Modelling and Prediction of Financial Time Series

Abstract

We consider statistical aspects of the modelling and prediction theory of time series in one and many dimensions. We discuss Lévy-based and general models, and the stationary and non-stationary cases. Our starting point is the recent pair of surveys, Szeg'ó's theorem and its probabilistic descendants and Multivariate prediction and matrix Szeg'ó theory, by this author.

Keywords:

• Elliptic distribution
• Ergodic diffusion
• Lévy process
• Ornstein-Uhlenbeck process
• Prediction
• Semi-parametric model
• Stationary
• Time series

Mathematics Subject Classification:

• 62M10
• 62M20
• 62H99

Acknowledgment

This is an extended version of my talk at the Conference on Markov and Semi-Markov Processes at the University of Thessaloniki in September 2011. I thank the organizers for their invitation and hospitality. I also thank Pierre Blacque-Florentin for many interesting discussions.

Notes

Worse: It has recently emerged that Libor quotes were manipulated at times, leading to the current so-called “Lie-bor scandal.”