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Nonlinear semiparametric autoregressive model with finite mixtures of scale mixtures of skew normal innovations

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  • A. Hajrajabi
  • M. Maleki

Abstract

We propose data generating structures which can be represented as the nonlinear autoregressive models with single and finite mixtures of scale mixtures of skew normal innovations. This class of models covers symmetric/asymmetric and light/heavy-tailed distributions, so provide a useful generalization of the symmetrical nonlinear autoregressive models. As semiparametric and nonparametric curve estimation are the approaches for exploring the structure of a nonlinear time series data set, in this article the semiparametric estimator for estimating the nonlinear function of the model is investigated based on the conditional least square method and nonparametric kernel approach. Also, an Expectation–Maximization-type algorithm to perform the maximum likelihood (ML) inference of unknown parameters of the model is proposed. Furthermore, some strong and weak consistency of the semiparametric estimator in this class of models are presented. Finally, to illustrate the usefulness of the proposed model, some simulation studies and an application to real data set are considered.

Suggested Citation

  • A. Hajrajabi & M. Maleki, 2019. "Nonlinear semiparametric autoregressive model with finite mixtures of scale mixtures of skew normal innovations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(11), pages 2010-2029, August.
    • Handle: RePEc:taf:japsta:v:46:y:2019:i:11:p:2010-2029
    DOI: 10.1080/02664763.2019.1575953
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    Cited by:

    1. Maleki, Mohsen & Mahmoudi, Mohammad Reza & Heydari, Mohammad Hossein & Pho, Kim-Hung, 2020. "Modeling and forecasting the spread and death rate of coronavirus (COVID-19) in the world using time series models," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Akram Hoseinzadeh & Mohsen Maleki & Zahra Khodadadi, 2021. "Heteroscedastic nonlinear regression models using asymmetric and heavy tailed two-piece distributions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(3), pages 451-467, September.
    3. Atefeh Zarei & Zahra Khodadadi & Mohsen Maleki & Karim Zare, 2023. "Robust mixture regression modeling based on two-piece scale mixtures of normal distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 181-210, March.

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