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Title in English Introduction to time series
Authors

VESELÝ Vítězslav

Year of publication 2004
Type Article in Proceedings
Conference Proceedings ANALÝZA DAT'2003/II
MU Faculty or unit

Faculty of Economics and Administration

Citation
Field General mathematics
Keywords time series; data analysis; modeling; parameter estimation
Description TIME SERIES AS A SPECIAL CASE OF RANDOM PROCESS: definition, examples of typical processes, consistent system of distribution functions, moment functions (mean, autocovariance and autocorrelation function), strict and weak stationarity, white noise, properties of the autocovariance and autocorrelation function, estimated autocovariance and autocorrelation function, the algebraic and statistical interpretation of this estimate. THE BEST LINEAR PREDICTION: the principle of orthogonal projection, Durbin-Levinson Algorithm, Innovations Algorithm. DECOMPOSITION MODEL FOR TIME SERIES ANALYSIS: choice of the model and its identification, the Box-Cox transformation, identification of periodic components (discrete Fourier transform, periodogram, periodicity tests), common methods for estimation of the deterministic components comprising both parametrized methods (linear regression) and nonparametric methods (digital filtration). BOX-JENKINS METHODOLOGY: (S)AR(I)MA models, causality and invertibility, identification, parameter estimation and verification of models.
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