Description

A time series is a series of data points indexed in time order. Time series data often arise when monitoring industrial processes or tracking corporate business metrics. Linear statistical models are popular tool for time series analysis and forecasting. For example the well-known ARIMA model is designed to account for the fact that data points taken over time may have an internal structure such as autocorrelation and trend. When the intrinsic dynamics of the system that generated the time series are governed by the linear paradigm, linear approaches are expected to be adequate to model the data. In reality, however, the intrinsic dynamics of the system are often governed by the nonlinear paradigm, where linear approaches are hampered by their linear assumptions.

In this project the student will learn how to construct various nonlinear statistical models for an actual time series observations of real-world process. They will explore both local nonlinear statistical models, for example local linear and local analogue models, which account for local structure of the underlying system; and global nonlinear models, for example Radial Basis Functions, which account for the global nonlinear structure directly. The forecast performance of using nonlinear models can then be compare with that of the traditional linear models.

Prerequisites

Resources

There are many standard time series analysis textbooks one could explore. But I would like to recommend “Chaos: A Very Short Introduction” by Leonard A. Smith. This is NOT a time series book, but it describes the properties of nonlinear dynamical systems intuitively instead of using sophisticated mathematics, which will help you to understand the difference between linear and nonlinear models.