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A Novel First-Order Autoregressive Moving Average Model to Analyze Discrete-Time Series Irregularly Observed

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Theory and Applications of Time Series Analysis and Forecasting (ITISE 2021)

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Abstract

A novel first-order autoregressive moving average model for analyzing discrete-time series observed at irregularly spaced times is introduced. Under Gaussianity, it is established that the model is strictly stationary and ergodic. In the general case, it is shown that the model is weakly stationary. The lowest dimension of the state-space representation is given along with the one-step linear predictors and their mean squared errors. The maximum likelihood estimation procedure is discussed, and their finite-sample behavior is assessed through Monte Carlo experiments. These experiments show that the bias, the root mean square error, and the coefficient of variation are smaller when the length of the series increases. Further, the method provides good estimations for the standard errors, even with relatively small sample sizes. Also, the irregularly spaced times seem to increase the estimation variability. The application of the proposed model is made through two real-life examples. The first is concerned with medical data, whereas the second describes an astronomical data set analysis.

This article is based on Chapter 3 of the first author’s doctoral thesis [28]. Supported by CONICYT PFCHA/2015-21151457 and the ANID Millennium Science Initiative ICN12_009, awarded to the Millennium Institute of Astrophysics.

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Author information

Authors and Affiliations

  1. Escuela de Estadística, Universidad del Valle, Cali, Colombia

    César Ojeda

  2. Millennium Institute of Astrophysics, Santiago, Chile

    Wilfredo Palma

  3. Faculty of Engineering and Sciences, Universidad Adolfo Ibañez, Santiago, Chile

    Susana Eyheramendy

  4. Department of Mathematics and Computer Science, Universidad de Santiago, Santiago, Chile

    Felipe Elorrieta

Authors
  1. César Ojeda
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  2. Wilfredo Palma
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  3. Susana Eyheramendy
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  4. Felipe Elorrieta
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Corresponding author

Correspondence to César Ojeda .

Editor information

Editors and Affiliations

  1. Faculty of Sciences, University of Granada, Granada, Spain

    Olga Valenzuela

  2. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Fernando Rojas

  3. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Luis Javier Herrera

  4. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Héctor Pomares

  5. ETSIIT, CITIC-UGR, University of Granada, Granada, Spain

    Ignacio Rojas

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Ojeda, C., Palma, W., Eyheramendy, S., Elorrieta, F. (2023). A Novel First-Order Autoregressive Moving Average Model to Analyze Discrete-Time Series Irregularly Observed. In: Valenzuela, O., Rojas, F., Herrera, L.J., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis and Forecasting. ITISE 2021. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-031-14197-3_7

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