An Overview of Gaussian process Regression for Volatility Forecasting

Forecasting financial time series using trading data has held the attention of academics and practitioners due to the complexity of the financial system and the profit it can generate for investors. Although investors aim to achieve a consistent attainment of returns, it is important for investors to understand the concept and measurement of volatility. A higher volatility indicates a wider potential range of future returns. But with higher potential returns, comes a higher potential risk. With Gaussian Processes (GPs) having been shown great potential in this field, this paper explores the application of GP regression in forecasting the volatility of foreign exchange returns. This paper builds on the existing literature by applying Gaussian processes for time series forecasting in new ways, namely the multivariate non-coregionalised and coregionalised GP. We show that a multivariate GP can match the accuracy of predictions of a univariate GP, with the added benefit of lower predictive uncertainty due to the incorporation of extra information. Furthermore, we give insight into the relative strengths of the GP methods with recommendations to the practitioner.

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