Магистратура
2021/2022
Анализ и прогнозирование временных рядов: методы и приложения
Статус:
Курс по выбору (Науки о данных (Data Science))
Направление:
01.04.02. Прикладная математика и информатика
Где читается:
Факультет компьютерных наук
Когда читается:
2-й курс, 1, 2 модуль
Формат изучения:
без онлайн-курса
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Громов Василий Александрович
Прогр. обучения:
Науки о данных
Язык:
русский
Кредиты:
8
Контактные часы:
54
Программа дисциплины
Аннотация
How to forecast rates of a national currency? How to identify an oncoming heart attack in good time? – the answers to these questions are associated with the problems (1) to predict a chaotic time series and (2) to reveal typical sequences in an observed time series, respectively. All these problems along with many others comprise the field of time series prediction. The course combines real-world applications with a strong theoretical background: the authors selected mathematical topics required to solve complex problems of actual practice. On the other hand, several topics focus on “mathematics of future” that is theories that will have become the basis of applications in the decades to come. The course starts with simple concepts and gradually works in more advanced applications. To be specific, the course deals with main models to examine and predict regular time series (exemplified by ARIMA and GARCH models), chaotic time series (predictive clustering, constructive neural networks, deep learning models and others) as well as with state-of-the-art approaches used to distinguish regular and chaotic time series, using observations of the time series at hand only; particular topics deal with the concepts of forecasting (time) and stationarity horizons. Applications considered range from econometrics problem to mobile health.
Цель освоения дисциплины
- To introduce the theoretical foundations of Prediction theory for regular and chaotic time series.
- To provide the students with practical skills of modelling real-world system.
- To overview the current applications of decision-making support systems in logistics.
Планируемые результаты обучения
- Analyse non-linear and chaotic time series and forecast them.
- Analyse regular time series.
- Design and develop real-world systems for forecasting tasks using Predictive regression models.
- Understand applications of predictive clustering.
- Understand fundamental concepts of Attractor reconstruction for chaotic time series.
- Understand fundamental concepts of bifurcation precursors and time series.
- Understand fundamental concepts of Linear regression analysis.
- Understand fundamental concepts of Maximum likelihood estimation of regression parameters.
- Understand fundamental concepts of Neural networks and time series predictions.
- Understand fundamental concepts of non-linear and chaotic time series.
- Understand fundamental concepts of Non-linear regression analysis.
- Understand fundamental concepts of Predictive regression models.
- Understand fundamental concepts of regular time series.
- Understand fundamental concepts of Stationarity horizon.
- Understand fundamental concepts, advantages and limitations of correlation analysis.
- Understand fundamental concepts, advantages and limitations of Predictive clustering.
- Understand fundamental concepts, advantages and limitations of АRIМА-models.
- Understand predicitve complexity.
Содержание учебной дисциплины
- Correlation analysis.
- Linear regression analysis.
- Non-linear regression analysis.
- Neural networks and time series predictions.
- Predictive regression models.
- Maximum likelihood estimation of regression parameters.
- Regular time series.
- АRIМА-models.
- Non-linear and chaotic time series. Forecasting horizon.
- Attractor reconstruction for chaotic time series.
- Predictive clustering.
- Applications of predictive clustering.
- Stationarity horizon.
- Bifurcation precursors and time series.
- Predicitve complexity.
Элементы контроля
- Intermediate task 1A practical tasks associated with regular time series.
- Intermediate task 2A practical tasks associated with chaotic time series.
- ExamThe final exam is oral. The prerequisite for the course is a course in basic statistics.
- Colloquium 1
- Colloquium 2
