Exponential Smoothing

The constructor of the ExponentialSmoothingModel class takes two arguments. The first is a VectorT that contains the time series data. The second argument determines the smoothing method that is to be used. It is of type ExponentialSmoothingMethod, and can take on the following values:

For single exponential smoothing models, this is all that is required. The example below creates a single exponential smoothing model for a vector y:

var model1 = new ExponentialSmoothingModel(y, ExponentialSmoothingMethod.Single);

Dim model1 = New ExponentialSmoothingModel(y, ExponentialSmoothingMethod.Single)

let model1 = new ExponentialSmoothingModel(y, ExponentialSmoothingMethod.Single)

For double exponential smoothing models, the TrendEstimator property, of type ExponentialSmoothingTrendEstimator determines how the initial value for the trend is determined. Its possible values are as follows:

The code below creates a double exponential smoothing model that uses the first 2 observations to initialize the trend:

var model2 = new ExponentialSmoothingModel(y, ExponentialSmoothingMethod.Double);
model2.TrendEstimator = ExponentialSmoothingTrendEstimator.Initial2;

Dim model2 = New ExponentialSmoothingModel(y, ExponentialSmoothingMethod.Double)
model2.TrendEstimator = ExponentialSmoothingTrendEstimator.Initial2

let model2 = new ExponentialSmoothingModel(y, ExponentialSmoothingMethod.Double)
model2.TrendEstimator <- ExponentialSmoothingTrendEstimator.Initial2

The Compute method finds the parameter values that minimize the squared error of the forecast.

The parameters of the model can be retrieved through the Parameters collection. The first argument is the smoothing parameter. For double smoothing, the second parameter represents the trend. The members of this collection are of type ParameterT, and can be used to obtain a wide range of information about the computed values, including the standard error, significance tests and confidence intervals. If you only need the values of the parameters, the ParameterValues property can be used.

model2.Fit();
Console.WriteLine("Trend: {0}", model2.Parameters[1].Value);
Console.WriteLine("Std.Err.: {0}", model2.Parameters[1].StandardError);
Console.WriteLine("t: {0}", model2.Parameters[1].Statistic);
Console.WriteLine(model2.ParameterValues);

model2.Fit()
Console.WriteLine("Trend: {0}", model2.Parameters(1).Value)
Console.WriteLine("Std.Err.: {0}", model2.Parameters(1).StandardError)
Console.WriteLine("t: {0}", model2.Parameters(1).Statistic)
Console.WriteLine(model2.ParameterValues)

model2.Fit()
printfn "Trend: %f" model2.Parameters.[1].Value
printfn "Std.Err.: %f" model2.Parameters.[1].StandardError
printfn "t: %f" model2.Parameters.[1].Statistic
printfn "%A" model2.ParameterValues

Once the model has been computed, the Forecast method can then be used to forecast new values. This method has three overloads.

Without arguments, the method returns the one step ahead forecast based on the computed model. With a single argument, it computes a point forecast the specified number of steps ahead. It returns a VectorT that contains the point forecast for the specified number of periods:

var forecast = model2.Forecast(4);

Dim forecast = model2.Forecast(4)

let forecast = model2.Forecast(4)

Reference