The Initialize command initializes the optimization process run by Optimize for finding suitable parameters and initial conditions for a specialized Exponential smoothing model.

It returns a table, indexed by the names of parameters or initial conditions. The value corresponding to an index is the number that that parameter or initial condition will be initialized to during the optimization process.

Parameters that are fixed beforehand are not given in the resulting table.

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

$\mathrm{ts}≔\mathrm{TimeSeries}\left(\left[1.8\,3.4\,2.1\,2.9\,2.4\,2.9\,2.5\,3.1\right]\,\mathrm{period}=2\right)$

$\mathrm{ts}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{data\; set}\\ \mathrm{8\; rows\; of\; data:}\\ \mathrm{2016\; -\; 2023}\end{array}\right]$

$\mathrm{models}≔\mathrm{Specialize}\left(\mathrm{ExponentialSmoothingModel}\left(\right)\,\mathrm{ts}\right)$

$\mathrm{models}≔\left[\mathrm{<\; an\; ETS(A,A,A)\; model\; >}\&comma;\mathrm{<\; an\; ETS(A,A,N)\; model\; >}\&comma;\mathrm{<\; an\; ETS(A,Ad,A)\; model\; >}\&comma;\mathrm{<\; an\; ETS(A,Ad,N)\; model\; >}\&comma;\mathrm{<\; an\; ETS(A,N,A)\; model\; >}\&comma;\mathrm{<\; an\; ETS(A,N,N)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,A,A)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,A,M)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,A,N)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,Ad,A)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,Ad,M)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,Ad,N)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,M,M)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,M,N)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,Md,M)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,Md,N)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,N,A)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,N,M)\; model\; >}\&comma;\mathrm{<\; an\; ETS(M,N,N)\; model\; >}\right]$

$\mathrm{initialization\_tables}≔\mathrm{map}\left(\mathrm{Initialize}\&comma;\mathrm{models}\&comma;\mathrm{ts}\right)$

$\mathrm{initialization\_tables}≔\left[table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;s=\left[\begin{array}{c}\mathrm{-0.375000000000000}\\ 0.512500000000000\end{array}\right]\&comma;\mathrm{b0}=0.0351190476190477\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{l0}=2.41071428571428\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;\mathrm{b0}=0.0773809523809526\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{l0}=2.28928571428571\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;s=\left[\begin{array}{c}\mathrm{-0.375000000000000}\\ 0.512500000000000\end{array}\right]\&comma;\mathrm{b0}=0.0351190476190477\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{\phi }=0.978\&comma;\mathrm{l0}=2.41071428571428\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;\mathrm{b0}=0.0773809523809526\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\phi }=0.978\&comma;\mathrm{l0}=2.28928571428571\right]\right)\&comma;table\left(\left[s=\left[\begin{array}{c}\mathrm{-0.381250000000000}\\ 0.518750000000000\end{array}\right]\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{l0}=2.56875000000000\right]\right)\&comma;table\left(\left[\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{l0}=2.63750000000000\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;s=\left[\begin{array}{c}\mathrm{-0.375000000000000}\\ 0.512500000000000\end{array}\right]\&comma;\mathrm{b0}=0.0351190476190477\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{l0}=2.41071428571428\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;s=\left[\begin{array}{c}0.867877797325560\\ 1.22504867885882\end{array}\right]\&comma;\mathrm{b0}=0.0471683829401126\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{l0}=2.31025399169193\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;\mathrm{b0}=0.0773809523809526\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{l0}=2.28928571428571\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;s=\left[\begin{array}{c}\mathrm{-0.375000000000000}\\ 0.512500000000000\end{array}\right]\&comma;\mathrm{b0}=0.0351190476190477\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{\phi }=0.978\&comma;\mathrm{l0}=2.41071428571428\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;s=\left[\begin{array}{c}0.866337320827478\\ 1.22045629439217\end{array}\right]\&comma;\mathrm{b0}=0.0474547670432530\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{\phi }=0.978\&comma;\mathrm{l0}=2.31594155793230\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;\mathrm{b0}=0.0773809523809526\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\phi }=0.978\&comma;\mathrm{l0}=2.28928571428571\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;s=\left[\begin{array}{c}0.866411911381189\\ 1.22047262484913\end{array}\right]\&comma;\mathrm{b0}=1.02015799136523\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{l0}=2.30027768778461\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;\mathrm{b0}=1.03693927243796\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{l0}=2.19796110842741\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;s=\left[\begin{array}{c}0.866411911381189\\ 1.22047262484913\end{array}\right]\&comma;\mathrm{b0}=1.02015799136523\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{\phi }=0.978\&comma;\mathrm{l0}=2.30027768778461\right]\right)\&comma;table\left(\left[\mathrm{\beta }=\frac{1}{10}\&comma;\mathrm{b0}=1.03693927243796\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\phi }=0.978\&comma;\mathrm{l0}=2.19796110842741\right]\right)\&comma;table\left(\left[s=\left[\begin{array}{c}\mathrm{-0.380989109177452}\\ 0.519010890822548\end{array}\right]\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{l0}=2.55701180603960\right]\right)\&comma;table\left(\left[s=\left[\begin{array}{c}0.869490084711176\\ 1.21615190130110\end{array}\right]\&comma;\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{\gamma }=\frac{1}{100}\&comma;\mathrm{l0}=2.51642347897302\right]\right)\&comma;table\left(\left[\mathrm{\alpha }=\frac{1}{2}\&comma;\mathrm{l0}=2.58767635294028\right]\right)\right]$

$\mathrm{map}\left(\mathrm{print}\&comma;\mathrm{map}\left(\left[\mathrm{indices}\right]\&comma;\mathrm{initialization\_tables}\&comma;'\mathrm{nolist}'\right)\right)\&colon;$

$\left[\mathrm{\beta }\&comma;s\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;s\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{\phi }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\phi }\&comma;\mathrm{l0}\right]$

$\left[s\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\alpha }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;s\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;s\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;s\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{\phi }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;s\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{\phi }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\phi }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;s\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;s\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{\phi }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\beta }\&comma;\mathrm{b0}\&comma;\mathrm{\alpha }\&comma;\mathrm{\phi }\&comma;\mathrm{l0}\right]$

$\left[s\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{l0}\right]$

$\left[s\&comma;\mathrm{\alpha }\&comma;\mathrm{\gamma }\&comma;\mathrm{l0}\right]$

$\left[\mathrm{\alpha }\&comma;\mathrm{l0}\right]$

$\mathrm{map}\left(x\mapsto x\left[\mathrm{l0}\right]\&comma;\mathrm{initialization\_tables}\right)$

$\left[2.41071428571428\&comma;2.28928571428571\&comma;2.41071428571428\&comma;2.28928571428571\&comma;2.56875000000000\&comma;2.63750000000000\&comma;2.41071428571428\&comma;2.31025399169193\&comma;2.28928571428571\&comma;2.41071428571428\&comma;2.31594155793230\&comma;2.28928571428571\&comma;2.30027768778461\&comma;2.19796110842741\&comma;2.30027768778461\&comma;2.19796110842741\&comma;2.55701180603960\&comma;2.51642347897302\&comma;2.58767635294028\right]$

$\mathrm{map}\left(x\mapsto x\left[\mathrm{\alpha }\right]\&comma;\mathrm{initialization\_tables}\right)$

$\left[\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\&comma;\frac{1}{2}\right]$

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[Initialize] command was introduced in Maple 18.

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