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Replicated INAR(1) Processes

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Abstract

Replicated time series are a particular type of repeated measures, which consist of time-sequences of measurements taken from several subjects (experimental units). We consider independent replications of count time series that are modelled by first-order integer-valued autoregressive processes, INAR(1). In this work, we propose several estimation methods using the classical and the Bayesian approaches and both in time and frequency domains. Furthermore, we study the asymptotic properties of the estimators. The methods are illustrated and their performance is compared in a simulation study. Finally, the methods are applied to a set of observations concerning sunspot data.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    Isabel Silva & M. Eduarda Silva

  2. Departamento de Matemática, Universidade de Aveiro, Aveiro, Portugal

    Isabel Pereira & Nélia Silva

  3. UI&D Matemática e Aplicações, Universidade de Aveiro, Aveiro, Portugal

    M. Eduarda Silva, Isabel Pereira & Nélia Silva

  4. Departamento de Engenharia Civil, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal

    Isabel Silva

Authors
  1. Isabel Silva
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  2. M. Eduarda Silva
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  3. Isabel Pereira
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  4. Nélia Silva
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Correspondence to M. Eduarda Silva.

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AMS 2000 Subject Classification

62M10, 91B70, 60G10

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Silva, I., Silva, M.E., Pereira, I. et al. Replicated INAR(1) Processes. Methodol Comput Appl Probab 7, 517–542 (2005). https://doi.org/10.1007/s11009-005-5006-x

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  • DOI: https://doi.org/10.1007/s11009-005-5006-x

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