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Time series

Code: 92990
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Bojan Basrak - Lectures
English level:

1,0,0

All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.
Load:

1. komponenta

Lecture typeTotal
Lectures 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
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.
Literature:
  1. P. J. Brockwell, R. A. Davis: Introduction to Time Series and Forecasting
  2. P. J. Brockwell, R. A. Davis: Time Series: Theory and Methods
  3. J. Fan and Q. Yao: Nonlinear Time Series. Nonparametric and Parametric Methods
  4. D. Bosq: Nonparametric Statistics for Stochastic Processes: Estimation and Prediction
  5. A. W. van der Vaart: Asymptotic Statistics
  6. J. D. Hamilton: Time Series Analysis
  7. P. Embrechts, C. Klueppelberg, T. Mikosch: Modelling extremal events. For insurance and finance
Prerequisit for:
Enrollment :
Passed : Markov chains
Passed : Mathematical statistics
3. semester
Izborni predmeti 4 i 5 - Regular study - Financial and Business Mathematics
Consultations schedule: