1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: :
The course objective is to introduce students to the fundamental concepts and results of time series analysis. Students will be introduced to classical and modern methods in modeling of real-life time series.

COURSE DESCRIPTION AND SYLLABUS:
The following topics will be discussed
1. Introduction (2 weeks) Examples of time series. Trend and seasonality. Autocorrelation function. Multivariate normal distribution.
2. Stationary sequences (5 weeks) Strong and week stationarity. Linear processes. ARMA models. Causality and invertibility of ARMA processes. MA(oo) processes. Partial autocorrelation function. Estimation of autocorrelation function and other parameters. Forecasting stationary time series. Modeling and forecasting for ARMA processes. Asymptotic behavior of the sample mean and the autocorrelation function. Parameter estimation for ARMA processes.
3. Spectral analysis (2 weeks) Spectral density. Periodogram. Spectral density of ARMA processes. Herglotz theorem.
4. Nonstationary and nonlinear time series models (3 weeks) ARIMA and SARIMA models. Nonlinear models. ARCH and GARCH models. Chaotic deterministic time series models.
5. Statistics for stationary process (3 weeks) Asymptotic results for stationary time series. Estimating trend and seasonality. Nonparametric methods.

1. Introduction to Time Series and Forecasting, P. J. Brockwell, R. A. Davis, Springer Verlag, 2002.
2. Time Series: Theory and Methods, P. J. Brockwell, R. A. Davis, Springer Verlag, 1991.
3. Nonlinear Time Series. Nonparametric and Parametric Methods, J. Fan and Q. Yao, Springer Verlag, 2003.
4. Nonparametric Statistics for Stochastic Processes: Estimation and Prediction, D. Bosq, Springer Verlag, 1998.
5. Asymptotic Statistics, A. W. van der Vaart, Cambridge University Press, 1998.
6. Time Series Analysis, J. D. Hamilton, Princeton University Press, 1994.
7. Modelling extremal events. For insurance and finance, P. Embrechts, C. Klueppelberg, T. Mikosch, Springer Verlag, 1997.

Enrollment :
Passed : Markov chains
Passed : Mathematical statistics

Mandatory course - Regular study - Mathematical Statistics