Asymptotic Theory of Integrated Conditional Moment Tests

Bierens, Herman J.; Ploberger, Werner

doi:10.2307/2171881

Cited by 266 publications

(226 citation statements)

References 23 publications

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“…Lee et al 1993, Bierens 1990), or computing test functionals like the supremum or average (Davies 1977, Bierens 1990, Hill 2008a. Alternatively, Bierens (1982) and Bierens and Ploberger (1997) integrate a scaled sample version of ([   ( 0   )]) 2 over ¡ for the ICM test. See Section 2, below, for the construction.…”

Section: An Interior Point Of ©mentioning

confidence: 99%

“…Davies (1977) and Bierens (1990). Instead, we operate directly on() a la Bierens (1982) and Bierens and Ploberger (1997).…”

Section: Stochastically Weighted Average Testmentioning

confidence: 99%

“…In this paper we propose a consistent Conditional Moment [CM] test of regression model function form in the spirit of the Integrated Conditional Moment [ICM] test of Bierens (1982) and Bierens and Ploberger (1997). We tackle the nuisance parameter problem by reducing the space to integers, e¤ectively reducing the ICM statistic to a weighted average.…”

Section: Introductionmentioning

confidence: 99%

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Stochastically weighted average conditional moment tests of functional form

Hill

2013

Studies in Nonlinear Dynamics and Econometrics

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We develop a new consistent conditional moment test of functional form based on nuisance parameter indexed sample moments first presented in Bierens (1982Bierens ( , 1990. We reduce the nuisance parameter space to known countable sets, which leads to a weighted average conditional moment test in the spirit of Bierens and Ploberger's (1997) Integrated Conditional Moment test. The weights are possibly stochastic in an arbitrary way, integer-indexed and flexible enough to cover a range of tests from average to higher quantile to maximum tests. The limit distribution under the null and local alternative belong to the same class as the ICM statistic, hence our test is admissible if the errors are Gaussian, and a flat weight leads to the greatest weighted average local power. * We thank two anonymous referees for their careful reading and feedback, and Editor Bruce Mizrach for helpful recommendations.

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Section: An Interior Point Of ©mentioning

confidence: 99%

“…Davies (1977) and Bierens (1990). Instead, we operate directly on() a la Bierens (1982) and Bierens and Ploberger (1997).…”

Section: Stochastically Weighted Average Testmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastically weighted average conditional moment tests of functional form

Hill

2013

Studies in Nonlinear Dynamics and Econometrics

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“…The exponential function w 0 ( e Y t;P ; x) = exp(ix 0 e Y t;P ); x 2 R; was …rst considered in Bierens (1982Bierens ( , 1984Bierens ( , 1990; see also Bierens and Ploberger (1997). One version of the Cramér-von Mises (CvM) test of Bierens (1984) leads to the test statistic…”

Section: Tests Based On a …Nite-dimensional Conditioning Setmentioning

confidence: 99%

Testing the Martingale Hypothesis

Escanciano¹,

Lobato²

2009

Palgrave Handbook of Econometrics

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This article examines testing the Martingale Di¤erence Hypothesis (MDH) and related statistical inference issues. The earlier literature on testing the MDH was based on linear measures of dependence, such as sample autocorrelations, for instance the classical Box-Pierce Portmanteau test and the Variance Ratio test. In order to account for the existing nonlinearity in economic and …nancial data, two directions have been entertained. First, to modify these classical approaches by taking into account the possible nonlinear dependence. Second, to use more sophisticated statistical tools such as those based on empirical processes theory or the use of generalized spectral analysis. This paper discusses these developments and applies them to exchange rate data.

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“…To the best of our knowledge, the asymptotic behavior of the nonlinearity tests for nonstationary processes has not yet been investigated. Our tests are also related to the model specification tests by Bierens(1990), Bierens andPloberger (1997) andde Jong (1996), see the next section for more discussions.…”

Section: Introductionmentioning

confidence: 99%

A Test of the Martingale Hypothesis

Park¹,

Whang²

2005

Studies in Nonlinear Dynamics &Amp; Econometrics

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This paper proposes a statistical test of the martingale hypothesis. It can be used to test whether a given time series is a martingale process against certain non-martingale alternatives. The class of alternative processes against which our test has power is very general and it encompasses many nonlinear non-martingale processes which may not be detected using traditional spectrum-based or variance-ratio tests. We look at the hypothesis of martingale, in contrast with other existing methods which test for the hypothesis of martingale difference. Two different types of test are considered: one is a generalized Kolmogorov-Smirnov test and the other is a Cramer-von Mises type test. For the processes that are first order Markovian in mean, in particular, our approach yields the test statistics that neither depend upon any smoothing parameter nor require any resampling procedure to simulate the null distributions. Their null limiting distributions are nicely characterized as functionals of a continuous stochastic process so that the critical values are easily tabulated. We prove consistency of our tests and further investigate their finite sample properties via simulation. Our tests are found to be rather powerful in moderate size samples against a wide variety of non-martingales including exponential autoregressive, threshold autoregressive, markov switching, chaotic, and some of nonstationary processes.

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Asymptotic Theory of Integrated Conditional Moment Tests

Cited by 266 publications

References 23 publications

Stochastically weighted average conditional moment tests of functional form

Stochastically weighted average conditional moment tests of functional form

Testing the Martingale Hypothesis

A Test of the Martingale Hypothesis

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