Testing for Zero Autocorrelation in the Presence of Statistical 
Dependence

Lobato, Ignacio N.; Nankervis, John C.; Savin, N. E.

doi:10.1017/s0266466602183083

Cited by 80 publications

(78 citation statements)

References 28 publications

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“…Assuming also that {ε θ 0 t } t∈Z follows a Gaussian GARCH process, then a (i,j) θ 0 = 0, i = j, which makes the estimation easier; see Lobato, Nankervis, and Savin (2002).…”

Section: Introductionmentioning

confidence: 99%

An Asymptotically Pivotal Transform of the Residuals Sample Autocorrelations With Application to Model Checking

Delgado

Velasco

2011

Journal of the American Statistical Association

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We propose an asymptotically distribution-free transform of the sample autocorrelations of residuals in general parametric time series models, possibly nonlinear in variables. The residuals autocorrelation function is the basic model checking tool in time series analysis, but it is not useful when its distribution is incorrectly approximated because the effects of parameter estimation and/or higher-order serial dependence have not been taken into account. The limiting distribution of the residuals sample autocorrelations may be difficult to derive, particularly when the underlying innovations are uncorrelated but not independent. In contrast, our proposal is easily implemented in fairly general contexts and the resulting transformed sample autocorrelations are asymptotically distributed as independent standard normals when innovations are uncorrelated, providing an useful and intuitive device for time series model checking in the presence of estimated parameters. We also discuss in detail alternatives to the classical Box-Pierce test, showing that our transform entails no efficiency loss under Gaussianity in the direction of MA and AR departures from the white noise hypothesis, as well as alternatives to Bartlett's T p -process test. The finite-sample performance of the procedures is examined in the context of a Monte Carlo experiment for the new goodness-of-fit tests discussed in the article. The proposed methodology is applied to modeling the autocovariance structure of the well-known chemical process temperature reading data already used for the illustration of other statistical procedures. Additional technical details are included in a supplemental material online.

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“…Assuming also that {ε θ 0 t } t∈Z follows a Gaussian GARCH process, then a (i,j) θ 0 = 0, i = j, which makes the estimation easier; see Lobato, Nankervis, and Savin (2002).…”

Section: Introductionmentioning

confidence: 99%

An Asymptotically Pivotal Transform of the Residuals Sample Autocorrelations With Application to Model Checking

Delgado

Velasco

2011

Journal of the American Statistical Association

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“…The …rst one is to modify the Q p statistic by introducing a consistent estimator of the asymptotic null covariance matrix of the sample autocorrelations, b T ; so that the modi…ed Q p statistic retains the 2 p asymptotic null distribution. Lobato, Nankervis and Savin (2002) name this 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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“…In other words, the standard portmanteau goodness-of-fit tests are not reliable when the model is ARMA and the DGP is nonlinear. Is is however possible to modified these tests to take into account conditional heteroscedasticity or any other dependence in the linear innovations (see [89] and [59]). …”

Section: Detection Of Autocorrelationsmentioning

confidence: 99%

“…In concrete applications the true significance limits are unknown, but can be estimated (see [105], [89] and [61]). Table 1 reports the results of the standard and modified portmanteau tests, for a simulation of length n = 5000 of the GARCH(1,1) model (13).…”

Section: Examplementioning

confidence: 99%

Concepts of and tools for Nonlinear Time‐Series Modelling

Amendola

Francq

2009

Handbook of Computational Econometrics

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Tools and approaches are provided for nonlinear time series modelling in econometrics. A wide range of topics is covered, including probabilistic properties, statistical inference and computational methods. The focus is on the applications but the ideas of the mathematical arguments are also provided. Techniques and concepts are illustrated by various examples, Monte Carlo experiments and a real application. 1

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Testing for Zero Autocorrelation in the Presence of Statistical Dependence

Cited by 80 publications

References 28 publications

An Asymptotically Pivotal Transform of the Residuals Sample Autocorrelations With Application to Model Checking

An Asymptotically Pivotal Transform of the Residuals Sample Autocorrelations With Application to Model Checking

Testing the Martingale Hypothesis

Concepts of and tools for Nonlinear Time‐Series Modelling

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