On a computationally-scalable sparse formulation of the multidimensional and non-stationary maximum entropy principle

05/07/2020
by   Horenko Illia, et al.
0

Data-driven modelling and computational predictions based on maximum entropy principle (MaxEnt-principle) aim at finding as-simple-as-possible - but not simpler then necessary - models that allow to avoid the data overfitting problem. We derive a multivariate non-parametric and non-stationary formulation of the MaxEnt-principle and show that its solution can be approximated through a numerical maximisation of the sparse constrained optimization problem with regularization. Application of the resulting algorithm to popular financial benchmarks reveals memoryless models allowing for simple and qualitative descriptions of the major stock market indexes data. We compare the obtained MaxEnt-models to the heteroschedastic models from the computational econometrics (GARCH, GARCH-GJR, MS-GARCH, GARCH-PML4) in terms of the model fit, complexity and prediction quality. We compare the resulting model log-likelihoods, the values of the Bayesian Information Criterion, posterior model probabilities, the quality of the data autocorrelation function fits as well as the Value-at-Risk prediction quality. We show that all of the considered seven major financial benchmark time series (DJI, SPX, FTSE, STOXX, SMI, HSI and N225) are better described by conditionally memoryless MaxEnt-models with nonstationary regime-switching than by the common econometric models with finite memory. This analysis also reveals a sparse network of statistically-significant temporal relations for the positive and negative latent variance changes among different markets. The code is provided for open access.

READ FULL TEXT

page 7

page 8

page 9

page 10

research
05/18/2013

Dynamic Covariance Models for Multivariate Financial Time Series

The accurate prediction of time-changing covariances is an important pro...
research
03/15/2023

A Bayesian Non-Stationary Heteroskedastic Time Series Model for Multivariate Critical Care Data

We propose a multivariate GARCH model for non-stationary health time ser...
research
07/20/2021

High-dimensional Multivariate Time Series Forecasting in IoT Applications using Embedding Non-stationary Fuzzy Time Series

In Internet of things (IoT), data is continuously recorded from differen...
research
03/05/2020

Non-stationary neural network for stock return prediction

We consider the problem of neural network training in a time-varying con...
research
05/07/2023

Inference for a New Signed Integer Valued Autoregressive Model Based on Pegram's Operator

In the current study, a brand-new SINARS(1) model is proposed for statio...
research
08/22/2019

Adaptive Configuration Oracle for Online Portfolio Selection Methods

Financial markets are complex environments that produce enormous amounts...
research
06/27/2022

Entropy-based Characterization of Modeling Constraints

In most data-scientific approaches, the principle of Maximum Entropy (Ma...

Please sign up or login with your details

Forgot password? Click here to reset