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ESTIMATION FOR THE PREDICTION OF POINT PROCESSES WITH MANY COVARIATES

Published online by Cambridge University Press:  24 April 2017

Alessio Sancetta
Alessio Sancetta*
Affiliation:
Royal Holloway, University of London
*
*Address correspondence to Alessio Sancetta, Department of Economics, Royal Holloway University of London, Egham TW20 0EX, UK; e-mail: [email protected], URL: http://sites.google.com/site/wwwsancetta/.
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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.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 3 , June 2018 , pp. 598 - 627
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

I would like to thank the Editor, the Co-Editor, the referees, and Luca Mucciante for comments that led to substantial improvements both in content and presentation.

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