Enhancing Mean-Reverting Time Series Prediction with Gaussian Processes: Functional and Augmented Data Structures in Financial Forecasting

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.

Analyzing Currency Fluctuations: A Comparative Study of GARCH, EWMA, and IV Models for GBP/USD and EUR/GBP Pairs

In this study, we examine the fluctuation in the value of the Great Britain Pound (GBP). We focus particularly on its relationship with the United States Dollar (USD) and the Euro (EUR) currency pairs. Utilizing data from June 15, 2018, to June 15, 2023, we apply various mathematical models to assess their effectiveness in predicting the 20-day variation in the pairs' daily returns. Our analysis involves the implementation of Exponentially Weighted Moving Average (EWMA), Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and Implied Volatility (IV) models. To evaluate their performance, we compare the accuracy of their predictions using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) metrics. We delve into the intricacies of GARCH models, examining their statistical characteristics when applied to the provided dataset. Our findings suggest the existence of asymmetric returns in the EUR/GBP pair, while such evidence is inconclusive for the GBP/USD pair. Additionally, we observe that GARCH-type models better fit the data when assuming residuals follow a standard t-distribution rather than a standard normal distribution. Furthermore, we investigate the efficacy of different forecasting techniques within GARCH-type models. Comparing rolling window forecasts to expanding window forecasts, we find no definitive superiority in either approach across the tested scenarios. Our experiments reveal that for the GBP/USD pair, the most accurate volatility forecasts stem from the utilization of GARCH models employing a rolling window methodology. Conversely, for the EUR/GBP pair, optimal forecasts are derived from GARCH models and Ordinary Least Squares (OLS) models incorporating the annualized implied volatility of the exchange rate as an independent variable.

Efficient Market Dynamics: Unraveling Informational Efficiency in UK Horse Racing Betting Markets Through Betfair's Time Series Analysis

Using Betfair's time series data, an analysis of the United Kingdom (UK) horse racing market reveals an interesting paradox: a market with short tails, rapidly decaying autocorrelations, and no long-term memory. There seems to be a remarkably high level of informational efficiency in betting exchange returns, in contrast to financial assets that are characterized by heavy tails and volatility clustering. The generalized Gaussian unconditional distribution with a light tail point to a market where knowledge is quickly assimilated and reflected in prices. This is further supported by the extremely quick fading of autocorrelations and the absence of gain-loss asymmetry. Therefore, in addition to measuring long-range memory, the Hurst exponent also shows mean reversion, a sign that markets respond quickly to fresh information.