Time series

elective courses

The course presents probabilistic and statistical theory for modelling time series data and forecasting. There is particular emphasis on the Box-Jenkins method of ARIMA processes, also further developments; GARCH modelling, cointegration and neural networks are also considered. The R programming language is used for implementation.

The course presents probabilistic and statistical theory for modelling time series data and forecasting. There is particular emphasis on the Box-Jenkins method of ARIMA processes, also further developments; GARCH modelling, cointegration and neural networks are also considered. The topics are:

1) Time series decomposition - trend, seasonal, stationary components: Lag operators, difference equations, Holt-Winters filtering.

2) Linear time series models: MA, AR, ARMA, ARIMA, generating polynomials, autocovariance, autocorrelation.

3) Estimating the mean, autocovariance and autocorrelation for a linear stationary time series.

4) Prediction: linear predictors and projections, the Durbin Levinson and Innovations algorithms large numbers of observations. Partial correlation. Computing the ACVF of an ARMA.

5) Estimation for the ARMA model: Yule-Walker equations, Burg's algorithm, Innovations, Hannan-Rissanen, Maximum Likelihood and Least Squares, Order selection.

6) ARCH and GARCH models.

7) Spectral Analysis, spectral representation of a time series, Orthogonal Increment Process, Interpolation and Detection.

8) Estimating the Spectral Density.

9) Multivariate Time Series and Granger causality..

10) Cointegration

11) The Kalman Filter

12) Neural networks in Time Series

The methods are implemented using R.

Brockwell P. J. and Davis R. A. (1987 or more recent 2009 edition) Time Series: Theory and Methods, Springer-Verlag, New York.

Tsay R. (2002 or more recent 2010 edition) Analysis of Financial Time Series, John Wiley & Sons Inc., New York.

Noble, J.M. Course notes, available on the course home page

https://www.mimuw.edu.pl/~noble/courses/TimeSeries/

Knowledge and skills:

1) Knows the basics of time series modelling; trend, seasonal, stationary components:

2) Can implement Holt-Winters filtering.

3) Knows the basic stationary time series models (ARIMA, ARCH-GARCH)

4) Can estimate parameters of a Time Series model and use the model for prediction.

5) Knows the basic algorithms (Durbin Levinson,Innovations algorithms

6) Knows about spectral analysis of time series, spectral representation of a time series, Orthogonal Increment Process and applications to Interpolation and Detection.

7) Understands the theory and techniques for Multivariate Time Series; Granger causality, Cointegration

8) Knows the theory of Kalman Filtering and can apply it to data analysis.

9) Knows about the use of Neural networks in Time Series.

By the end of the course, the student should be able to apply the methods discused using R.

1) Written examination (for the theory of stationary processes)

2) Computer assignments (for practical data analysis). Assessment is based on (a) correctness of the data analysis and (b) clarity of presenting the conclusions.

Both aspects of the course are given equal weight.