Semiparametric estimation in perturbed long memory series

Arteche, Josu

doi:10.1016/j.csda.2006.07.023

Cited by 28 publications

(14 citation statements)

References 21 publications

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“…MGSE and GSE estimates are similar for absolute values and squares, confirming the previous impression that these two series do not suffer from the effect of an added noise. The MGSE for the logs of squares, however, gives higher estimates with m < 20 but from m = 20 the MGSE estimates stabilize at around 0.5, reinforcing the results obtained with GSE for the lower bandwidth (similar results are obtained with the log periodogram extension proposed by Arteche 2006). It should also be taken into account that the asymptotic properties ofď are not yet established, although it can be conjectured that the results in Hurvich et al (2005) can be extended to the multiple frequency perturbed SCLM to get consistency (for d < 1) and asymptotic normality (for d < 3/4) after appropriate normalisation.…”

Section: The Persistence Of Volatility Before 1974supporting

confidence: 72%

Standard and seasonal long memory in volatility: an application to Spanish inflation

Arteche

2010

Empir Econ

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The historical series of many economic variables, such as inflation, are characterized by a strong persistent behaviour in the form of long memory, not only in the long run or at zero frequency but often also at seasonal frequencies. In financial series, long memory is not apparent in levels but strong persistence in higher order moments such as volatility has been proven to be a stylized fact in stock returns. Interest in economic time series has, however, focused on the persistence of levels and little attention has been paid to higher order dependence, which can be important for assessing the stability of the series. We propose a semiparametric analysis of the standard and seasonal persistence of the volatility of a monthly Spanish inflation series. The conclusions can be summarized in three main results. First volatility shows strong persistence implying an unstable trend in prices, but its structure depends on the proxy used, the absolute values, the squares or the logarithms of squares. Second, the structure of the persistence of volatility changed with the first oil crisis in 1973, with a persistent trend in both periods, in contrast with levels. Third, the Taylor effect, which is well documented in financial series, does not apply in this series.

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Section: The Persistence Of Volatility Before 1974supporting

confidence: 72%

Standard and seasonal long memory in volatility: an application to Spanish inflation

Arteche

2010

Empir Econ

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“…Furthermore, it is not obvious how to obtain expressions of the asymptotic variances of the estimator using the expressions given by Zaffaroni (2005). On the other hand, there are several estimators proposed to estimate separately asymmetric SV models or long-memory SV models; see, for example, Omori and Watanabe (2007) and Arteche (2006), respectively, for some very recent references. However, none of these estimators have been considered for the estimation of models with the simultaneous presence of long-memory and leverage effect.…”

Section: Empirical Illustrationmentioning

confidence: 99%

Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH

Ruiz

Veiga

2008

Computational Statistics & Data Analysis

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A new stochastic volatility model, called A-LMSV, is proposed to cope simultaneously with leverage effect and long-memory in volatility. Its statistical properties are derived and compared with the properties of the FIEGARCH model. It is shown that the dependence of the autocorrelations of squares on the parameters measuring the asymmetry and the persistence is different in both models. The kurtosis and autocorrelations of squares do not depend on the asymmetry in the A-LMSV model while they increase with the asymmetry in the FIEGARCH model. Furthermore, the autocorrelations of squares increase with the persistence in the A-LMSV model and decrease in the FIEGARCH model. On the other hand, if the correlation between returns and future volatilities is negative, the autocorrelations of absolute returns increase with the magnitude of the asymmetry in the FIEGARCH model while they decrease in the A-LMSV model. Finally, the cross-correlations between squares and original observations are, in general, larger in absolute value in the FIEGARCH model than in the A-LMSV model. The results are illustrated by fitting both models to represent the dynamic evolution of volatilities of daily returns of the S&P500 and DAX indexes.

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“…Therefore, estimating long memory in perturbed time series can be challenging, and calls for an estimator which explicitly accounts for the perturbation. Sun & Phillips (2003), Hurvich & Ray (2003), Hurvich et al (2005), and Arteche (2006), among others, have proposed such estimators with y ( ) and w ( ) locally approximated by constants as ! 0, see section 2 below.…”

Section: Introductionmentioning

confidence: 99%

Local Polynomial Whittle Estimation of Perturbed Fractional Processes

Nielsen

2008

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract We propose a semiparametric local polynomial Whittle with noise estimator of the memory parameter in long memory time series perturbed by a noise term which may be serially correlated. The estimator approximates the log-spectrum of the short-memory component of the signal as well as that of the perturbation by two separate polynomials. Including these polynomials we obtain a reduction in the order of magnitude of the bias, but also in ‡ate the asymptotic variance of the long memory estimator by a multiplicative constant. We show that the estimator is consistent for d 2 (0; 1), asymptotically normal for d 2 (0; 3=4), and if the spectral density is su¢ ciently smooth near frequency zero, the rate of convergence can become arbitrarily close to the parametric rate, p n. A Monte Carlo study reveals that the proposed estimator performs well in the presence of a serially correlated perturbation term. Furthermore, an empirical investigation of the 30 DJIA stocks shows that this estimator indicates stronger persistence in volatility than the standard local Whittle (with noise) estimator. Terms of use: Documents inJEL Classi…cations: C22.

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Semiparametric estimation in perturbed long memory series

Cited by 28 publications

References 21 publications

Standard and seasonal long memory in volatility: an application to Spanish inflation

Standard and seasonal long memory in volatility: an application to Spanish inflation

Modelling long-memory volatilities with leverage effect: A-LMSV versus FIEGARCH

Local Polynomial Whittle Estimation of Perturbed Fractional Processes

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