Gaussian Process Imputation of Multiple Financial Series

Abstract

In Financial Signal Processing, multiple time series such as financial indicators, stock prices and exchange rates are strongly coupled due to their dependence on the latent state of the market and therefore they are required to be jointly analysed. We focus on learning the relationships among financial time series by modelling them through a multi-output Gaussian process (MOGP) with expressive covariance functions. Learning these market dependencies among financial series is crucial for the imputation and prediction of financial observations. The proposed model is validated experimentally on two realworld financial datasets for which their correlations across channels are analysed. We compare our model against other MOGPs and the independent Gaussian process on real financial data.

Bayesian Reconstruction of Fourier Pairs

“…This is due to the large literature on covariance design [19], [20], [21], which allows to Gaussian models to replicate well-known models in the literature. However, we acknowledge that realworld data such as the number of words in a stream of text [22], a price series in finance [23] or discrete-state series can exhibit non-Gaussian features. These non-Gaussian signals can be modelled through a latent Gaussian model with an appropriate non-Gaussian likelihood that ensures the desired properties such as non-negativity, skewness or kurtosis.…”