 Decomposition of time series

The decomposition of time series is a statistical method that deconstructs a time series into notional components. There are two principal types of decomposition which are outlined below.
Contents
Decomposition based on rates of change
This is an important technique for all types of time series analysis, especially for seasonal adjustment.^{[1]} It seeks to construct, from an observed time series, a number of component series (that could be used to reconstruct the original by additions or multiplications) where each of these has a certain characteristic or type of behaviour. For example, monthly or quarterly economic time series are usually decomposed into:
 the Trend Component T_{t} that reflects the long term progression of the series (secular variation)
 the Cyclical Component C_{t} that describes repeated but nonperiodic fluctuations, possibly caused by the economic cycle
 the Seasonal Component S_{t} reflecting seasonality (Seasonal variation)
 the Irregular Component I_{t} (or "noise") that describes random, irregular influences. Compared to the other components it represents the residuals of the time series.
An example of statistical software for this type of decomposition is the program BV4.1 that is based on the socalled Berlin procedure.
Kendall^{[2]} shows an example of a decomposition into smooth, seasonal and irregular factors for a set of data containing values of the monthly aircraft miles flown by UK airlines.
Decomposition based on predictability
The theory of time series analysis make use of the idea of decomposing a times series into deterministic and nondeterministic components (or predictable and unpredictable components).^{[1]} See Wold's theorem and Wold decomposition.
See also
 Hilbert–Huang transform
 Stochastic drift
References
 ^ ^{a} ^{b} Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0199206139
 ^ Kendall, Sir M.G. (1976) TimeSeries, Second Edition, Charles Griffin & Co.. ISBN 0852642415 (Fig. 5.1)
Categories: Time series analysis
Wikimedia Foundation. 2010.
Look at other dictionaries:
Time series — Time series: random data plus trend, with best fit line and different smoothings In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at … Wikipedia
Seriesparallel graph — In graph theory, series parallel graphs are graphs with two distinguished vertices called terminals , formed recursively by two simple composition operations. They can be used to model series and parallel electric circuits.Definition and… … Wikipedia
Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… … Wikipedia
Wold decomposition — In operator theory, the Wold decomposition, or Wold von Neumann decomposition, is a classification theorem for isometric linear operators on a given Hilbert space. It states that any isometry is a direct sums of copies of the unilateral shift and … Wikipedia
Fourier series — Fourier transforms Continuous Fourier transform Fourier series Discrete Fourier transform Discrete time Fourier transform Related transforms … Wikipedia
Firsthittingtime model — In statistics, first hitting time models are a sub class of survival models. The first hitting time, also called first passage time, of a set A with respect to an instance of a stochastic process is the time until the stochastic process first… … Wikipedia
Empirical Mode Decomposition — EMD (англ. Empirical Mode Decomposition) метод разложения сигналов на функции, которые получили название «эмпирических мод». Метод EMD представляет собой итерационную вычислительную процедуру, в результате которой исходные данные… … Википедия
Tree decomposition — A graph with eight vertices, and a tree decomposition of it onto a tree with six nodes. Each graph edge connects two vertices that are listed together at some tree node, and each graph vertex is listed at the nodes of a contiguous subtree of the… … Wikipedia
Modular decomposition — In graph theory, the modular decomposition is a decomposition of an undirected graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph. Unlike connected components, however, one module can… … Wikipedia
Functional decomposition — refers broadly to the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed (i.e., recomposed) from those parts by function composition. In general, this process of … Wikipedia