decompose a time series into level, residuals, and potentially trend and seasonal components - Maple Help

Online Help

All Products    Maple    MapleSim

Home : Support : Online Help : Statistics : Time Series Analysis Package : TimeSeriesAnalysis/Decomposition

TimeSeriesAnalysis[Decomposition] - decompose a time series into level, residuals, and potentially trend and seasonal components

Calling Sequence

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:=TimeSeries41.7,24.0,32.3,37.3,46.2,29.3,36.5,43.0,48.9,31.2,37.7,40.4,51.2,31.9,41.0,43.8,55.6,33.9,42.1,45.6,59.8,35.2,44.3,47.9,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:=< an ETS(M,A,M) model >


Create the decomposition. Since this is a model with both trend and seasonal components, you get four data sets.


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.


See Also




Hyndman, R.J. and Athanasopoulos, G. (2013) Forecasting: principles and practice. 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.

Download Help Document

Was this information helpful?

Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam