Hazard rate model and statistical analysis of a compound point process

Petr Volf

Kybernetika (2005)

  • Volume: 41, Issue: 6, page [773]-786
  • ISSN: 0023-5954

Abstract

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A stochastic process cumulating random increments at random moments is studied. We model it as a two-dimensional random point process and study advantages of such an approach. First, a rather general model allowing for the dependence of both components mutually as well as on covariates is formulated, then the case where the increments depend on time is analyzed with the aid of the multiplicative hazard regression model. Special attention is devoted to the problem of prediction of process behaviour. To this end, certain results on risk processes and crossing probabilities are recalled and utilized. The application deals with the process of financial transactions and the problem of detection of outlied trajectories.

How to cite

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Volf, Petr. "Hazard rate model and statistical analysis of a compound point process." Kybernetika 41.6 (2005): [773]-786. <http://eudml.org/doc/33787>.

@article{Volf2005,
abstract = {A stochastic process cumulating random increments at random moments is studied. We model it as a two-dimensional random point process and study advantages of such an approach. First, a rather general model allowing for the dependence of both components mutually as well as on covariates is formulated, then the case where the increments depend on time is analyzed with the aid of the multiplicative hazard regression model. Special attention is devoted to the problem of prediction of process behaviour. To this end, certain results on risk processes and crossing probabilities are recalled and utilized. The application deals with the process of financial transactions and the problem of detection of outlied trajectories.},
author = {Volf, Petr},
journal = {Kybernetika},
keywords = {counting process; compound process; Cox regression model; financial series; intensity; prediction; counting process; Cox regression model; financial series; prediction},
language = {eng},
number = {6},
pages = {[773]-786},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Hazard rate model and statistical analysis of a compound point process},
url = {http://eudml.org/doc/33787},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Volf, Petr
TI - Hazard rate model and statistical analysis of a compound point process
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 6
SP - [773]
EP - 786
AB - A stochastic process cumulating random increments at random moments is studied. We model it as a two-dimensional random point process and study advantages of such an approach. First, a rather general model allowing for the dependence of both components mutually as well as on covariates is formulated, then the case where the increments depend on time is analyzed with the aid of the multiplicative hazard regression model. Special attention is devoted to the problem of prediction of process behaviour. To this end, certain results on risk processes and crossing probabilities are recalled and utilized. The application deals with the process of financial transactions and the problem of detection of outlied trajectories.
LA - eng
KW - counting process; compound process; Cox regression model; financial series; intensity; prediction; counting process; Cox regression model; financial series; prediction
UR - http://eudml.org/doc/33787
ER -

References

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  1. Andersen P. K., Borgan O., Gill R. D., Keiding M., Statistical Models Based on Counting Processes, Springer, New York 1993 Zbl0824.60003MR1198884
  2. Arjas E., 10.1080/01621459.1988.10478588, J. Amer. Statist. Assoc. 83 (1988), 204–212 (1988) DOI10.1080/01621459.1988.10478588
  3. Asmussen S., Ruin Probabilities, World Scientific, Singapore 2000 Zbl1229.91151MR1794582
  4. Brémaud P., Point Processes and Queues: Martingale Dynamics, Springer, Berlin 1981 Zbl0478.60004MR0636252
  5. Embrechts P., Klüppelberg, K., Mikosch T., Modeling Extremal Events, Springer, Berlin 1997 MR1458613
  6. Hastie T. J., Tibshirani R. J., Generalized Additive Models, Wiley, New York 1990 Zbl0747.62061MR1082147
  7. Jacod J., Shirjajev A. N., Limit Theorems for Stochastic Processes, Springer, Berlin 2003 MR1943877
  8. Kooperberg C., Stone C. J., Truong Y. K., The L 2 rate of convergence for hazard regression, Scand. J. Statist. 22 (1995), 143–157 (1995) MR1339748
  9. Marzec L., Marzec P., 10.1214/aos/1031833669, Ann. Statist. 25 (1997), 683–714 (1997) MR1439319DOI10.1214/aos/1031833669
  10. McKeague I. W., Utikal K. J., 10.1214/aos/1176347745, Ann. Statist. 18 (1990), 1172–1187 (1990) MR1062704DOI10.1214/aos/1176347745
  11. McKeague I. W., Utikal K. J., Goodness-of-fit tests for additive hazard and proportional hazard models, Scand. J. Statist. 18 (1991), 177–195 (1991) MR1146176
  12. Rolski T., Schmidli H., Schmidt, V., Teugels J., Stochastic Processes for Insurance and Finance, Wiley, New York 1999 Zbl1152.60006MR1680267
  13. Stone C. J., 10.1214/aos/1176325361, With discussion. Ann. Statist. 22 (1994), 118–184 (1994) Zbl0827.62038MR1272079DOI10.1214/aos/1176325361
  14. Volf P., A nonparametric analysis of proportional hazard regression model, Problems Control Inform. Theory 18 (1989), 311–322 (1989) Zbl0698.62039MR1025942
  15. Volf P., Analysis of generalized residuals in hazard regression models, Kybernetika 32 (1993), 501–510 (1993) MR1420139
  16. Volf P., On cumulative process model and its statistical analysis, Kybernetika 36 (2000), 165–176 MR1760023

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