Informácie pre študentov
Beáta Stehlíková
Katedra aplikovanej matematiky a štatistiky, M266
E-mail: stehlikova@pc2.iam.fmph.uniba.sk
Web: http://pc2.iam.fmph.uniba.sk/institute/stehlikova/
:: Obsah stránky ::
:: Time series analysis ::
ECTS: 4 credits
Syllabus:
- Introduction. Time series and their moments. Stationarity and ergodicity. White noise. Wald representation.
- Correlations between the values of a process, autocorrelation function. Testing white noise, Ljung-Box Q-statistics.
- Autoregressive (AR) moving average (MA), ARMA models. Stationarity and invertibility conditions. Computation of the expected value, dispersion and covariances. Autocorrelation and partial autocorrelation functions and their use in identification of a model. Estimation of parameters. Predictions.
- Differencing the time series, integrated processes. Unit root tests.
- Seasonality, SARIMA models.
- Modelling volatility, ARCH and GARCH models and their generalizations. Application to analysis of risk, calculation of Value at Risk.
- Other approaches to time series modeling: Nonlinear least squares. Modelling trend - exponential smoothing, Holt-Winters method, Hodrick-Prescott filter.
Lectures:
| Topic | Slides |
| Introduction | 1_intro.pdf |
| AR processes | 2_ar.pdf |
| MA processes | 3_ma.pdf |
| ARMA processes | 4_arma.pdf |
| Unit root | 5_unit_root.pdf |
| Seasonal SARIMA models | 6_sarima.pdf |
| GARCH models | 7_garch.pdf, garch_data.R |
| GARCH models | 8_spectrum.pdf |
Exercises:
| Topic | Slides |
| White noise | see the lecture slides |
| Nonlinear least squares, Bass model | ex02_bass.pdf |
| AR processes - part 1 | ex03_ar.pdf, data: RSQ.txt, R20Q.txt |
| AR processes - part 2 | ex04_ar.pdf |
| Trend - part 1 | ex05_trend_1.pdf, data: motor.txt, wine.txt |
| Trend - part 2 | ex06_trend_2.pdf |
| ARIMA modelling exercises from past exams | arima-exam.pdf |
| ARIMA modelling - review | arima-review.pdf |
| SARIMA modelling - datasets from the lecture exercises | spain.txt, souvenirs.txt |
| Spectrum | ex07_spectrum.pdf |
| Modelling exercise | modelling_exercise.pdf, results: yen.png |
Homework:
| Topic | PDF file | Deadline |
| HW1: White noise, Bass model | hw1.pdf | 8th March 2016 |
| HW2: AR(1) model for the GDP growth | hw2.pdf | 15th March 2016 |
| HW3: Modelling trend | hw3.pdf | 5th April 2016 |
| HW4: ARIMA models | hw4.pdf | 19th April 2016 |
| HW5: ARMA and ARIMA models - theory | hw5.pdf | 26th April 2016 | HW6: SARIMA models | hw6.pdf | 3rd May 2016 |
References:
- Introduction to modern time series analysis / Gebhard Kirchgässner, Jürgen Wolters. Berlin : Springer, 2008
- Time series analysis and its applications : with R examples / Robert H. Shumway, David S. Stoffer. New York : Springer, 2011. Available for free online with a consent of the publisher: http://www.stat.pitt.edu/stoffer/tsa3
- Introductory time series with R / Paul S. P. Cowpertwait, Andrew V. Metcalfe. Dordrecht : Springer, 2009
- Forecasting With Univariate Box-Jenkins Models : Concepts and Cases / Alan Pankratz. New York : John Wiley, 1983. Second part of the book - case studies - is avaliable for free on publisher's website: http://onlinelibrary.wiley.com/book/10.1002/9780470316566
Grading:
- During the term:
- 6 assignments, 10 points each, the worst one is dropped
- Exam:
- open-book, computational and theoretical problems, 50 points
- part of the exam is a problem on checking stationarity and invertibility of the given process and a problem on finding a suitable ARIMA model for the given data - together 20 points, getting at least 12 points from this part is a necessary condition for passing the course
- Grades: A: [90, 100], B: [80, 90), C: [70, 80), D: [60, 70), E: [50, 60)
Beáta Stehlíková
Department of Applied Mathematics and Statistics
Faculty of Mathematics, Physics and Informatics
Comenius University
Bratislava
Slovak Republic
E-mail: stehlikova@pc2.iam.fmph.uniba.sk
Web: http://pc2.iam.fmph.uniba.sk/institute/stehlikova/
Department of Applied Mathematics and Statistics
Faculty of Mathematics, Physics and Informatics
Comenius University
Bratislava
Slovak Republic
E-mail: stehlikova@pc2.iam.fmph.uniba.sk
Web: http://pc2.iam.fmph.uniba.sk/institute/stehlikova/
