## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-60-12-M-4

## Module Identification

Module Number Module Name CP (Effort)
MAT-60-12-M-4 Regression and Time Series Analysis 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. in SuSe [4] Bachelor (Specialization) [EN] English Redenbach, Claudia, Prof. Dr. (PROF | DEPT: MAT) 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 [MAT-88.105-SG] M.Sc. Mathematics [NORM] Active

## Notice

Without a proof of successful participation in the exercise classes, only 6 credit points will be awarded for the module.

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-60-12-K-4
Regression and Time Series Analysis
P 84 h 186 h
U-Schein
- PL1 9.0 SuSe
• About [MAT-60-12-K-4]: Title: "Regression and Time Series Analysis"; Presence-Time: 84 h; Self-Study: 186 h
• About [MAT-60-12-K-4]: The study achievement "[U-Schein] proof of successful participation in the exercise classes (ungraded)" must be obtained.

## Examination achievement PL1

• Form of examination: oral examination (20-30 Min.)
• Examination Frequency: each semester
• Examination number: 84330 ("Regression and Time Series Analysis")

## 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.

They understand the proofs presented in the lecture and are able to comprehend and explain them.By completing the exercises, the students have developed a skilled, precise and independent handling of the terms, propositions and techniques taught in the lecture. They are familiar with the software forstatistics and they are able to apply independently 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.

## Registration

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

None

## References to Module / Module Number [MAT-60-12-M-4]

Course of Study Section Choice/Obligation
[INF-88.79-SG] M.Sc. Computer Science [Core Modules (non specialised)] Formal Fundamentals [WP] Compulsory Elective
[MAT-88.105-SG] M.Sc. Mathematics [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective
[MAT-88.118-SG] M.Sc. Industrial Mathematics [Core Modules (non specialised)] General Mathematics [WP] Compulsory Elective
[MAT-88.276-SG] M.Sc. Business Mathematics [Core Modules (non specialised)] General Mathematics [WP] Compulsory Elective
[MAT-88.706-SG] M.Sc. Mathematics International [Core Modules (non specialised)] Applied Mathematics [WP] Compulsory Elective