@misc{10481/72028,
year = {2019},
month = {2},
url = {http://hdl.handle.net/10481/72028},
abstract = {Compound Cox processes (CCP) are flexible marked point processes due to the
stochastic nature of their intensity. This paper states closed-form expressions of their
counting and time statistics in terms of the intensity and of the mean processes. They
are forecast by means of principal components prediction models applied to the mean
process in order to reach attainable results. A proposition proves that only weak restrictions are needed to estimate the probability of a new occurrence. Additionally, the
phase type process is introduced, which important feature is that its marginal distributions are phase type with random parameters. Since any non-negative variable can be
approximated by a phase-type distribution, the new stochastic process is proposed to
model the intensity process of any point process. The CCP with this type of intensity
provides an especially general model. Several simulations and the corresponding study
of the estimation errors illustrate the results and their accuracy. Finally, an application
to real data is performed; extreme temperatures in the South of Spain are modeled by
a CPP and forecast.},
organization = {Ministerio de Economía y Competitividad (project MTM2013-47929-P)},
organization = {Consejería de Innovación de la Junta de Andalucía (Grants FQM-307 and FQM246)},
publisher = {Springer},
keywords = {Compound Cox process},
keywords = {Estimation},
keywords = {Principal Components Prediction},
keywords = {Phase type process},
title = {Forecasting counting and time statistics of compound Cox processes: a focus on intensity phase type process, deletions and simultaneous events},
doi = {https://doi.org/10.1007/s00362-019-01092-0},
author = {Rodríguez Bouzas, Paula and Ruiz-Fuentes, Nuria and Montes Gijón, María del Carmen and Ruiz Castro, Juan Eloy},
}