Abstract
The analysis of low integer-valued time series is an area of growing interest as time series of counts arising from many different areas have become available in the last three decades. Statistical quality control, computer science, economics and finance, medicine and epidemiology and environmental sciences are just some of the fields that we can mention to point out the wide variety of contexts from which discrete time series have emerged.
In many of these areas it is not just the statistical modelling of count data that matters. For instance, in environmental sciences or epidemiology, surveillance and risk analysis are critical and timely intervention is mandatory in order to ensure safety and public health. Actually, a major issue in the analysis of a large variety of random phenomena relates to the ability to detect and warn the occurrence of a catastrophe or some other event connected with an alarm system.
In this work, the principles for the construction of optimal alarm systems are discussed and their implementation is described. As there is no unifying approach to the modelling of all integer-valued time series, we will focus our attention in the class of observation-driven models. The implementation of the optimal alarm system will be described in detail for a particular non-linear model in this class, the INteger-valued Asymmetric Power ARCH, or, in short, INAPARCH(p, q).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
A catastrophe is generally defined as any event of interest in the σ-field generated by Y 3.
References
Antunes, M., Amaral-Turkman, M., Turkman, K.: A Bayesian approach to event prediction. J. Time Ser. Anal. 24, 631–646 (2003)
Brännäs, K., Quoreshi, A.M.M.S.: Integer-valued moving average modelling of the number of transactions in stocks. Appl. Financ. Econ. 20, 1429–1440 (2010)
Costa, M.C.: Optimal alarm systems and its application to financial time series. PhD Thesis in Mathematics, University of Aveiro, Portugal (2014). http://hdl.handle.net/10773/12872
Costa, M.C., Scotto, M.G., Pereira, I.: Integer-valued APARCH processes. In: Rojas, I., Pomares, H. (eds.) Time Series Analysis and Forecasting, pp. 189–202. Springer International Publishing, Berlin (2016)
de Maré, J.: Optimal prediction of catastrophes with applications to Gaussian processes. Ann. Probab. 8, 841–850 (1980)
Ding, Z., Engle, R.F., Granger, C.W.J.: A long memory property of stock market returns and a new model. J. Emp. Financ. 1, 83–106 (1993)
Lindgren, G.: Optimal prediction of level crossings in Gaussian processes and sequences. Ann. Probab. 13, 804–824 (1985)
Svensson, A., Holst, J., Lindquist, R., Lindgren, G.: Optimal prediction of catastrophes in autoregressive moving average processes. J. Time Ser. Anal. 17, 511–531 (1996)
Acknowledgements
This work was supported in part by the Portuguese Foundation for Science and Technology (FCT—Fundação para a Ciência e a Tecnologia) through CIDMA—Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Costa, M.d., Pereira, I., Scotto, M.G. (2018). Surveillance in Discrete Time Series. In: Oliveira, T., Kitsos, C., Oliveira, A., Grilo, L. (eds) Recent Studies on Risk Analysis and Statistical Modeling. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-76605-8_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-76605-8_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-76604-1
Online ISBN: 978-3-319-76605-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)