Publication details
Základy analýzy časových řad
| Title in English | Basics of Time Series Analysis |
|---|---|
| Authors | |
| Year of publication | 2010 |
| Type | Article in Proceedings |
| Conference | Analýza dat 2010/I (Statistické metody pro technologii a výzkum), Ed. K. Kupka |
| MU Faculty or unit | |
| Citation | |
| Field | Applied statistics, operation research |
| 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. |