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.
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.
In this paper we propose a model for the conditional multivariate density of integer count variables defined on the set Z n . Applying the concept of copula functions, we allow for a general form of dependence between the marginal processes, which is able to pick up the complex nonlinear dynamics of multivariate financial time series at high frequencies. We use the model to estimate the conditional bivariate density of the high frequency changes of the EUR/GBP and the EUR/USD exchange rates. Keywords Integer count hurdle · Copula functions · Discrete multivariate distributions · Foreign exchange market JEL Classification G10 · F30 · C30 IntroductionIn this paper we propose a model for the multivariate conditional density of integer count variables. Our modelling framework can be used for a broad set of applications to multivariate processes where the primary characteristics of the variables are: first, their discrete domain spaces, each being the whole space Z; and second, their contemporaneous dependence.
In this paper we propose a model for the conditional multivariate density of integer count variables defined on the set Z n . Applying the concept of copula functions, we allow for a general form of dependence between the marginal processes, which is able to pick up the complex nonlinear dynamics of multivariate financial time series at high frequencies. We use the model to estimate the conditional bivariate density of the high frequency changes of the EUR/GBP and the EUR/USD exchange rates. Keywords Integer count hurdle · Copula functions · Discrete multivariate distributions · Foreign exchange market JEL Classification G10 · F30 · C30 IntroductionIn this paper we propose a model for the multivariate conditional density of integer count variables. Our modelling framework can be used for a broad set of applications to multivariate processes where the primary characteristics of the variables are: first, their discrete domain spaces, each being the whole space Z; and second, their contemporaneous dependence.
In this paper we model the dynamic multivariate density of discrete bid and ask quote changes and their associated depths. We account for the contemporaneous relationship between these trading marks by exploiting the concept of copula functions. Thereby we show how to model truncations of the multivariate density in an easy way. A Metropolized-Independence Sampler is applied to draw from the dynamic multivariate density. The samples drawn serve to construct the dynamic density function of the quote slope liquidity measure, which enables us to quantify time varying liquidity risk. We analyze the influence of the decimalization at the NYSE on liquidity.JEL classification: G10, F 30, C30
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