Bootstrapping the Box–Pierce Q test: A robust test of uncorrelatedness

Horowitz, Joel L.; Lobato, Ignacio N.; Nankervis, John C.; Savin, N. E.

doi:10.1016/j.jeconom.2005.06.014

Cited by 70 publications

(46 citation statements)

References 33 publications

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“…These existing tests are roughly categorized into two types: time domain correlation-based tests and frequency domain 40 periodogram-based tests. The tests in the first category usually use the autocorrelations up to lag m (a user-chosen integer), so they are unable to detect serial correlations beyond lag m; see, e.g., Romano and Thombs (1996), Lobato (2001), and Horowitz, Lobato, Nankervis, and Savin (2006) for observable series, or Francq, Roy, and Zakoïan (2005) and Delgado and Velasco (2011) for residual series. To avoid selecting m, Escanciano and Lobato (2009) and Escanciano,45 Lobato, and Zhu (2013) derived a data-driven portmanteau test under the assumption that ε t is a martingale difference sequence (MDS).…”

Section: Introductionmentioning

confidence: 99%

A bootstrapped spectral test for adequacy in weak ARMA models

Zhu

2015

Journal of Econometrics

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SUMMARYThis paper proposes a Cramer-von Mises (CM) test statistic to check the adequacy of weak ARMA models. Without posing a martingale difference assumption on the error terms, the asymptotic null distribution of the CM test is obtained by using the Hillbert space approach. Moreover, this CM test is consistent, and has nontrivial power against the local alternative of 15 order n −1/2 . Due to the unknown dependence of error terms and the estimation effects, a new block-wise random weighting method is constructed to bootstrap the critical values of the test statistic. The new method is easy to implement and its validity is justified. The theory is illustrated by a small simulation study and an application to S&P 500 stock index.

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Section: Introductionmentioning

confidence: 99%

A bootstrapped spectral test for adequacy in weak ARMA models

Zhu

2015

Journal of Econometrics

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“…However, the convergence is typically slow. Horowitz et al (2006) proposed a double blockwise bootstrap method to test for white noise that is not independent and identically distributed.…”

Section: Introductionmentioning

confidence: 99%

Testing for high-dimensional white noise using maximum cross-correlations

Chang¹,

Yao²,

Zhou³

2017

Biometrika

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SUMMARYWe propose a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross-correlations of the component series. Based on an approximation by the L ∞ -norm of a normal random vector, the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution. In contrast to the conventional white noise test, the new method is proved to be valid for testing the departure from white noise that is not independent and identically distributed. We illustrate the accuracy and the power of the proposed test by simulation, which also shows that the new test outperforms several commonly used methods including, for example, the Lagrange multiplier test and the multivariate Box-Pierce portmanteau tests, especially when the dimension of time series is high in relation to the sample size. The numerical results also indicate that the performance of the new test can be further enhanced when it is applied to pre-transformed data obtained via the time series principal component analysis proposed by Chang, Yao (arXiv:1410.2323). The proposed procedures have been implemented in an R package.

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“…Second, we did not consider other tests of autocorrelations such as the Box-Pierce test, the Ljung-Box test and their extended versions (e.g., Box & Pierce, 1970;Horowitz, Lobato, Nankervis, & Savin, 2006;Ljung & Box, 1978;Lobato, Nankervis, & Savin, 2001. The Box-Pierce and Ljung-Box tests examine whether the autocorrelations up to lag l are all zero.…”

Section: Discussionmentioning

confidence: 99%

Testing autocorrelation and partial autocorrelation: Asymptotic methods versus resampling techniques

Zhang

2017

Brit J Math & Statis

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Autocorrelation and partial autocorrelation, which provide a mathematical tool to understand repeating patterns in time series data, are often used to facilitate the identification of model orders of time series models (e.g., moving average and autoregressive models). Asymptotic methods for testing autocorrelation and partial autocorrelation such as the 1/T approximation method and the Bartlett's formula method may fail in finite samples and are vulnerable to non-normality. Resampling techniques such as the moving block bootstrap and the surrogate data method are competitive alternatives. In this study, we use a Monte Carlo simulation study and a real data example to compare asymptotic methods with the aforementioned resampling techniques. For each resampling technique, we consider both the percentile method and the bias-corrected and accelerated method for interval construction. Simulation results show that the surrogate data method with percentile intervals yields better performance than the other methods. An R package pautocorr is used to carry out tests evaluated in this study.

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Bootstrapping the Box–Pierce Q test: A robust test of uncorrelatedness

Cited by 70 publications

References 33 publications

A bootstrapped spectral test for adequacy in weak ARMA models

A bootstrapped spectral test for adequacy in weak ARMA models

Testing for high-dimensional white noise using maximum cross-correlations

Testing autocorrelation and partial autocorrelation: Asymptotic methods versus resampling techniques

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