number of parameters of an exponential smoothing model
Exponential smoothing model
The NumberOfParameters command returns the number of fixed or optimizable parameters that occur in model.
This includes the initial values for states such as ℓt 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.
An A,N,N model has two parameters: α and l0.
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.
model ≔ ExponentialSmoothingModel⁡A,N,A:
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.
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.
The TimeSeriesAnalysis[NumberOfParameters] command was introduced in Maple 18.
For more information on Maple 18 changes, see Updates in Maple 18.
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