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TimeSeriesAnalysis

 NumberOfParameters
 number of parameters of an exponential smoothing model

 Calling Sequence NumberOfParameters(model)

Parameters

 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 ${\mathrm{\ell }}_{t}$ and, if applicable, ${b}_{t}$ and ${s}_{t}$, but it does not include $\mathrm{\sigma }$ or, for example, $\mathrm{period}$ or $\mathrm{trend}$. It also doesn't include parameters that don't actually occur in the model; for example, $\mathrm{\beta }$ does not occur in an $\left(A,N,N\right)$ 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 $\mathrm{undefined}$.

Examples

 > $\mathrm{with}\left(\mathrm{TimeSeriesAnalysis}\right):$

An $\left(A,N,N\right)$ model has two parameters: $\mathrm{\alpha }$ and $\mathrm{l0}$.

 > $\mathrm{NumberOfParameters}\left(\mathrm{ExponentialSmoothingModel}\left(A,N,N\right)\right)$
 ${2}$ (1)

An $\left(A,N,A\right)$ model additionally has $\mathrm{\gamma }$ 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.

 > $\mathrm{model}≔\mathrm{ExponentialSmoothingModel}\left(A,N,A\right):$
 > $\mathrm{NumberOfParameters}\left(\mathrm{model}\right)$
 ${\mathrm{undefined}}$ (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.

 > $\mathrm{SetParameter}\left(\mathrm{model},\mathrm{period}=12\right)$
 > $\mathrm{NumberOfParameters}\left(\mathrm{model}\right)$
 ${14}$ (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.