  A Hidden Markov Model for intraday momentum trading is presented which
specifies a latent momentum state responsible for generating the observed
securities' noisy returns. Existing momentum trading models suffer from
time-lagging caused by the delayed frequency response of digital filters.
Time-lagging results in a momentum signal of the wrong sign, when the market
changes trend direction. A key feature of this state space formulation, is no
such lagging occurs, allowing for accurate shifts in signal sign at market
change points. The number of latent states in the model is estimated using
three techniques, cross validation, penalized likelihood criteria and
simulation-based model selection for the marginal likelihood. All three
techniques suggest either 2 or 3 hidden states. Model parameters are then found
using Baum-Welch and Markov Chain Monte Carlo, whilst assuming a single
(discretized) univariate Gaussian distribution for the emission matrix. Often a
momentum trader will want to condition their trading signals on additional
information. To reflect this, learning is also carried out in the presence of
side information. Two sets of side information are considered, namely a ratio
of realized volatilities and intraday seasonality. It is shown that splines can
be used to capture statistically significant relationships from this
information, allowing returns to be predicted. An Input Output Hidden Markov
Model is used to incorporate these univariate predictive signals into the
transition matrix, presenting a possible solution for dealing with the signal
combination problem. Bayesian inference is then carried out to predict the
securities $t+1$ return using the forward algorithm. Simple modifications to
the current framework allow for a fully non-parametric model with asynchronous
prediction.
