A Semiparametric Estimation for the First-Order Nonlinear Autoregressive Time Series Model with Independent and Dependent Errors

Farnoosh, Rahman; Hajebi, Mahtab; Samadi, S. Yaser

doi:10.1007/s40995-018-0538-4

Cited by 5 publications

(3 citation statements)

References 12 publications

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“…To investigate asymptotic behaviors of the estimators, we consider the following assumptions A1-A12 of Farnoosh et al [21]: (A1) f(•) is Lipschitz continuous and all moments of innovations are finite with Lipschitz density function. Also, the sequence Z t 􏼈 􏼉 is a stationary ergodic sequence of integrable random variables.…”

Section: Appendixmentioning

confidence: 99%

A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations

Sakhabakhsh

Farnoosh

Fallah

et al. 2022

Advances in Mathematical Physics

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The nonlinear autoregressive models under normal innovations are commonly used for nonlinear time series analysis in various fields. However, using this class of models for modeling skewed data leads to unreliable results due to the disability of these models for modeling skewness. In this setting, replacing the normality assumption with a more flexible distribution that can accommodate skewness will provide effective results. In this article, we propose a partially linear autoregressive model by considering the skew normal distribution for independent and dependent innovations. A semiparametric approach for estimating the nonlinear part of the regression function is proposed based on the conditional least squares approach and the nonparametric kernel method. Then, the conditional maximum-likelihood approach is used to estimate the unknown parameters through the expectation-maximization (EM) algorithm. Some asymptotic properties for the semiparametric method are established. Finally, the performance of the proposed model is verified through simulation studies and analysis of a real dataset.

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Section: Appendixmentioning

confidence: 99%

A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations

Sakhabakhsh

Farnoosh

Fallah

et al. 2022

Advances in Mathematical Physics

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“…Our goal is to estimate the unknown vector function F ( X ). To this end, similarly to Yu, Wang & Shi (), Farnoosh & Mortazavi () and Farnoosh, Hajebi & Samadi () for the univariate case, we assume a parametric framework for the vector autoregression function F ( X ), that is, G ( X , Θ ). However, unlike in Yu, Wang & Shi () and Farnoosh & Mortazavi (), instead of making a crude guess of the true density function F (·), we use a multivariate Taylor series expansion approximation to estimate the parametric function G ( X , Θ ).…”

Section: Introductionmentioning

confidence: 99%

A semiparametric approach for modelling multivariate nonlinear time series

2019

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In this article, a semiparametric time‐varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short‐run interest rates and long‐run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach. The Canadian Journal of Statistics 47: 668–687; 2019 © 2019 Statistical Society of Canada

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“…Desvina dan Juliana (2016) melakukan pemodelan VAR untuk pemodelan pencemaran udara di kepulauan Riau. Farnoosh, et al, (2017) telah mengembangkan model VAR berbasis nonlinier. Correa et al, (2017) (Zhao and Chen, 2015):…”

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Modelling Inflation Sectors in Indonesia Using Vector Autoregressive (VAR)

Prahutama¹,

Suparti²,

Ispriyanti³

et al. 2019

J. I. Dasar

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Analisis time series dapat dibagi menjadi dua yaitu analisis time series univariat dan analisis time series multivariat. Analisis time series univariat salah satunya menggunakan ARIMA, sedangkan analisis time series multivariat dapat menggunakan VAR. VAR merupakan pemodelan persamaan simultan yang memiliki beberapa variabel endogen secara bersamaan. Asumsi dalam model VAR antara lain terjadi kausalitas antar variabel (kausalitas Granger), residual white noise dan berdistribusi normal multivariat. Pada paper ini, metode VAR diimplementasikan dalam memodelkan sektor-sektor Inflasi di Indonesia. Adapun sektor-sektor tersebut antara lain sektor makanan (Y1t),Sektor Makanan Jadi, Minuman, Rokok dan Tembakau (Y2), Sektor perumahan, listrik, air, gas dan bahan bakar (Y3), Sektor Sandang (Y4), Sektor Kesehatan (Y5), Sektor Pendidikan dan Olahraga (Y6), Sektor Transportasi, Komunikasi dan Jasa Keuangan (Y7). Hasilnya adalah tidak semua variabel sektor inflasi berpengaruh terhadap sektor lainnya. Hanya beberapa variabel yang berpengaruh terhadap suatu sektor. Asumsi kausalitas Granger tidak semua dipenuhi oleh semua variabel. Begitu juga dengan normal multivariat juga tidak terpenuhi. Akan tetapi residual model sudah white noise. Keywords: vector autoregressive model, sectors of inflation, Granger Causality.

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A Semiparametric Estimation for the First-Order Nonlinear Autoregressive Time Series Model with Independent and Dependent Errors

Cited by 5 publications

References 12 publications

A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations

A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations

A semiparametric approach for modelling multivariate nonlinear time series

Modelling Inflation Sectors in Indonesia Using Vector Autoregressive (VAR)

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