decompose a time series into level, residuals, and potentially trend and seasonal components
Decomposition(model, ts, extraparameters)
Exponential smoothing model
Time series consisting of a single data set
(optional) table of parameter values
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.
Consider the following time series. It represents international tourist visitor nights in Australia.
ts := TimeSeries(<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>, startdate="2005", frequency=quarterly, header="Visitor nights");
ts≔Time seriesVisitor nights24 rows of data:2005-Jan-01 - 2010-Oct-01
Fit an exponential smoothing model to it.
esm := ExponentialSmoothingModel(ts);
Create the decomposition. Since this is a model with both trend and seasonal components, you get four data sets.
dc := Decomposition(esm, ts);
dc≔Time seriesVisitor nights (residuals), ..., Visitor nights (seasonal)24 rows of data:2005-Jan-01 - 2010-Oct-01
Since the error and seasonal components are multiplicative, it makes sense to display them together. The trend and level components are displayed separately.
TimeSeriesPlot(dc, 'split' = [[dc, 1, 4], [dc, 2], [dc, 3]], 'color = red .. blue');
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.
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