The Decomposition command takes a time series and decomposes it according to an exponential smoothing model.

It returns a time series with two, three, or four data sets in it: one for the level, one for the residuals, if the model has a trend component then one data set for the trends, and if the model has a seasonal component then a data set for the seasonal component.

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

$\mathrm{ts}≔\mathrm{TimeSeries}\left(⟨41.7\,24.0\,32.3\,37.3\,46.2\,29.3\,36.5\,43.0\,48.9\,31.2\,37.7\,40.4\,51.2\,31.9\,41.0\,43.8\,55.6\,33.9\,42.1\,45.6\,59.8\,35.2\,44.3\,47.9⟩\,\mathrm{startdate}=''2005''\,\mathrm{frequency}=\mathrm{quarterly}\,\mathrm{header}=''Visitor\; nights''\right)$

$\mathrm{ts}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Visitor\; nights}\\ \mathrm{24\; rows\; of\; data:}\\ \mathrm{2005-Jan-01\; -\; 2010-Oct-01}\end{array}\right]$

$\mathrm{esm}≔\mathrm{ExponentialSmoothingModel}\left(\mathrm{ts}\right)$

$\mathrm{esm}≔\mathrm{<\; an\; ETS(M,A,M)\; model\; >}$

$\mathrm{dc}≔\mathrm{Decomposition}\left(\mathrm{esm}\&comma;\mathrm{ts}\right)$

$\mathrm{dc}≔\left[\begin{array}{c}\mathrm{Time\; series}\\ \mathrm{Visitor\; nights\; (residuals),\; ...,\; Visitor\; nights\; (seasonal)}\\ \mathrm{24\; rows\; of\; data:}\\ \mathrm{2005-Jan-01\; -\; 2010-Oct-01}\end{array}\right]$

$\mathrm{TimeSeriesPlot}\left(\mathrm{dc}\&comma;'\mathrm{split}'=\left[\left[\mathrm{dc}\&comma;1\&comma;4\right]\&comma;\left[\mathrm{dc}\&comma;2\right]\&comma;\left[\mathrm{dc}\&comma;3\right]\right]\&comma;'\mathrm{color}=\mathrm{red}..\mathrm{blue}'\right)$

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[Decomposition] command was introduced in Maple 18.

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