## Marcel Dettling: Catalogue data in Spring Semester 2019 |

Name | Dr. Marcel Dettling |

Address | ZHAW - IDP 8401 Winterthur SWITZERLAND |

Telephone | 058 934 70 23 |

marcel.dettling@math.ethz.ch | |

Department | Mathematics |

Relationship | Lecturer |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-0622-00L | Mathematical Foundations II: Linear Algebra and Statistics | 3 credits | 2V + 1U | M. Dettling | |

Abstract | Systems of linear equations; matrix algebra, determinants; vector spaces, norms and scalar products; linear maps, basis transformations; eigenvalues and eigenvectors. Random variables and probability, discrete and continuous distribution models; expectation, variance, central limit theorem, parameter estimation; statistical hypothesis tests; confidence intervals; regression analysis. | ||||

Objective | A sound knowledge of mathematics is an essential prerequisite for a quantitative and computer-based approach to natural sciences. In an intensive two-semester course the most important basic concepts of mathematics, namely univariate and multivariate calculus, linear algebra and statistics are taught. | ||||

Content | Systems of linear equations; matrix algebra, determinants; vector spaces, norms and scalar products; linear maps, basis transformations; eigenvalues and eigenvectors. - Least squares fitting and regression models; random variables, statistical properties of least-squares estimators; tests, confidence and prediction intervals in regression models; residual analysis. | ||||

Lecture notes | For the part on Linear Algebra, there is a short script (in German) which summarizes the main concepts and results without examples. For a self-contained presentation, the book by Nipp and Stoffer should be used. For the part on Statistics there is a detailed script (in German) available which should be self-contained. The book by Stahel can be used for additional information. | ||||

Literature | Linear Algebra: K. Nipp/D. Stoffer: "Lineare Algebra", vdf, 5th edition, 2002. Statistics: W. Stahel, "Statistische Datenanalyse", Vieweg, 5rd edition, 2008. | ||||

401-6624-11L | Applied Time Series | 5 credits | 2V + 1U | M. Dettling | |

Abstract | The course starts with an introduction to time series analysis (examples, goal, mathematical notation). In the following, descriptive techniques, modeling and prediction as well as advanced topics will be covered. | ||||

Objective | Getting to know the mathematical properties of time series, as well as the requirements, descriptive techniques, models, advanced methods and software that are necessary such that the student can independently run an applied time series analysis. | ||||

Content | The course starts with an introduction to time series analysis that comprises of examples and goals. We continue with notation and descriptive analysis of time series. A major part of the course will be dedicated to modeling and forecasting of time series using the flexible class of ARMA models. More advanced topics that will be covered in the following are time series regression, state space models and spectral analysis. | ||||

Lecture notes | A script will be available. | ||||

Prerequisites / Notice | The course starts with an introduction to time series analysis that comprises of examples and goals. We continue with notation and descriptive analysis of time series. A major part of the course will be dedicated to modeling and forecasting of time series using the flexible class of ARMA models. More advanced topics that will be covered in the following are time series regression, state space models and spectral analysis. |