Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form

Pavlidis, Efthymios; Paya, Iván; Peel, David

doi:10.2202/1558-3708.1702

Cited by 15 publications

(16 citation statements)

References 83 publications

(114 reference statements)

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“…Wong and Li (1997) show that a test for threshold autoregression can be heavily oversized in the presence of ARCH innovations. A similar finding is provided by Hurn and Becker (2009) for the neural network test of Teräsvirta, Lin, and Granger (1993), and by Pavlidis, Ivan, and Peel (2010) for the test of Escribano and Jordá (1999).…”

Section: Introductionsupporting

confidence: 85%

“…A bootstrap technique that appears to perform particularly well in the context of linearity testing is the fixeddesign wild bootstrap (WB) of Wu (1986) and Mammen (1993). For a detailed description of the WB, see Pavlidis et al (2010).…”

Section: A Maximum Likelihood Approachmentioning

confidence: 99%

“…The findings of Wong and Li (1997), Hurn and Becker (2009), and Pavlidis et al (2010) are based on Monte Carlo simulations. In this paper, we adopt a simple theoretical framework to investigate analytically the properties of three popular linearity tests against smooth transitional nonlinearity in the presence of ARCH dynamics.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The spurious effect of ARCH errors on linearity tests: a theoretical note and an alternative maximum likelihood approach

Pavlidis

Tsionas

2017

Studies in Nonlinear Dynamics &Amp; Econometrics

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Linearity tests against smooth transition nonlinearity are typically based on the standard least-squares (LS) covariance matrix estimator. We derive an expression for the bias of the LS estimator in the presence of ARCH errors. We show that the bias is downward, and increases dramatically with the persistence of the variance process. As a consequence, conventional tests spuriously indicate nonlinearity. Next, we examine an alternative maximum likelihood approach. Our findings suggest that this approach has substantially better size properties than tests based on least-squares and heteroskedasticity-consistent matrix estimators, and performs comparably to a bootstrap technique.

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Section: Introductionsupporting

confidence: 85%

Section: A Maximum Likelihood Approachmentioning

confidence: 99%

See 1 more Smart Citation

The spurious effect of ARCH errors on linearity tests: a theoretical note and an alternative maximum likelihood approach

Pavlidis

Tsionas

2017

Studies in Nonlinear Dynamics &Amp; Econometrics

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“…In the general case (case 1) we use the constant variance (homoscedasticity) in the estimation of the asymptotic critical values. Using conventional tests is dangerous [18] though the best performance among these is a HCCME used by [19]. We have also used the hetroscedastic consistent covariance matrix (HCCM) in the estimation of standard error which was introduced by [20] and [21].…”

Section: Testing Unit Root Hypothesis Against Estar Using Heteroscedamentioning

confidence: 99%

Unit Root Testing and Estimation in Nonlinear ESTAR Models with Normal and Non-Normal Errors

et al. 2016

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Exponential Smooth Transition Autoregressive (ESTAR) models can capture non-linear adjustment of the deviations from equilibrium conditions which may explain the economic behavior of many variables that appear non stationary from a linear viewpoint. Many researchers employ the Kapetanios test which has a unit root as the null and a stationary nonlinear model as the alternative. However this test statistics is based on the assumption of normally distributed errors in the DGP. Cook has analyzed the size of the nonlinear unit root of this test in the presence of heavy-tailed innovation process and obtained the critical values for both finite variance and infinite variance cases. However the test statistics of Cook are oversized. It has been found by researchers that using conventional tests is dangerous though the best performance among these is a HCCME. The over sizing for LM tests can be reduced by employing fixed design wild bootstrap remedies which provide a valuable alternative to the conventional tests. In this paper the size of the Kapetanios test statistic employing hetroscedastic consistent covariance matrices has been derived and the results are reported for various sample sizes in which size distortion is reduced. The properties for estimates of ESTAR models have been investigated when errors are assumed non-normal. We compare the results obtained through the fitting of nonlinear least square with that of the quantile regression fitting in the presence of outliers and the error distribution was considered to be from t-distribution for various sample sizes.

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“…In that case, such a 'parent' model is the mean equation and the (GARCH) model is the variance equation. The innovations of the STAR model are expected follow normal distribution (homoscedasticity) but in case this is not true, the innovations are said to possess heteroscedasticity, which can be of various forms (Pavlidis, Paya and Peel, 2010). The mean and variance equations are then compounded as STAR-GARCH model.…”

Section: Introductionmentioning

confidence: 99%

Specifying Asymmetric STAR models with Linear and Nonlinear GARCH Innovations: Monte Carlo Approach

Yaya

Shittu

2014

J. Mod. App. Stat. Meth.

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Economic and finance time series are typically asymmetric and are expected to be modeled using asymmetrical nonlinear time series models. Smooth Transition Autoregressive (STAR) models: Logistic (LSTAR) and Exponential (ESTAR) are known to be asymmetric and symmetric respectively. Under non-normal and heteroscedastic innovations, the residuals of these models are estimated using Generalized Autoregressive Conditionally Heteroscedastic (GARCH) models with variants which include linear and nonlinear forms. The small sample properties of STAR-GARCH variants are yet to be established but these properties are investigated using Monte Carlo (MC) simulation. An MC investigation was conducted to investigate the performance of selections of STAR-GARCH models by classical nonlinear selection approaches. The ARCH(1) and GARCH(1,1) models were the linear GARCH specifications while the Logistic Smooth Transition-ARCH (LST-ARCH(1,1)), Logistic Smooth Transition-GARCH (LST-GARCH(1,1)) and Asymmetric Nonlinear Smooth Transition-GARCH (ANST-GARCH(1,1)) models were the nonlinear GARCH specifications. The nonlinearity parameter in the variance equations and Autoregressive (AR) parameters were varied along with different sample sizes. With the assumption of normality, the results showed that the selection of LSTAR models were actually affected by the structure of the innovations and this improved as sample size increased. Misspecification tests showed that these models cannot be misrepresented in the real sense.

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Specifying Smooth Transition Regression Models in the Presence of Conditional Heteroskedasticity of Unknown Form

Cited by 15 publications

References 83 publications

The spurious effect of ARCH errors on linearity tests: a theoretical note and an alternative maximum likelihood approach

The spurious effect of ARCH errors on linearity tests: a theoretical note and an alternative maximum likelihood approach

Unit Root Testing and Estimation in Nonlinear ESTAR Models with Normal and Non-Normal Errors

Specifying Asymmetric STAR models with Linear and Nonlinear GARCH Innovations: Monte Carlo Approach

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