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TimeSeriesAnalysis

  

NumberOfParameters

  

number of parameters of an exponential smoothing model

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

NumberOfParameters(model)

Parameters

model

-

Exponential smoothing model

Description

• 

The NumberOfParameters command returns the number of fixed or optimizable parameters that occur in model.

• 

This includes the initial values for states such as t and, if applicable, bt and st, but it does not include σ or, for example, period or trend. It also doesn't include parameters that don't actually occur in the model; for example, β does not occur in an A,N,N model. (Commands such as GetParameters will still return these parameters, but they are set to their default value.)

• 

If a model is not specialized (see the Specialize command), then its number of parameters is not yet determined. In that case, NumberOfParameters will return undefined.

Examples

withTimeSeriesAnalysis:

An A,N,N model has two parameters: α and l0.

NumberOfParametersExponentialSmoothingModelA,N,N

2

(1)

An A,N,A model additionally has γ and one initial value for s for every time period within one season. However, the initial values for s are constrained: their sum needs to be 0 for additive seasonality, or equal to the period for multiplicative seasonality. This reduces the number of free parameters by one.

modelExponentialSmoothingModelA,N,A:

NumberOfParametersmodel

undefined

(2)

The period is not yet set, so the number of parameters is not determined. Once we do set it, we get a well-defined answer.

SetParametermodel,period=12

NumberOfParametersmodel

14

(3)

References

  

Hyndman, R.J. and Athanasopoulos, G. (2013) Forecasting: principles and practice. http://otexts.org/fpp/. Accessed on 2013-10-09.

  

Hyndman, R.J., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008) Forecasting with Exponential Smoothing: The State Space Approach. Springer Series in Statistics. Springer-Verlag Berlin Heidelberg.

Compatibility

• 

The TimeSeriesAnalysis[NumberOfParameters] command was introduced in Maple 18.

• 

For more information on Maple 18 changes, see Updates in Maple 18.

See Also

TimeSeriesAnalysis

TimeSeriesAnalysis[GetParameter]

TimeSeriesAnalysis[GetParameters]

TimeSeriesAnalysis[SetParameter]

 


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