Sign tests for long-memory time series

Delgado, Miguel; Velasco, Carlos

doi:10.1016/j.jeconom.2004.08.013

Cited by 7 publications

(10 citation statements)

References 33 publications

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“…where (2) i is the second derivative of i ( ) and is some point between 0 and T : Note that (2) i ( ) Ci 1 log 2 i, i = 1; : : : ; T by Lemma 1(b) of Delgado and Velasco (2005).…”

Section: Appendixmentioning

confidence: 99%

Efficient Wald Tests for Fractional Unit Roots

2007

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In this article we introduce efficient Wald tests for testing the null hypothesis of unit root against the alternative of fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson (1991Robinson ( , 1994a) Lagrange Multiplier tests. Our results contrast with the tests for fractional unit roots introduced by Dolado, Gonzalo and Mayoral (2002) which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first order asymptotic properties of the proposed tests are not affected by the pre-estimation of short or long memory parameters * Acknowledgements: We thank the co-editor and two referees for very useful comments, J. AbstractIn this article we introduce e¢ cient Wald tests for testing the null hypothesis of unit root against the alternative of fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson (1991Robinson ( , 1994a Lagrange Multiplier tests. Our results contrast with the tests for fractional unit roots introduced by Dolado, Gonzalo and Mayoral (2002) which are ine¢ cient. In the presence of short range serial correlation, we propose a simple and e¢ cient two-step test that avoids the estimation of a nonlinear regression model. In addition, the …rst order asymptotic properties of the proposed tests are not a¤ected by the pre-estimation of short or long memory parameters.We thank the co-editor and two referees for very useful comments,

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“…where (2) i is the second derivative of i ( ) and is some point between 0 and T : Note that (2) i ( ) Ci 1 log 2 i, i = 1; : : : ; T by Lemma 1(b) of Delgado and Velasco (2005).…”

Section: Appendixmentioning

confidence: 99%

Efficient Wald Tests for Fractional Unit Roots

2007

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“…In sharp contrast, fractional integration testing has barely received attention in this context. Li and Li (2008) discuss the asymptotic properties of LAD estimators in a fully parametric modelling context for a class of ARFIMA-GARCH models in a Laplace quasi-maximum likelihood estimation setting, while Delgado and Velasco (2005) propose a nonparametric sign test for fractional integration under zero-median errors. The QRLM test at the median = 1=2 o¤ers robustness against excess kurtosis and constitutes a valid alternative to these tests.…”

Section: Introductionmentioning

confidence: 99%

Quantile Regression for Long Memory Testing: A Case of Realized Volatility

Hassler

Rodrigues

Rubia

2016

JOURNAL OF FINANCIAL ECONOMETRICS

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In this paper we derive a quantile regression approach to formally test for long memory in time series. We propose both individual and joint quantile tests which are useful to determine the order of integration along the di¤erent percentiles of the conditional distribution and, therefore, allow to address more robustly the overall hypothesis of fractional integration. The null distributions of these tests obey standard laws (e.g., standard normal) and are free of nuisance parameters. The …nite sample validity of the approach is established through Monte Carlo simulations, showing, for instance, large power gains over several alternative procedures under non-Gaussian errors. An empirical application of the testing procedure on di¤erent measures of daily realized volatility is presented. Our analysis reveals several interesting features, but the main …nding is that the suitability of a long-memory model with a constant order of integration around 0.4 cannot be rejected along the di¤erent percentiles of the distribution, which provides strong support to the existence of long memory in realized volatility from a completely new perspective.

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“…where π i is the first derivative of π i and θ * is some point between 0 and θ T . Note that π i (−θ * ) ≤ C i −1 log i by lemma 1 of Delgado and Velasco (2005). Since (14) is O p (1) as it is showen next, it is straightforward to show that (15) is o p (1).…”

Section: Appendixmentioning

confidence: 72%

Optimal Fractional Dickey–Fuller tests

Lobato

Velasco

2006

The Econometrics Journal

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SummaryThis article analyzes the fractional Dickey-Fuller (FDF) test for unit roots recently introduced by Dolado, Gonzalo and Mayoral (2002 Econometrica 70, 1963-2006 within a more general setup. These authors motivate their test with a particular analogy with the Dickey-Fuller test, whereas we interpret the FDF test as a class of tests indexed by an auxiliary parameter, which can be chosen to maximize the power of the test. Within this framework, we investigate optimality aspects of the FDF test and show that the version of the test proposed by these authors is not optimal. For the white noise case, we derive simple optimal FDF tests based on consistent estimators of the true degree of integration. For the serial correlation case, optimal augmented FDF (AFDF) tests are difficult to implement since they depend on the short-term component. Hence, we propose a feasible procedure that automatically optimizes a prewhitened version of the AFDF test and avoids this problem.

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Sign tests for long-memory time series

Cited by 7 publications

References 33 publications

Efficient Wald Tests for Fractional Unit Roots

Efficient Wald Tests for Fractional Unit Roots

Quantile Regression for Long Memory Testing: A Case of Realized Volatility

Optimal Fractional Dickey–Fuller tests

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