Conditional Duration Model and Unobserved Market Heterogeneity of Traders. An Infinite Mixture of Non–Exponentials

Modelo de duración condicionada y heterogeneidad inobservada de los agentes. Una mezcla infinita de distribuciones no exponenciales

This paper extends the conditional duration model proposed by De Luca and Zuccolotto (2003), proposing an infinite mixture of distributions based on non–exponentials which accounts for the unobserved market heterogeneity of traders. The model we propose takes into account the fact that reaction times follow a gamma distribution and that the intensity parameter follows the reciprocal of an inverse Gaussian distribution. This extension allows us to capture not only various density shapes of durations, but also non–monotonic shapes of hazard functions. The model also allows us to test the unobserved heterogeneity of traders. This mixture model is easy to fit and characterises the behaviour of the conditional durations reasonably well.

Este trabajo extiende el modelo de duración condicionada propuesto por
Luca & Zuccolotto (2003) introduciendo una mezcla infinita de distribuciones no exponenciales que permite incorporar la heterogeneidad inobservada en el mercado por los agentes. El modelo propuesto tiene en cuenta el hecho de que el tiempo de respuesta sigue una distribución gamma y que el parámetro que mide la intensidad sigue una distribución recíproca inversa Gaussiana. Esta modelización permite no sólo capturar distintas formas de la distribución de la duración sino que también captura funciones de azar no monótonas. El modelo propuesto es fácil de ajustar a datos de duración proporcionando resultados razonables y competitivos con otros modelos utilizados en la literatura.

https://doi.org/10.15446/rce.v39n2.51584

Conditional Duration Model and the Unobserved Market Heterogeneity of Traders: An Infinite Mixture of Non-Exponentials Modelo de duración condicionada y heterogeneidad inobservada de los agentes. Una mezcla infinita de distribuciones no exponenciales EMILIO GÓMEZ-DÉNIZ¹, JORGE V. PÉREZ-RODRÍGUEZ²

¹University of Las Palmas de Gran Canaria and TIDES Institute, Department of Quantitative Methods, Las Palmas de Gran Canaria, Spain. Professor. Email: emilio.gomez-deniz@ulpgc.es
²University of Las Palmas de Gran Canaria, Department of Quantitative Methods, Las Palmas de Gran Canaria, Spain. Professor. Email: jv.perez-rodriguez@ulpgc.es

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Abstract

This paper extends the conditional duration model proposed by Luca & Zuccolotto (2003) proposing an infinite mixture of distributions based on non-exponentials that account for the unobserved market heterogeneity of traders. The model we propose takes into account the fact that reaction times follow a gamma distribution and that the intensity parameter follows the reciprocal of an inverse Gaussian distribution. This extension allows us to capture, not only various density shapes of durations, but also non-monotonic shapes of hazard functions. The model also allows us to test the unobserved heterogeneity of traders. This mixture model is easy to fit and characterises the behaviour of the conditional durations reasonably well.

Key words: Autoregressive conditional duration model, Exponentialdistribution, Gamma distribution, Heterogeneity, Reciprocalinverse gaussian distribution.

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Resumen

Palabras clave: modelo deduración autorregresivo condicional, distribución exponencial, distribución Gamma, heterogeneidad, distribución recíproca inversagaussiana.

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[Recibido en junio de 2015. Aceptado en marzo de 2016]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv39n2a09,
    AUTHOR  = {Gómez-Déniz, Emilio and Pérez-Rodríguez, Jorge V.},
    TITLE   = {{Conditional Duration Model and the Unobserved Market Heterogeneity of Traders: An Infinite Mixture of Non-Exponentials}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2016},
    volume  = {39},
    number  = {2},
    pages   = {307-325}
}

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