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The decomposition of time series is a statistical task that deconstructs a time series into several components, each representing one of the underlying categories of patterns. [1] There are two principal types of decomposition, which are outlined below.
Time series analysis comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series forecasting is the use of a model to predict future values based on previously observed values.
Seasonal adjustment or deseasonalization is a statistical method for removing the seasonal component of a time series.It is usually done when wanting to analyse the trend, and cyclical deviations from trend, of a time series independently of the seasonal components.
The Hodrick–Prescott filter (also known as Hodrick–Prescott decomposition) is a mathematical tool used in macroeconomics, especially in real business cycle theory, to remove the cyclical component of a time series from raw data.
For an additive decomposition of a monthly time series, for example, the algorithm follows the following pattern: An initial estimate of the trend is obtained by calculating centered moving averages for 13 observations (from t − 6 {\displaystyle t-6} to t + 6 {\displaystyle t+6} ).
According to Wold's decomposition theorem, [4] [5] [6] the ARMA model is sufficient to describe a regular (a.k.a. purely nondeterministic [6]) wide-sense stationary time series, so we are motivated to make such a non-stationary time series stationary, e.g., by using differencing, before we can use ARMA.
The Berlin procedure (BV) is a mathematical procedure for time series decomposition and seasonal adjustment of monthly and quarterly economic time series. The mathematical foundations of the procedure were developed in 1960's at Technische Universität Berlin and the German Institute for Economic Research (DIW).
The secular variation of a time series is its long-term, non-periodic variation (see Decomposition of time series).Whether a variation is perceived as secular or not depends on the available timescale: a variation that is secular over a timescale of centuries may be a segment of what is, over a timescale of millions of years, a periodic variation.