In statistics, signal processing, pattern recognition, econometrics, mathematical finance, Weather forecasting, Earthquake prediction, Electroencephalography, Control engineering and Communications engineering a time series is a sequence of data points, measured typically at successive time instants spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the Nile River at Aswan. 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. Time series are very frequently plotted via line charts.
Time series data have a natural temporal ordering. This makes time series analysis distinct from other common data analysis problems, in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where the observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for a given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility.)
Methods for time series analyses may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and recently wavelet analysis; the latter include auto-correlation and cross-correlation analysis.
Additionally time series analysis techniques may be divided into parametric and non-parametric methods. The parametric approaches assume that the underlying stationary Stochastic process has a certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving average model). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure.
Additionally methods of time series analysis may be divided into linear and non-linear, univariate and multivariate.
Time series analysis can be applied to:
- real-valued, continuous data
- discrete numeric data
- discrete symbolic data (i.e. sequences of characters, such as letters and words in English language).
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... In time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method ... It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing ... lie in the classical Karhunen (1946)–Loève (1945, 1978) spectral decomposition of time series and random fields and in the Mañé (1981)–Takens (1981) embedding theorem ...
... SSA (or M-SSA) is a natural extension of SSA to for analyzing multivariate time series, where the size of different univariate series does not have to be the same ... The trajectory matrix of multi-channel time series consists of stacked trajectory matrices of separate times series ... System of series can be forecasted analogously to SSA recurrent and vector algorithms (Golyandina and Stepanov, 2005) ...
... In an additive time-series model, the seasonal component is estimated as S = Y – (T+C+I) Where S is for Seasonal values Y is for actual data values of the time-series T is for trend values C is for cyclical ... In a multiplicative time-series model, the seasonal component is expressed in terms of ratio and percentage as Seasonal effect = (T*S*C*I)/( T*C*I)*100 = Y/(T*C*I )*100 However in practice the ... The deseasonalized time-series data will have only trend (T) cyclical(C) and irregular (I) components and is expressed as Multiplicative model Y/S*100 =( T*S*C*I)/S*100 = (T ...
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