How to find optimal parameters for Holt-Winters forecasting model?

Let provide you with an overview of a commonly used optimization method called the grid search algorithm, which you can implement in C/C++ to find optimal parameters for the Holt-Winters model. The grid search algorithm is a simple but effective approach for parameter optimization.

Here's how the grid search algorithm works:

Define a range of values for each parameter you want to optimize. For example, if you have three parameters (alpha, beta, and gamma) for the Holt-Winters model, you can define a range of values for each parameter.

Create a grid or set of combinations by taking all possible combinations of parameter values within the defined ranges. This grid represents all the parameter combinations that will be evaluated.

For each combination of parameter values, evaluate the performance of the Holt-Winters model using these parameters. Typically, you would use a performance metric such as mean squared error (MSE) or root mean squared error (RMSE) to measure the forecasting error.

Select the combination of parameter values that results in the lowest forecasting error. This combination represents the optimal parameters for your Holt-Winters model.

Optionally, you can refine your search by using a smaller grid centered around the optimal parameters you found in the previous step. This can help you fine-tune the parameters and achieve even better results.

Here's a pseudo-code representation of the grid search algorithm in C++:

// Define ranges for each parameter

double alphaMin = 0.0;

double alphaMax = 1.0;

double betaMin = 0.0;

double betaMax = 1.0;

double gammaMin = 0.0;

double gammaMax = 1.0;

// Define step size for each parameter

double alphaStep = 0.1;

double betaStep = 0.1;

double gammaStep = 0.1;

// Define variables to store optimal parameters and error

double optimalAlpha, optimalBeta, optimalGamma;

double minError = std::numeric_limits::max();

// Perform grid search

for (double alpha = alphaMin; alpha

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