StatTimeSerAnalysis

MSE, evaluated at minimum.

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: 

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.

TripleExpForecast

Generate 24 random values representing 4 quarters x 6 years = 24, perform smoothing and read Alpha,Beta,Gamma + MSE.

Uses MtxExpr,StatTimeSerAnalysis, Math387;
procedure Example;
var Data,S,b,L: Vector;
    Alpha,Beta,Gamma,MSE: double;
begin
  Data.Size(24,false);
  Data.RandGauss;
  // smooth data, initial alpha = 0.1, beta=0.1, gamma = 0.3
  Alpha := 0.1;
  Beta := 0.1;
  Gamma := 0.3;
  // Period = 4
  MSE := TripleExpSmooth(Data,S,b,L,Alpha,Beta,Gamma,4);
  // results: MSE and MLE estimate for Alpha,Beta,Gamma
end;

#include "MtxExpr.hpp"
#include "Math387.hpp"
#include "StatTimeSerAnalysis.hpp"
void __fastcall Example();
{
  sVector Data,S,b,L;
  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 = TripleExpSmooth(Data,S, b, L, alpha,beta,gamma,4);
  // results: MSE and MLE estimate for Alpha,Beta,Gamma
}

Functions