/**
* For the given value of the alpha smoothing constant, returns the best fit model where the value
* of the beta (trend) smoothing constant is between betaMin and betaMax. This method will
* continually try to refine the estimate of beta until a tolerance of less than betaTolerance is
* achieved.
*
* <p>Note that the descriptions of the parameters below include a discussion of valid values.
* However, since this is a private method and to help improve performance, we don't provide any
* validation of these parameters. Using invalid values may lead to unexpected results.
*
* @param dataSet the data set for which a best fit model is required.
* @param alpha the (fixed) value of the alpha smoothing constant to use for the best fit model.
* @param betaMin the minimum value of the beta (trend) smoothing constant accepted in the
* resulting best fit model. Must be greater than (or equal to) 0.0 and less than betaMax.
* @param betaMax the maximum value of the beta (trend) smoothing constant accepted in the
* resulting best fit model. Must be greater than betaMin and less than (or equal to) 1.0.
* @param betaTolerance the tolerance within which the beta value is required. Must be
* considerably less than 1.0. However, note that the smaller this value the longer it will
* take to diverge on a best fit model.
*/
private static TripleExponentialSmoothingModel findBestBeta(
DataSet dataSet, double alpha, double betaMin, double betaMax, double betaTolerance) {
int stepsPerIteration = 10;
if (betaMin < 0.0) betaMin = 0.0;
if (betaMax > 1.0) betaMax = 1.0;
TripleExponentialSmoothingModel bestModel =
new TripleExponentialSmoothingModel(alpha, betaMin, 0.0);
bestModel.init(dataSet);
double initialMSE = bestModel.getMSE();
boolean betaImproving = true;
double betaStep = (betaMax - betaMin) / stepsPerIteration;
double beta = betaMin + betaStep;
for (; beta <= betaMax || betaImproving; ) {
TripleExponentialSmoothingModel model = new TripleExponentialSmoothingModel(alpha, beta, 0.0);
model.init(dataSet);
if (model.getMSE() < bestModel.getMSE()) bestModel = model;
else betaImproving = false;
beta += betaStep;
if (beta > 1.0) betaImproving = false;
}
// If we're making progress, then try to refine the beta estimate
if (bestModel.getMSE() < initialMSE && betaStep > betaTolerance) {
// Can this be further refined - improving efficiency - by
// only searching in the range beta-betaStep/2 to
// beta+betaStep/2 ?
return findBestBeta(
dataSet,
bestModel.getAlpha(),
bestModel.getBeta() - betaStep,
bestModel.getBeta() + betaStep,
betaTolerance);
}
return bestModel;
}
