M9121 Time Series I

Faculty of Science
Autumn 2001
Extent and Intensity
2/0/0. 2 credit(s). Type of Completion: z (credit).
Teacher(s)
doc. RNDr. Vítězslav Veselý, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Vítězslav Veselý, CSc.
Prerequisites (in Czech)
NOW( MA122 Time Series II ) && ( M7110 Statistics I || M5300 Statistics || M5301 Statistics I ) && ((( M5170 Mathematical Programming || M6170 Complex Analysis ) && M6150 Linear Functional Analysis I ) || M4140 Selected Topic in Math.Anal. )
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Random process: definition, examples of typical processes, consistent system of distribution functions, Kolmogorov theorem, gaussian process, moment characteristics (mean, autocovariance and autocorrelation function), strict and weak stationarity, white noise, ergodicity, special cases of stationary random processes, properties of the autocovariance and autocorrelation function, estimated autocovariance and autocorrelation function, the algebraic and statistical interpretation of this estimate.
Decomposition model in time series analysis: choice of the model and its identification, the Box-Cox transformation, common methods for estimation of the deterministic components comprising both parametric methods (polynomial regression, growth curves etc.) and nonparametric methods (digital filtration, exponential weighting, spline and kernel smoothing, wavelet shrinkage etc.), randomness tests.
Identification of the periodic components: the small trend method, moving average method, the simultaneous estimate of the trend and seasonal component using linear regression, discrete Fourier transform, periodogram, periodicity tests.
Note: Computer-aided exercises are supported by the system MATLAB.
See http://www.math.muni.cz/~vesely/educ/cr1sylle.ps for more details.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
General note: Současně s tímto předmětem je potřeba zapsat si v podzimnim semestru 2001 také předmět Časové řady II (MA122), který byl přesunut z jarního semestru.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~vesely/educ_cz.html#cas_rady
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2000, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2001, recent)
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