  In this paper, we explore the application of Gaussian Processes (GPs) for
predicting mean-reverting time series with an underlying structure, using
relatively unexplored functional and augmented data structures. While many
conventional forecasting methods concentrate on the short-term dynamics of time
series data, GPs offer the potential to forecast not just the average
prediction but the entire probability distribution over a future trajectory.
This is particularly beneficial in financial contexts, where accurate
predictions alone may not suffice if incorrect volatility assessments lead to
capital losses. Moreover, in trade selection, GPs allow for the forecasting of
multiple Sharpe ratios adjusted for transaction costs, aiding in
decision-making. The functional data representation utilized in this study
enables longer-term predictions by leveraging information from previous years,
even as the forecast moves away from the current year's training data.
Additionally, the augmented representation enriches the training set by
incorporating multiple targets for future points in time, facilitating
long-term predictions. Our implementation closely aligns with the methodology
outlined in, which assessed effectiveness on commodity futures. However, our
testing methodology differs. Instead of real data, we employ simulated data
with similar characteristics. We construct a testing environment to evaluate
both data representations and models under conditions of increasing noise, fat
tails, and inappropriate kernels-conditions commonly encountered in practice.
By simulating data, we can compare our forecast distribution over time against
a full simulation of the actual distribution of our test set, thereby reducing
the inherent uncertainty in testing time series models on real data. We enable
feature prediction through augmentation and employ sub-sampling to ensure the
feasibility of GPs.
