Time Series

Subject description

Introduction: Examples of time series. Trend and seasonality. Autocorrelation function. Strong and week stationarity. Prediction.

Stationary sequences: linear processes. ARMA models. Causality and invertibility of ARMA processes. Infinite order MA processes. Properties. Autocorrelation function. Partial autocorrelation function.. Forecasting stationary time series.

Modeling and forecasting for ARMA processes.. Parameter estimation, diagnostics, forecasting.

Multidimensional time series: stacionarity, multidimensional ARMA and ARIMA models, parameter estimation, forecasting, variance decomposition.

The subject is taught in programs

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.

Teaching and learning methods

Lectures, exercises, homeworks, consultations, seminars

Part of the pedagogical process will be carried out with the help of ICT technologies and the opportunities they offer.

Expected study results

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.

Basic sources and literature

  • 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.

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E:  dekanat@fe.uni-lj.si T:  01 4768 411