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

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

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.
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$\mathrm{model}\u2254\mathrm{ExponentialSmoothingModel}\left(A\,N\,A\right)\:$

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$\mathrm{NumberOfParameters}\left(\mathrm{model}\right)$

${\mathrm{undefined}}$
 (2) 
The period is not yet set, so the number of parameters is not determined. Once we do set it, we get a welldefined answer.
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$\mathrm{SetParameter}\left(\mathrm{model}\,\mathrm{period}=12\right)$

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$\mathrm{NumberOfParameters}\left(\mathrm{model}\right)$
