An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics

39 Pages Posted: 1 Mar 2007 Last revised: 25 Jun 2009

See all articles by Katarzyna Bien

Katarzyna Bien

University of Konstanz - Department of Economics & Center of Finance & Econometrics (CoFE)

Ingmar Nolte

Lancaster University - Department of Accounting and Finance

Winfried Pohlmeier

University of Konstanz - Department of Economics & Center of Finance & Econometrics (CoFE)

Date Written: June 9, 2009

Abstract

In this paper we develop a model for the conditional inflated multivariate density of integer count variables with domain Z^n. Our modelling framework is based on a copula approach and can be used for a broad set of applications where the primary characteristics of the data are: (i) discrete domain, (ii) the tendency to cluster at certain outcome values and (iii) contemporaneous dependence. These kind of properties can be found for high or ultra-high frequent data describing the trading process on financial markets. We present a straightforward method of sampling from such an inflated multivariate density through the application of an Independence Metropolis-Hastings sampling algorithm.

We demonstrate the power of our approach by modelling the conditional bivariate density of bid and ask quote changes in a high frequency setup. We show how to derive the implied conditional discrete density of the bid-ask spread, taking quote clusterings (at multiples of 5 ticks) into account.

Keywords: Multivariate Discrete Distributions, Conditional Inflation, Copula Functions, Truncations, Metropolized-Independence Sampler

JEL Classification: G10, F30, C30

Suggested Citation

Bien, Katarzyna and Nolte, Ingmar and Pohlmeier, Winfried, An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics (June 9, 2009). Available at SSRN: https://ssrn.com/abstract=967253 or http://dx.doi.org/10.2139/ssrn.967253

Katarzyna Bien

University of Konstanz - Department of Economics & Center of Finance & Econometrics (CoFE) ( email )

Universitätsstr. 10
Box: D 124
78457 Konstanz
Germany

Ingmar Nolte (Contact Author)

Lancaster University - Department of Accounting and Finance ( email )

Lancaster, Lancashire LA1 4YX
United Kingdom

Winfried Pohlmeier

University of Konstanz - Department of Economics & Center of Finance & Econometrics (CoFE) ( email )

Konstanz, D-78457
Germany

HOME PAGE: http://econometrics.wiwi.uni-konstanz.de

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