The Bierens test for certain nonstationary models

Kasparis, Ioannis

doi:10.1016/j.jeconom.2010.01.008

Cited by 16 publications

(7 citation statements)

References 26 publications

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“…Certain nonlinear transformations (e.g. concave, bounded, integrable transformations) reduce the signal of the data (see Park and Phillips, 1998;Marmer, 2007;Kasparis, 2010;Berenguer-Rico and Gonzalo, 2014). The effects of such nonlinear transformations on the signal of a persistent process is demonstrated in Fig.…”

Section: Stock Market Return Predictabilitymentioning

confidence: 99%

Nonparametric predictive regression

Kasparis

Andreou

Phillips

2015

Journal of Econometrics

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a b s t r a c tA unifying framework for inference is developed in predictive regressions where the predictor has unknown integration properties and may be stationary or nonstationary. Two easily implemented nonparametric F-tests are proposed. The limit distribution of these predictive tests is nuisance parameter free and holds for a wide range of predictors including stationary as well as non-stationary fractional and near unit root processes. Asymptotic theory and simulations show that the proposed tests are more powerful than existing parametric predictability tests when deviations from unity are large or the predictive regression is nonlinear. Empirical illustrations to monthly SP500 stock returns data are provided.

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Section: Stock Market Return Predictabilitymentioning

confidence: 99%

Nonparametric predictive regression

Kasparis

Andreou

Phillips

2015

Journal of Econometrics

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“…where g(·, ·; θ) is a known parametric function indexed by θ, a vector of unknown parameters, θ 0 ∈ Θ 0 with Θ 0 being a compact subset of R k for k ≥ 1, and ∆ n (x, z) is a sequence of nonparametrically unknown departure functions. Recent studies in the field of nonparametric model specification of integrated time series models include Marmer (2007), Kasparis (2008), Gao et al (2009a;, Hong and Phillips (2010), Kasparis (2010), , , and Wang and Phillips (2012). The proposed tests by Gao et al (2009a), and Wang and Phillips (2012) use exactly the same type of tests as those originally developed for the stationary time series case (see, for example, Chapter 3 of Gao 2007).…”

Section: Introductionmentioning

confidence: 99%

Specification testing for nonlinear multivariate cointegrating regressions

Dong

Gao

Tjøstheim

et al. 2017

Journal of Econometrics

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This paper considers a general model specification test for nonlinear multivariate cointegrating regressions where the regressor consists of a univariate integrated time series and a vector of stationary time series. The regressors and the errors are generated from the same innovations, so that the model accommodates endogeniety. A new and simple test is proposed and the resulting asymptotic theory is established. The test statistic is constructed based on a natural distance function between a nonparametric estimate and a smoothed parametric counterpart. The asymptotic distribution of the test statistic under the parametric specification is proportional to that of a local-time random variable with a known distribution. In addition, the finite sample performance of the proposed test is evaluated through using both simulated and real data examples.

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“…For example, Hill (2008) extends Bierens'and de Jong's approach to construct a consistent test that has maximal power against smooth transition autoregressive (STAR) alternatives. Kasparis (2010) extends Bierens test in the context of non-stationary regressors. Whang (2000Whang ( , 2001 and Delgado, Dominguez and Lavergne (2006) propose consistent tests in an i.i.d.…”

Section: Introductionmentioning

confidence: 91%

Consistent Testing of Functional Form in Time Series Models

Halunga¹,

Davidson²

2014

Essays in Nonlinear Time Series Econometrics

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We develop a consistent procedure for testing the adequacy of parametric time series models. The approach is to extend Herman Bierens' idea of examining the covariances between regression residuals and an exponential weight function, to check the full range of orthogonalities predicted for the score contributions in quasi-maximum likelihood estimation. Tests of this type, which involve nuisance parameters, are constructed as either 'sup'ed or integrated conditional moment tests, and are often implemented using bootstrap methods. However, our emphasis in this study is on practical implementation. We study a two-statistic approach that aims to exploit the available power while keeping computing requirements to a minimum.

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The Bierens test for certain nonstationary models

Cited by 16 publications

References 26 publications

Nonparametric predictive regression

Nonparametric predictive regression

Specification testing for nonlinear multivariate cointegrating regressions

Consistent Testing of Functional Form in Time Series Models

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