A semiparametric method for estimating nonlinear autoregressive model with dependent errors

Farnoosh, Rahman; Mortazavi, Seyed Javad

doi:10.1016/j.na.2011.06.016

Cited by 15 publications

(11 citation statements)

References 18 publications

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“…) + σ u t , Farnoosh and Mortazavi [5] introduced a semi-parametric method to estimate autoregression function f . At the first, we illustrate their algorithm and then extend this procedure to our mixture model.…”

Section: The Em Algorithmmentioning

confidence: 99%

“…and then extend a semi-parametric method to estimate regression function introduced by Farnoosh and Mortazavi [5] for the single-regime models. These models are applied to the time series in which errors have periodic variations in econometric time series data and financial studies.…”

Section: Introductionmentioning

confidence: 99%

“…Tong [19] and Li [14] investigated algorithms for estimation of these models. Farnoosh and Mortazavi [5] applied this model for monetary data and proposed a semi-parametric algorithm for the estimation of regression function.…”

Section: Introductionmentioning

confidence: 99%

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Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach

Nademi

Farnoosh

2013

Journal of Applied Statistics

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We propose data generating structures which can be represented as a mixture of autoregressiveautoregressive conditionally heteroscedastic models. The switching between the states is governed by a hidden Markov chain. We investigate semi-parametric estimators for estimating the functions based on the quasi-maximum likelihood approach and provide sufficient conditions for geometric ergodicity of the process. We also present an expectation-maximization algorithm for calculating the estimates numerically.

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Section: The Em Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach

Nademi

Farnoosh

2013

Journal of Applied Statistics

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“…Farnoosh & Mortazavi () used a similar idea and presented a semiparametric estimation method for a univariate autoregressive model with dependent errors. They considered the first‐order nonlinear autoregressive model

y_{t} = f false(y_{t - 1} false) + ε_{t}, ε_{t} = ρ ε_{t - 1} + u_{t}, false| ρ false| < 1, t = 1, 2, …, n .

…”

Section: Introductionmentioning

confidence: 99%

“…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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Asymptotic properties of wavelet estimators in partially linear errors-in-variables models with long-memory errors

Cui

2018

Acta Math. Appl. Sin. Engl. Ser.

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A semiparametric method for estimating nonlinear autoregressive model with dependent errors

Cited by 15 publications

References 18 publications

Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach

Mixtures of autoregressive-autoregressive conditionally heteroscedastic models: semi-parametric approach

A semiparametric approach for modelling multivariate nonlinear time series

Asymptotic properties of wavelet estimators in partially linear errors-in-variables models with long-memory errors

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