Timeseries Forecasting

Instructor(s):

Prof. M. Drakaki, Dr. S.G. Stavrinides

Teaching Hours and Credit Allocation:

30 Hours, 6 Credits

Course Assessment:

Exam & Coursework

Time series analysis has been established as a tool for understanding and representing data associated with complex real-life problems. Time series analysis, modelling and forecasting has been widely applied to solve practical problems in a wide range of scientific disciplines including natural, social and political sciences, economics and engineering. Early revolutionary works on applications of time series analysis by using mathematical linear models have demonstrated the suitability of the linear time series methodology in understanding and representing dynamic real time series data. On the other hand, the paradigm of deterministic chaos has influenced thinking in many fields of science. Chaotic systems show rich and surprising mathematical structures. In the applied sciences, deterministic chaos provides a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. Experimental technique and data analysis have seen such dramatic progress that, by now, most fundamental properties of nonlinear dynamical systems have been observed in the laboratory. Great efforts are being made to exploit ideas from chaos theory wherever the data displays more structure than can be captured by traditional methods. Problems of this kind are typical in biology and physiology but also in geophysics, economics, and many other sciences.

Aims

This course aims in providing solid knowledge on a domain that is beneficial to those studying AI and machine learning. Timeseries analysis and forecasting is a domain where computer science, and coding meet mathematics, physics and other natural sciences, engineering, economics, finance and social sciences. Comprehensive knowledge on the theoretical foundations of the area (fundamental principles, elements etc.) is offered. The course includes timeseries analysis by utilizing both linear approaches and nonlinear dynamics. Both modules move towards the final goal which is timeseries forecasting for practical applications.

Learning Outcomes

On completing the course students will be able to:

· Understand the essential mathematics and algorithms behind contemporary timeseries analysis.

· Understand the methods utilized for forecasting the temporal evolution of dynamical systems.

· Implement timeseries analysis both by utilizing linear and nonlinear methods.

· Learn how to analyze, model and forecast time series data by using statistical software packages.

· Successfully implement timeseries modelling and forecasting.

· Understand and estimate the limits of proper and reliable forecasting.

· Have the background needed and experience, to understand the upcoming methods and approaches in the area.

Content

· Introduction to time series analysis

· Basic characteristics of stationary processes

· Time series models (ARMA, ARIMA, SARIMA)

· Time series forecasting

  • Short introduction to Chaos Theory

· Basic characteristics of nonlinear timeseries and their analysis

  • Reconstruction of phase space
  • Dimensions, entropies and other invariant metrics
  • Timeseries forecasting methods and models

Reading

· “Introduction to time series and forecasting” by Brockwell P.J. and Davis R.A., 3rd edition, Springer, 2016.

· “Introduction to Time Series Analysis and Forecasting” by D. C. Montgomery, C. L. Jennings, M. Kulahci, 2nd edition, Wiley, 2015.

· “Nonlinear Timeseries Analysis” by Holger Kantz and Thomas Schreiber (2 nd edition).

· “Elements of Nonlinear Timeseries Analysis and Forecasting” by Jan G. De Gooijer