Estimating Short-Term Returns with Volatilities for High Frequency Stock Trades in Emerging Economies Using Gaussian Processes (GPs)

Fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic in nature. One of the complexities is the volatilities associated with stock prices. Price volatility is often detrimental to the return economics and thus investors should factor it in when making investment decisions, choices, and temporal or permanent moves. It is therefore crucial to make necessary and regular stock price volatility forecasts for the safety and economics of investors' returns. These forecasts should be accurate and not misleading. Different traditional models and methods such as ARCH, GARCH have been intuitively implemented to make such forecasts, however they fail to effectively capture the short-term volatility forecasts. In this paper we investigate and implement a combination of numeric and probabilistic models towards short-term volatility and return forecasting for high frequency trades. The essence is that: one-day-ahead volatility forecasts were made with Gaussian Processes (GPs) applied to the outputs of a numerical market prediction (NMP) model. Firstly, the stock price data from NMP was corrected by a GP. Since it not easy to set price limits in a market due to its free nature, and randomness of the prices, a censored GP was used to model the relationship between the corrected stock prices and returns. To validate the proposed approach, forecasting errors were evaluated using the implied and estimated data.