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<p>In this work, we propose an extension of the Generalized Linear Autoregressive Moving Average model for positive continuous time series. The observations, conditioned on the past information, are independent and assumed to follow the Gamma or Inverse Gaussian distributions. We also introduce a semiparametric approach to allow for non-linear relationships between the auxiliary variables and the response, linking the Generalized Additive Model to our proposal. Model parameters are estimated using the Maximum Likelihood approach. We obtain quantities that characterize the model. Simulation studies are implemented to evaluate the parameter estimation performance for finite sample sizes. The ability of the procedure to model and forecast real data is presented for time series of air pollution and mortality.</p>

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Generalized additive model for positive continuous time series

  • 期刊论文

  • 发表日期：

    2026年2月3日

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  • Gisele de Oliveira Maia,
  • Glaura da Conceição Franco

摘要

In this work, we propose an extension of the Generalized Linear Autoregressive Moving Average model for positive continuous time series. The observations, conditioned on the past information, are independent and assumed to follow the Gamma or Inverse Gaussian distributions. We also introduce a semiparametric approach to allow for non-linear relationships between the auxiliary variables and the response, linking the Generalized Additive Model to our proposal. Model parameters are estimated using the Maximum Likelihood approach. We obtain quantities that characterize the model. Simulation studies are implemented to evaluate the parameter estimation performance for finite sample sizes. The ability of the procedure to model and forecast real data is presented for time series of air pollution and mortality.