Course for international guest/part time students
- Faculty
- Faculty of Science
- Organization
- TTK Department of Probability Theory and Statistics
- Code
- idosor1u0um17em
- Title
- Analysis of time series 1 (l)
- Usual semester
- Spring
- Published semester
- 2025/26/2
- ECTS
- 3
- Language
- hu
- Learning outcomes
- Knowledge: getting familiar with the modern notions of time series Ability: to understand and use the theory of time series Attitude: the need to extend the mathematical knowledge, to gain new analytic and applied programming skills Autonomy and Responsibility: based on the gained knowledge in time series, the students are able to decide which tools are the most suitable to solve applied problems
- Course content
- Basic concepts of stationary processes. Weak, strong, k-order stationarity, ergodicity. Autocovariance, autocorrelation, partial autocorrelation, dynamic copulas. Fourier production of a stationary time series. Representation of a stationary process with an orthogonal stochastic measure. Spectral density function, Herglotz theorem. AR(p), MA(q), ARIMA(p,d,q). Existence of the stationary solution. Vector AR processes. Nonlinear processes, ARCH. Lyapunov exponent, the existence of a stationary solution of a general stochastic recursion equation, the Kesten-Vervaat-Goldie theorem. GARCH processes. Bilinear processes. Random coefficient AR and the SETAR model. Estimation theory of time series. Estimation of expected value. Estimation of the autocorrelation function. Periodogram and its properties. Estimation of the spectral density function, windowing. Pre-whitening, CAT criteria.
- Assessment method
- exam
- Bibliography
- lecture notes