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A notable Gamma‐Lindley first‐order autoregressive process: An application to hydrological data

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  • Alice B. V. Mello
  • Maria C. S. Lima
  • Abraão D. C. Nascimento

Abstract

A new Gamma‐Lindley (GaL) first‐order autoregressive process (AR) is introduced, called GaL‐AR(1). The distribution for the GaL‐AR(1) innovation process and some of its structural properties are derived, such as the Laplace transform for its bivariate distribution, the conditional variance and expected value, and the spectral and autocorrelation functions. We propose two different estimation procedures whose asymptotic properties are studied by Monte Carlo experiments. An application to actual data from hydrology is performed. Results point out that our process outperforms other six non‐Gaussian AR(1) models that are well defined in the time series literature.

Suggested Citation

  • Alice B. V. Mello & Maria C. S. Lima & Abraão D. C. Nascimento, 2022. "A notable Gamma‐Lindley first‐order autoregressive process: An application to hydrological data," Environmetrics, John Wiley & Sons, Ltd., vol. 33(4), June.
    • Handle: RePEc:wly:envmet:v:33:y:2022:i:4:n:e2724
    DOI: 10.1002/env.2724
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    1. Vinícius T. Scher & Francisco Cribari‐Neto & Guilherme Pumi & Fábio M. Bayer, 2020. "Goodness‐of‐fit tests for βARMA hydrological time series modeling," Environmetrics, John Wiley & Sons, Ltd., vol. 31(3), May.
    2. Caroline Keef & Jonathan A. Tawn & Rob Lamb, 2013. "Estimating the probability of widespread flood events," Environmetrics, John Wiley & Sons, Ltd., vol. 24(1), pages 13-21, February.
    3. Xiaoting Li & Christian Genest & Jonathan Jalbert, 2021. "A self‐exciting marked point process model for drought analysis," Environmetrics, John Wiley & Sons, Ltd., vol. 32(8), December.
    4. B. Abraham & N. Balakrishna, 1999. "Inverse Gaussian Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(6), pages 605-618, November.
    5. Olivia Grigg & Jonathan Tawn, 2012. "Threshold models for river flow extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 23(4), pages 295-305, June.
    6. Vinod, Hrishikesh D. & Lopez-de-Lacalle, Javier, 2009. "Maximum Entropy Bootstrap for Time Series: The meboot R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i05).
    7. Ed McKenzie, 1985. "An Autoregressive Process for Beta Random Variables," Management Science, INFORMS, vol. 31(8), pages 988-997, August.
    8. Jose, K.K. & Tomy, Lishamol & Sreekumar, J., 2008. "Autoregressive processes with normal-Laplace marginals," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2456-2462, October.
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