PAPAIOANNOU, PANAGIOTIS Forecasting high-dimensional time series using Manifold and Machine Learning with Applications in Financial Markets and Epidemiology. [Tesi di dottorato]

Testo Doctoral_Thesis_Panagiotis_Papaioannou_RC.pdf Download (8MB)

Abstract

The aim of this Ph.D. Thesis is to exploit the arsenal of recent theoretical advances in manifold and machine learning thus developing a new computational framework, integrating also well established mathematical tools from the non-linear time series analysis theory for the forecasting, i.e. out-of-sample extrapolation of high dimensional time series. This is a three-fold task: (a) find the dimension of a low dimensional manifold where the dynamics evolve and embed the high dimensional dataset on this manifold, (b) construct low-dimensional models on the embedded manifold using machine learning with a focus on Gaussian Processes, and (c) forecast, i.e. perform out-of-sample extrapolation in the ambient original space. This is a conceptually different task with respect to the interpolation problem of the model reduction of well-defined dynamical models in the form of Ordinary and or Partial Differential Equations. Applications include Financial and Electricity Markets modelling and forecasting, market inefficiencies identification, trading and portfolio management strategies deployment tested on a wide spectrum of financial assets, the task of challenging the Efficient Market Hypothesis on all of its efficiency forms, as well as the recent COVID-19 pandemic’s dynamics short-term forecasting challenge.

Downloads

Actions (login required)

Modifica documento