Time series, i.e. sequences of discrete-time data, are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series analysis comprises methods for analysis of time series data in order to extract meaningful statistics and other characteristics of the data. Models for time series data can have many forms and represent different stochastic processes. The broad classes of practical importance are the autoregressive (AR) models and the moving-average (MA) models. Combinations of these ideas produce autoregressive moving-average (ARMA) models. These classes depend linearly on previous data points. Among non-linear time series models, there are models to represent the changes of variance over time (heteroskedasticity). These models include autoregressive conditional heteroskedasticity (ARCH) and further generalizations (e.g., GARCH) and are widely used e.g. in mathematical finance.
Prüfungsnummer Prüfungsname
724023 Angewandte Statistik (Modul: MScMath MV02)
722033 Spezialvorlesung Stochastics (Modul: MScMath MV32)
722035 Stochastische Modellierung und Simulation (Modul: MScMath MV33)
Zuordnung zu Einrichtungen
FB 10 Mathematik und Naturwissenschaften
FB 10 IfM Analysis und Angewandte Mathematik
Lehrveranstaltungsart VL 4 SWS + Ü 2 SWS
Voraussetzungen für die Teilnahme am Modul / Recommended skills:
Modul „Einführung in die Stochastik“ / Module „Introduction to Stochastics“
Leistungsnachweis: Studienleistung (Voraussetzung für Zulassung zur Prüfungsleistung): Regelmäßige Bearbeitung von Übungsaufgaben. Das genaue Kriterium wird zu Beginn des Moduls bekannt gegeben. / Nongraded learning assignments (prerequesite for admission to examination): Regular solving of exercises on exercise sheets. The precise criterion will be announced by the lecturer at the beginning of the module.
Zielgruppe: Bachelor Mathematik und Technomathematik, Master Mathematics, Master Technomathematik
Literatur:
1. Peter J. Brockwell, Richard A. Davis, Introduction to Time Series and Forecasting, Springer 2016.
2. Jens-Peter Kreiß, Georg Neuhaus, Einführung in die Zeitreihenanalyse, Springer 2006.
3. Jochen Hirschle, Machine Learning für Zeitreihen. Einstieg in Regressions-, ARIMA und Deep-Learning-Verfahren mit Python, Carl Hanser Verlag München 2021.