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Time series

Financial Mathematics, Second cycle
1 ali 2 year
first or second
slovenian, english
Hours per week – 1. or 2. semester:

There are no prerequisites.

Content (Syllabus outline)

Introduction: Examples of time series. Trend and seasonality. Autocorrelation function. Mul-
tivariate normal distribution. Strong and week stationarity. Hilbert spaces and prediction.
Introduction to R.
Stationary sequences: Linear processes. ARMA models. Causality and invertibility of ARMA
processes. Infinite order MA 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.
Spectral analysis: Spectral density. Spectral density of ARMA processes. Herglotz theorem.
Nonlinear and nonstationary time series models: ARCH and GARCH models. Moments and stationary distrbutiopn of GARCH process. Exponential GARCH. ARIMA models. SARIMA models. orecasting nonstationary time series.
Statistics for stationary process: Asymptotic results for stationary time series. Estimating trend and seasonality. Nonparametric methods.
Multidimensional time series: stacionarity, multidimensional ARMA and ARIMA models, parameter estimation, forecasting, variance decomposition.


P. J. Brockwell, R. A. Davis: Introduction to Time Series and Forecasting,
2nd edition, Springer, 2002.
C. Chatfield: The Analysis of Time Series: An Introduction, 6th Edition, Chapman & Hall/CRC, 2003.
P.J. Brockwell, R.A. Davis: Time Series: Theory and Methods, Springer, 1991.
W.N. Venables, B.D. Ripley: Modern Applied Statistics with S-Plus, Springer, 1994.
W.N. Shumway, D. Stoffer: Time Series Analysis and Its Applications, Springer, 2006.

Objectives and competences

Time series course isone of fundamental courses of applied statistics with several applications to engineering and economics. Basic concepts of the time series analysis are part of necessary background of any statistical education. They deepen and shed new light on basic notions of statistics.
Since the content is of great practical importance we expect that also specialists from financial practice will present their work experience during the course.

Intended learning outcomes

Knowledge and understanding:
Understanding of statistical applications to economics, modelling of economics and financial data.
In macroeconomic analysis or on energy markets, time series methods are the fundamental forecasting tool. This analysis deepens and sheds new light on basic notions of statistics.
The interplay between application, statistical modelling, economics feedback information, and application stimulation for mathematical reasoning.
Transferable skills:
The skills are directly applicable in finance and insurance. They are also an important tool for the economists.

Learning and teaching methods

Lectures, exercises, homeworks, consultations, seminars


Written exam
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Mihael Perman:
BLEJEC, Matjaž, LOVREČIČ SARAŽIN, Marko, PERMAN, Mihael, ŠTRAUS, Mojca. Statistika. Piran: Gea College, Visoka šola za podjetništvo, 2003. X, 150 str., graf. prikazi, tabele. ISBN 961-6347-43-8. [COBISS-SI-ID 122243328]
PERMAN, Mihael. Order statistics for jumps of normalised subordinators. Stochastic Processes and their Applications, ISSN 0304-4149. [Print ed.], 1993, vol. 46, no. 2, str. 267-281. [COBISS-SI-ID 12236633]
HUZAK, Miljenko, PERMAN, Mihael, ŠIKIĆ, Hrvoje, VONDRAČEK, Zoran. Ruin probabilities and decompositions for general perturbed risk processes. Annals of applied probability, ISSN 1050-5164, 2004, vol. 14, no. 3, str. 1378-1397. [COBISS-SI-ID 13168985]