The Chen Autoregressive Moving Average Model for Modeling Asymmetric Positive Continuous Time Series

Author:

Stone Renata F.12ORCID,Loose Laís H.1ORCID,Melo Moizés S.13ORCID,Bayer Fábio M.124ORCID

Affiliation:

1. Departamento de Estatística, Universidade Federal de Santa Maria, Santa Maria 97105-900, Brazil

2. Programa de Pós-Graduação em Engenharia de Produção, Universidade Federal de Santa Maria, Santa Maria 97105-900, Brazil

3. Programa de Pós-Graduação em Ambientometria, Universidade Federal do Rio Grande, Rio Grande 96203-900, Brazil

4. Santa Maria Space Science Laboratory (LACESM), Universidade Federal de Santa Maria, Santa Maria 97105-900, Brazil

Abstract

In this paper, we introduce a new dynamic model for time series based on the Chen distribution, which is useful for modeling asymmetric, positive, continuous, and time-dependent data. The proposed Chen autoregressive moving average (CHARMA) model combines the flexibility of the Chen distribution with the use of covariates and lagged terms to model the conditional median response. We introduce the CHARMA structure and discuss conditional maximum likelihood estimation, hypothesis testing inference along with the estimator asymptotic properties of the estimator, diagnostic analysis, and forecasting. In particular, we provide closed-form expressions for the conditional score vector and the conditional information matrix. We conduct a Monte Carlo experiment to evaluate the introduced theory in finite sample sizes. Finally, we illustrate the usefulness of the proposed model by exploring two empirical applications in a wind-speed and maximum-temperature time-series dataset.

Funder

Fundação de Amparo à Pesquisa do Estado do Rio Grande do Sul (FAPERGS), Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Reference29 articles.

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4. McCullagh, P., and Nelder, J. (1989). Generalized Linear Models, Chapman and Hall. [2nd ed.].

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