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Müller, Gernot and Czado, Claudia (2002): Regression Models for Ordinal Valued Time Series with Application to High Frequency Financial Data. Collaborative Research Center 386, Discussion Paper 301
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Abstract

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.