STA-2003 Time series - 10 stp

Time series analysis is a crucial discipline in data science, offering insights into patterns over time that are invaluable for forecasting, anomaly detection, and understanding temporal dynamics. The aim of this course is to introduce fundamental concepts of time series analysis from multiple perspectives: statistical, dynamical systems, machine learning, and signal processing. This interdisciplinary approach aims to give the students a broad view on the world of time series.

Whether you are new to time series analysis or looking to refine your expertise, this course offers a broad exploration of the field, with Python as your toolkit!

Applicants from Nordic countries: Generell studiekompetanse og følgende spesielle opptakskrav:

Matematikk R1 + R2 og i tillegg enten:

• Fysikk 1 + 2 eller
• Kjemi 1+ 2 eller
• Biologi 1 + 2 eller
• Informasjonsteknologi 1 + 2 eller
• Geofag 1 + 2 eller
• Teknologi og forskningslære 1 + 2

Recommended prerequisites are STA-1001 Statistics and Probability or equivalent, and INF-0102 Computational Programming (Python)

Application code is 9336 - enkeltemner i realfag.

The course is designed to combine high-level theoretical knowledge with practical programming skills. Each chapter introduces key concepts of time series analysis, followed by hands-on coding sections in Python. This structure allows the students to immediately apply the theoretical concepts as they learn them, seeing first-hand how these translate into functional tools in data analytics. Through this process, each student will gain both the knowledge to understand complex time series data and the skills to analyze and predict it effectively. To reinforce learning and encourage active engagement, each chapter concludes with exercises. These are designed to test the level of understanding and help the students to apply the theory in practical contexts.

The course is divided into 12 modules, which cover the following topics.

1. Introduction to time series analysis

• Definition of time series data

• Main applications of time series analysis

• Statistical vs dynamical models perspective

• Components of a time series

• Additive vs multiplicative models

• Time series decomposition techniques

2. Stationarity in time series

• Stationarity in time series

• Weak vs strong stationarity

• Autocorrelation and autocovariance

• Common stationary and nonstationary time series

• How to identify stationarity

• Transformations to achieve stationarity

3. Smoothing

• Smoothing in time series data

• The mean squared error

• Simple average, moving average, and weighted moving average

• Single, double, and triple exponential smoothing

4. AR-MA

• The autocorrelation function

• The partial autocorrelation function

• The Auto-Regressive model

• The Moving-Average model

• Reverting stationarity transformations in forecasting

5. ARMA, ARIMA, SARIMA

• Autoregressive Moving Average (ARMA) models

• Autoregressive Integrated Moving Average (ARIMA) models

• SARIMA models (ARIMA model for data with seasonality)

• Automatic model selection with AutoARIMA

• Model selection with exploratory data analysis

6. Unit root test and Hurst exponent

• Unit root test

• Mean Reversion

• The Hurst exponent

• Geometric Brownian Motion

• Applications in quantitative finance

7. Kalman filter

• Introduction to Kalman Filter

• Model components and assumptions

• The Kalman Filter algorithm

• Application to static and dynamic one-dimensional data

• Application to higher-dimensional data

8. Signal transforms and filters

• Introduction to Fourier Transform, Discrete Fourier Transform, and FFT

• Fourier Transform of common signals

• Properties of the Fourier Transform

• Signal filtering with low-pass, high-pass, band-pass, and bass-stop filters

• Application of Fourier Transform to time series forecasting

9. Prophet

• Introduction to Prophet for time series forecasting

• Advanced modeling of trend, seasonality, and holidays components

• The Prophet library in Python

10. Neural networks and Reservoir Computing

• Windowed approaches and Neural Networks for time series forecasting

• Forecasting with a Multi-Layer Perceptron

• Recurrent Neural Networks: advantages and challenges

• Reservoir Computing and the Echo State Network

• Dimensionality reduction with Principal Component Analysis

• Forecasting electricity consumption with Multi-Layer Perceptron and Echo State Network

11. Non-linear time series analysis

• Dynamical systems and nonlinear dynamics

• Bifurcation diagrams

• Chaotic systems

• High-dimensional continuous-time systems

• Fractal dimensions

• Phase space reconstruction and Taken's embedding theorem

• Forecasting time series from nonlinear systems

12. Time series classification and clustering

• Multivariate time series

• Time series similarities and dissimilarities

• Dynamic Time Warping

• Time series kernels

• Embedding time series into vectors

• Classification of time series

• Clustering of time series

• Visualize time series with kernel PCA