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Metody pro periodické a nepravidelné časové řady
Title: Methods for periodic and irregular time series Author: Mgr. Tomáš Hanzák Department: Department of Probability and Mathematical Statistics Supervisor: Prof. RNDr. Tomáš Cipra, DrSc. Abstract: The thesis primarily deals with modifications of exponential smoothing type methods for univariate time series with periodicity and/or certain types of irregularities. A modified Holt method for irregular times series robust to the problem of "time-close" observations is suggested. The general concept of seasonality modeling is introduced into Holt-Winters method including a linear interpolation of seasonal indices and usage of trigonometric functions as special cases (the both methods are applicable for irregular observations). The DLS estimation of linear trend with seasonal dummies is investigated and compared with the additive Holt-Winters method. An autocorrelated term is introduced as an additional component in the time series decomposition. The suggested methods are compared with the classical ones using real data examples and/or simulation studies. Keywords: Discounted Least Squares, Exponential smoothing, Holt-Winters method, Irregular observations, Time series periodicityNázev práce: Metody pro periodickĂ© a nepravidelnĂ© ÄŤasovĂ© Ĺ™ady Autor: Mgr. Tomáš Hanzák Katedra: Katedra pravdÄ›podobnosti a matematickĂ© statistiky VedoucĂ disertaÄŤnĂ práce: Prof. RNDr. Tomáš Cipra, DrSc. Abstrakt: DisertaÄŤnĂ práce se primárnÄ› zabĂ˝vá modifikacemi metod typu exponenciálnĂ vyrovnávánĂ pro jednorozmÄ›rnĂ© ÄŤasovĂ© Ĺ™ady s periodicitou a/nebo urÄŤitĂ˝mi typy nepravidelnostĂ. Je navrĹľena modifikovaná Holtova metoda pro nepravidelnĂ© ÄŤasovĂ© Ĺ™ady robustnĂ vĹŻÄŤi problĂ©mu "ÄŤasovÄ› blĂzkĂ˝ch" pozorovánĂ. ObecnĂ˝ koncept modelovánĂ sezĂłnnosti je zaveden do Holtovy-Wintersovy metody vÄŤetnÄ› lineárnĂ interpolace sezĂłnnĂch indexĹŻ a pouĹľitĂ goniometrickĂ˝ch funkcĂ jako speciálnĂch pĹ™ĂpadĹŻ (obÄ› metody jsou pouĹľitelnĂ© pro nepravidelná pozorovánĂ). Je zkoumán DLS odhad regrese s lineárnĂm trendem a sezĂłnnĂmi indexy a metoda je porovnána s aditivnĂ Holtovou-Wintersovou metodou. AutokorelovanĂ˝ ÄŤlen je navrĹľen jako dalšà sloĹľka dekompozice ÄŤasovĂ© Ĺ™ady. NavrĹľenĂ© metody jsou porovnávány s klasickĂ˝mi na reálnĂ˝ch datech a/nebo prostĹ™ednictvĂm simulaÄŤnĂch studiĂ. KlĂÄŤová slova: DiskontovanĂ© nejmenšà čtverce, exponenciálnĂ vyrovnávánĂ, Holtova-Wintersova metoda, nepravidelná pozorovánĂ, periodicita ÄŤasovĂ˝ch Ĺ™adKatedra pravdÄ›podobnosti a matematickĂ© statistikyDepartment of Probability and Mathematical StatisticsFaculty of Mathematics and PhysicsMatematicko-fyzikálnĂ fakult