## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Course MAT-60-12-K-4

## Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U)
4 V Lecture 6.0 CP 56 h 124 h
2 U Exercise class (in small groups) 3.0 CP 28 h 62 h
(4V+2U) 9.0 CP 84 h 186 h

## Basedata

SWS 4V+2U 9.0 CP = 270 h 1 Sem. in SuSe [4] Bachelor (Specialization) [EN] English Korn, Ralf, Prof. Dr. (PROF | DEPT: MAT) Redenbach, Claudia, Prof. Dr. (PROF | DEPT: MAT) Sass, Jörn, Prof. Dr. (PROF | DEPT: MAT) [MAT-STO] Stochastics/Statistics/Financial Mathematics [NORM] Active

## Possible Study achievement

• Verification of study performance: proof of successful participation in the exercise classes (ungraded)
• Examination number (Study achievement): 84033 ("Exercise Class Regression and Time Series Analysis")
• Details of the examination (type, duration, criteria) will be announced at the beginning of the course.

## Contents

• Linear regression models,
• Methods of least squares and maximum likelihood estimation,
• Confidence bands for regression curves,
• Tests for regression parameters (t and F tests), likelihood-ratio test,
• Model validation with residual analysis,
• Data adaptive choice of models (stepwise regression, R² and Mallows C_p),
• Variance analysis (ANOVA),
• Stationary stochastic processes in discrete time,
• Autocovariances, projection-valued measure and spectral density,
• Linear processes, especially ARMA models,
• Estimator for ARMA parameters (Yule-Walker, least squares, CML),
• Data adaptive choice of models with AIC, BIC and FPE,
• Time series with trend or seasonality (SARIMA),
• Prediction of time series.

## Competencies / intended learning achievements

The students have studied and understand standard models, estimation procedures, test procedures and forecasting methods of regression, variance and time series analysis. They will know exemplary mathematical methods required for data-driven selection and validation of models in complex application scenarios.

By successfully participating in the exercise classes they are familiar with software for statistics and they are able to independently apply the models and techniques taught in the lecture on real and simulated data.

## Literature

• J. Franke: Grundlagen der Statistik,
• J. Franke: Time Series Analysis;
• L. Breiman: Statistics,
• P. Bickel, K. Doksum: Mathematical Statistics,
• P.J. Brockwell, R.A. Davis: Time Series: Theory and Methods.

## Materials

Further literature will be announced in the lecture; Exercise material is provided.

## Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de)

None

## References to Course [MAT-60-12-K-4]

Module Name Context
[MAT-30-10L-M-5] Specialisation Module (Teachers Training Programme Mathematics) WP: Obligation to choose in Obligatory-Modulteil #A (Lectures) 4V, 6.0 LP
[MAT-60-12-M-4] Regression and Time Series Analysis P: Obligatory 4V+2U, 9.0 LP
Course-Pool Name
[MAT-50-4V-KPOOL-4] Elective Courses Optimisation and Stochastics (4V, B.Sc.)
[MAT-50-KPOOL-4] Specialisation Optimisation and Stochastics (B.Sc.)
[MAT-70-4V-KPOOL-4] Elective Courses Analysis and Stochastics (4V, B.Sc.)