  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.
