Regression Models for Ordinal Valued Time Series with Application to High Frequency Financial Data

In financial time series transaction price changes often occur in
discrete increments, for example in eights of a dollar. We consider
these price changes as discrete random variables which are assumed
to be generated by a latent process which incorporates both
exogenous variables and autoregressive components. A standard Gibbs
sampling algorithm has been developed to estimate the parameters of
the model. However this algorithm exhibits bad convergence
properties. To improve the standard Gibbs sampler we utilize
methods proposed by Liu and Sabatti (2000, Biometrika 87), based on
transformation groups on the sample space. A simulation study will
be given to demonstrate the substantial improvement by this new
algorithm. Finally we apply our model to the data of the IBM stock
on Nov 13, 2000, and estimate the influence of the duration between
transactions, the volume, and the bid-offer-spread both to model
fit and prediction.