Long Memory in Stock-Market Trading Volume

Lobato, Ignacio N.; Velasco, Carlos

doi:10.2307/1392223

Cited by 74 publications

(77 citation statements)

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“…Unfortunately, prior knowledge of existence of the trend would presumably be required here, since if a trend is assumed the asymptotic distribution of the estimator of the cointegrating parameter would be di erent according to whether the trend is present or absent. Another way of handling deterministic trends in an undi erenced series would be to use Kolmogorov-Zhurbenko tapers on a restricted grid of Fourier frequencies, as was done in Velasco (1999a, b), Lobato and Velasco (2000), and in Velasco and Robinson (2000). This approach with ÿxed m would presumably lead to an asymptotic distribution theory similar to the one we develop here, though it should be mentioned that it was shown in Hurvich and Chen (2000) that using Kolmogorov-Zhurbenko tapers on undi erenced data leads to asymptotically less e cient semiparametric estimators of the long memory parameter than use of the corresponding Hurvich-Chen taper on the di erences.…”

Section: Discussionmentioning

confidence: 99%

“…See, for instance, Hurvich and Ray (1995), Deo and Hurvich (1998), Hurvich and Chen (2000), Hurvich et al (2002). With a class of tapers due to Kolmogorov (see Zhurbenko, 1979), Velasco (1999a, b), Lobato and Velasco (2000), obtained general consistency and asymptotic normality results for periodogram and log-periodogram semiparametric estimates of d in the potential presence of additive polynomial trends of arbitrary degree by tapering the observations without di erencing. A family of tapers introduced by Hurvich and Chen (2000), used on di erenced data, was proven to be more ecient for periodogram-based semiparametric estimation of d. The narrow-band tapered NBLS estimator introduced in this paper is an application of this family of tapers on the (p − 1)th di erenced data.…”

Section: The Tapered Narrow-band Least Squares Estimatormentioning

confidence: 99%

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Estimating fractional cointegration in the presence of polynomial trends

Hurvich

2003

Journal of Econometrics

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We propose and derive the asymptotic distribution of a tapered narrow-band least squares estimator (NBLSE) of the cointegration parameter ÿ in the framework of fractional cointegration. This tapered estimator is invariant to deterministic polynomial trends. In particular, we allow for arbitrary linear time trends that often occur in practice. Our simulations show that, in the case of no deterministic trends, the estimator is superior to ordinary least squares (OLS) and the nontapered NBLSE proposed by P.M. Robinson when the levels have a unit root and the cointegrating relationship between the series is weak. In terms of rate of convergence, our estimator converges faster under certain circumstances, and never slower, than either OLS or the nontapered NBLSE. In a data analysis of interest rates, we ÿnd stronger evidence of cointegration if the tapered NBLSE is used for the cointegration parameter than if OLS is used.

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Section: Discussionmentioning

confidence: 99%

Section: The Tapered Narrow-band Least Squares Estimatormentioning

confidence: 99%

Estimating fractional cointegration in the presence of polynomial trends

Hurvich

2003

Journal of Econometrics

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“…[14,15]) and still is a hot topic of active research [16,17,18,19,20,21,22,23,24]. Historical records of economic and financial data typically exhibit nonperiodic cyclical patterns that are indicative of the presence of significant long memory.…”

Section: Introductionmentioning

confidence: 99%

Estimating long-range dependence: finite sample properties and confidence intervals

Weron

2002

Physica A: Statistical Mechanics and its Applications

349

232

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A major issue in financial economics is the behavior of asset returns over long horizons. Various estimators of long range dependence have been proposed. Even though some have known asymptotic properties, it is important to test their accuracy by using simulated series of different lengths. We test R/S analysis, Detrended Fluctuation Analysis and periodogram regression methods on samples drawn from Gaussian white noise. The DFA statistics turns out to be the unanimous winner. Unfortunately, no asymptotic distribution theory has been derived for this statistics so far. We were able, however, to construct empirical (i.e. approximate) confidence intervals for all three methods. The obtained values differ largely from heuristic values proposed by some authors for the R/S statistics and are very close to asymptotic values for the periodogram regression method.

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“…For example, Marinucci (2000), Robinson & Yajima (2002), Chen & Hurvich (2003a, 2003b, Christensen & Nielsen (2006), Hualde & Robinson (2006), and Robinson (2008) consider theoretical issues, whereas Lobato & Velasco (2000) and Fleming & Kirby (2006) apply the model to stock market trading volume, Bandi & Perron (2006), Christensen & Nielsen (2006), and Berger, Chaboud & Hjalmarsson (2009) to stock return volatility, and Robinson & Yajima (2002) to spot prices for crude oil. Hence, this model has become an important tool for the analysis of long-run relations, especially in …nancial economics.…”

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confidence: 99%

Fully modified narrow‐band least squares estimation of weak fractional cointegration

Nielsen

Frederiksen²

2011

The Econometrics 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 consider estimation of the cointegrating relation in the weak fractional cointegration model, where the strength of the cointegrating relation (di¤erence in memory parameters) is less than one-half. A special case is the stationary fractional cointegration model, which has found important application recently, especially in …nancial economics. Previous research on this model has considered a semiparametric narrow-band least squares (NBLS) estimator in the frequency domain, but in the stationary case its asymptotic distribution has been derived only under a condition of non-coherence between regressors and errors at the zero frequency. We show that in the absence of this condition, the NBLS estimator is asymptotically biased, and also that the bias can be consistently estimated. Consequently, we introduce a fully modi…ed NBLS estimator which eliminates the bias, and indeed enjoys a faster rate of convergence than NBLS in general. We also show that local Whittle estimation of the integration order of the errors can be conducted consistently based on NBLS residuals, but the estimator has the same asymptotic distribution as if the errors were observed only under the condition of non-coherence. Furthermore, compared to much previous research, the development of the asymptotic distribution theory is based on a di¤erent spectral density representation, which is relevant for multivariate fractionally integrated processes, and the use of this representation is shown to result in lower asymptotic bias and variance of the narrow-band estimators. We present simulation evidence and a series of empirical illustrations to demonstrate the feasibility and empirical relevance of our methodology. Terms of use: Documents in

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Long Memory in Stock-Market Trading Volume

Cited by 74 publications

References 0 publications

Estimating fractional cointegration in the presence of polynomial trends

Estimating fractional cointegration in the presence of polynomial trends

Estimating long-range dependence: finite sample properties and confidence intervals

Fully modified narrow‐band least squares estimation of weak fractional cointegration

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