gamma are used in smoothing equations (no minimization is performed).

Overload 1: double DoubleExpSmooth(TVec *Y, TVec *S, TVec *B, double &Alpha, double &Gamma, const int InitMethod = 0);

Double exponential smoothing.

#NameTypeDescription
1YTVec *Time series data set.
2STVec *Smoothed values (see above equation). Size and complex properties of S are set automatically.
3BTVec *Trend values (see above equation). Size and complex properties of b are set automatically.
4Alphadouble &Defines initial estimate for Alpha, returns Alpha which minimizes MSE.
5Gammadouble &Defines initial estimate for Gamma, returns Gamma which minimizes MSE.
6InitMethod = 0const intDefines how the initial values for b[0] are calculated.

Returns: MSE,evaluated at minimum.

Remarks:

Performs double exponential smoothing using the following equations:

S[i]=α⋅Y[i]+(1−α)(S[i−1]+b[i−1]),0≤α≤1b[i]=γ(S[i]−S[i−1])+(1−γ)b[i−1],0≤γ≤1\begin{aligned} S[i] &= \alpha \cdot Y[i] + (1-\alpha)(S[i-1]+b[i-1]) \quad , \quad 0\leq \alpha \leq 1 \\ b[i] &= \gamma (S[i]-S[i-1])+(1-\gamma)b[i-1] \quad, \quad 0\leq \gamma \leq 1 \end{aligned}

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

b[0]=Y[1]−Y[0]b[0]=13(Y[3]−Y[0])b[0]=1n−1(Y[n−1]−Y[0])\begin{aligned} b[0] &= Y[1]-Y[0] \\ b[0] &= \cfrac{1}{3}(Y[3]-Y[0]) \\ b[0] &= \cfrac{1}{n-1}\left(Y[n-1]-Y[0]\right) \end{aligned}

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: StatTimeSerAnalysis::DoubleExpForecast
Declared in Dew::Stats::Units::StatTimeSerAnalysis · Dew.Stats/Units.StatTimeSerAnalysis.h · Cross-compiler

Overload 2: void DoubleExpSmooth(TVec *Y, TVec *S, TVec *B, const double Alpha, const double Gamma, double &MSE, const int InitMethod = 0);

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

#NameTypeDescription
1YTVec *Time series data set.
2STVec *Smoothed values (see above equation). Size and complex properties of S are set automatically.
3BTVec *Trend values (see above equation). Size and complex properties of b are set automatically.
4Alphaconst doubleDefines initial estimate for Alpha, returns Alpha which minimizes MSE.
5Gammaconst doubleDefines initial estimate for Gamma, returns Gamma which minimizes MSE.
6MSEdouble &Returns MSE, evaluated for constant Alpha and Gamma.
7InitMethod = 0const intDefines how the initial values for b[0] are calculated.
Declared in Dew::Stats::Units::StatTimeSerAnalysis · Dew.Stats/Units.StatTimeSerAnalysis.h · Cross-compiler