Course type: elective
Lecturer: Mihael Perman, Ph.D., Associate Professor
 

For the timeline see Curriculum.

Prerequisites:

• Regular inscription.

Content (Syllabus outline):

Introduction: Examples of time series. Trend and seasonality. Autocorrelation function. Multivariate 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.

Periodogram.

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.

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:

Understanding of statistical applications to economics, modelling of economics and financial data.