Modelling informative time points: an evolutionary process approach

Andreia Monteiro (), Raquel Menezes and Maria Eduarda Silva
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Andreia Monteiro: University of Minho
Raquel Menezes: University of Minho
Maria Eduarda Silva: University of Porto

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 2, No 4, 364-382

Abstract: Abstract Real time series sometimes exhibit various types of “irregularities”: missing observations, observations collected not regularly over time for practical reasons, observation times driven by the series itself, or outlying observations. However, the vast majority of methods of time series analysis are designed for regular time series only. A particular case of irregularly spaced time series is that in which the sampling procedure over time depends also on the observed values. In such situations, there is stochastic dependence between the process being modelled and the times of the observations. In this work, we propose a model in which the sampling design depends on all past history of the observed processes. Taking into account the natural temporal order underlying available data represented by a time series, then a modelling approach based on evolutionary processes seems a natural choice. We consider maximum likelihood estimation of the model parameters. Numerical studies with simulated and real data sets are performed to illustrate the benefits of this model-based approach.

Keywords: Evolutionary processes; Informative time points; Continuous-time autoregressive process; 62M10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11749-020-00722-2

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