Martingale Approach in the Theory of Goodness-of-Fit Tests

Khmaladze, Estáte V.

doi:10.1137/1126027

Cited by 209 publications

(175 citation statements)

References 9 publications

Supporting

Mentioning

175

Contrasting

Order By: Relevance

“…To obtain the pivotal property of the test they use a martingale transform (cf. Khmaladze, 1981). Alternatively, He and Zhu (2003) develop a bootstrap-based test for linear and nonlinear quantile regressions.…”

Section: Introductionmentioning

confidence: 99%

Specification tests of parametric dynamic conditional quantiles

Escanciano

Velasco

2010

Journal of Econometrics

View full text Add to dashboard Cite

This article proposes omnibus speci…cation tests of parametric dynamic quantile regression models. Contrary to the existing procedures, we allow for a ‡exible and general speci…cation framework where a possibly continuum of quantiles are simultaneously speci…ed. This is the case for many econometric applications for both time series and cross section data which require a global diagnostic tool. We study the asymptotic distribution of the test statistics under fairly weak conditions on the serial dependence in the underlying data generating process. It turns out that the asymptotic null distribution depends on the data generating process and the hypothesized model. We propose a subsampling procedure for approximating the asymptotic critical values of the tests. An appealing property of the proposed tests is that they do not require estimation of the non-parametric (conditional) sparsity function. A Monte Carlo study compares the proposed tests and shows that the asymptotic results provide good approximations for small sample sizes. Finally, an application to some European stock indexes provides evidence that our methodology is a powerful and ‡exible alternative to standard backtesting procedures in evaluating market risk by using information from a range of quantiles in the lower tail of returns.

show abstract

Section: Introductionmentioning

confidence: 99%

Specification tests of parametric dynamic conditional quantiles

Escanciano

Velasco

2010

Journal of Econometrics

View full text Add to dashboard Cite

show abstract

“…In the introduction of [7] the following transformation was considered as an example (of more general case, which then followed): if v is the standard Brownian bridge, then the process b, defined as…”

Section: Some Previous Results Revisitedmentioning

confidence: 99%

Some new connections between Brownian bridges and Brownian motions

Khmaladze¹

2015

COSA

View full text Add to dashboard Cite

“…Therefore, critical values for the tests statistics can not be tabulated for general cases. One possibility, only explored in the literature for the case P = 1 by Koul and Stute (1997), consists of applying the so-called Khmaladze's transformation (Khmaladze, 1981) to get asymptotically distribution free tests. Extensions to P > 1 are not available yet.…”

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

confidence: 99%

Testing the Martingale Hypothesis

Escanciano¹,

Lobato²

2009

Palgrave Handbook of Econometrics

View full text Add to dashboard Cite

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.

show abstract

Martingale Approach in the Theory of Goodness-of-Fit Tests

Cited by 209 publications

References 9 publications

Specification tests of parametric dynamic conditional quantiles

Specification tests of parametric dynamic conditional quantiles

Some new connections between Brownian bridges and Brownian motions

Testing the Martingale Hypothesis

Contact Info

Product

Resources

About