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Estimation for the Prediction of Point Processes with Many Covariates

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  • Alessio Sancetta

Abstract

Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the counting process is observed. Interest lies in estimating the intensity conditional on the covariates. The impact of the covariates is modelled by an additive model where each component can be written as a linear combination of possibly unknown functions. The focus is on prediction as opposed to variable screening. Conditions are imposed on the coefficients of this linear combination in order to control the estimation error. The rates of convergence are optimal when the number of active covariates is large. As an application, the intensity of the buy and sell trades of the New Zealand dollar futures is estimated and a test for forecast evaluation is presented. A simulation is included to provide some finite sample intuition on the model and asymptotic properties.

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  • Alessio Sancetta, 2017. "Estimation for the Prediction of Point Processes with Many Covariates," Papers 1702.05315, arXiv.org.
    • Handle: RePEc:arx:papers:1702.05315
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    References listed on IDEAS

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    1. Hasbrouck, Joel, 1991. "Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
    2. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    3. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2003. "Master curve for price-impact function," Nature, Nature, vol. 421(6919), pages 129-130, January.
    4. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    5. Sancetta, Alessio, 2015. "A Nonparametric Estimator For The Covariance Function Of Functional Data," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1359-1381, December.
    6. Hall, Anthony D. & Hautsch, Nikolaus, 2007. "Modelling the buy and sell intensity in a limit order book market," Journal of Financial Markets, Elsevier, vol. 10(3), pages 249-286, August.
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