  The fundamental theorem behind financial markets is that stock prices are
intrinsically complex and stochastic. One of the complexities is the volatility
associated with stock prices. Volatility is a tendency for prices to change
unexpectedly [1]. Price volatility is often detrimental to the return
economics, and thus, investors should factor it in whenever making investment
decisions, choices, and temporal or permanent moves. It is, therefore, crucial
to make necessary and regular short and long-term stock price volatility
forecasts for the safety and economics of investors returns. These forecasts
should be accurate and not misleading. Different models and methods, such as
ARCH GARCH models, have been intuitively implemented to make such forecasts.
However, such traditional means fail to capture the short-term volatility
forecasts effectively. This paper, therefore, investigates and implements a
combination of numeric and probabilistic models for 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 is not easy to set price limits
in a market due to its free nature and randomness, a Censored GP was used to
model the relationship between the corrected stock prices and returns.
Forecasting errors were evaluated using the implied and estimated data.
