Root--consistent estimation of weak fractional cointegration

Hualde, Javier; Robinson, Peter

doi:10.1016/j.jeconom.2006.07.004

Cited by 43 publications

(39 citation statements)

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“…When = d u the condition d x < 1=2 is equivalent to d x d u < 1=2, termed weak fractional cointegration by Hualde & Robinson (2007). It is thus seen that the weak fractional cointegration model (4) is a transformation of the stationary fractional cointegration model (3).…”

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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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confidence: 99%

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

Nielsen

Frederiksen²

2011

The Econometrics Journal

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“…Hualde and Robinson (2007) propose an estimator of ν in (5) and (6) in the case when d − γ < 0.5 (named weak cointegration). As in Robinson and Hualde (2003), this method is based on a GLS-type correction.…”

Section: Fractional Integrationmentioning

confidence: 99%

“…In the final part of the analysis, we apply the methods of Robinson and Hualde (2003) and Hualde and Robinson (2007). We identify parametric models for f (λ) with u t in (5) and (6) having the form,…”

Section: Multivariate Analysis: Fractional Cointegrationmentioning

confidence: 99%

“…(17-19), using wide-ranging values for the orders of integration from the previous tables. Here, we employ both the Robinson and Hualde (2003) and Hualde and Robinson (2007) approaches based on the approximate difference between the order of integration of the parent series and the estimated residuals. Using a Box-Jenkinstype methodology we identified at most AR(1) structures in all cases.…”

Section: Real Stock Market Prices and Real Earningsmentioning

confidence: 99%

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Fractional integration and cointegration in US financial time series data

Caporale

Gil-Alana

2013

Empir Econ

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This paper examines several US monthly financial time series using fractional integration and cointegration techniques. The univariate analysis based on fractional integration aims to determine whether the series are I(1) (in which case markets might be efficient) or alternatively I(d) with d < 1, which implies mean reversion. The multivariate framework exploiting recent developments in fractional cointegration allows to investigate in greater depth the relationships between financial series. We show that there might exist many (fractionally) cointegrated bivariate relationships among the variables examined, for some of which only standard cointegration tests had previously been carried out.

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“…Indeed, for Gaussian estimation of cointegrating vectors it is whether b < 1=2 or not that is more important. For instance Robinson & Hualde (2003) and Hualde & Robinson (2007) show that when b < 1=2 their estimator is asymptotically normal and otherwise mixed normality is obtained.…”

Section: Cointegration Rank Testmentioning

confidence: 99%

Nonparametric cointegration analysis of fractional systems with unknown integration orders

Nielsen

2010

Journal of Econometrics

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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 In this paper a nonparametric variance ratio testing approach is proposed for determining the cointegration rank in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables with possibly multiple cointegrating vectors. Since the test is nonparametric, it does not require the speci…cation of a particular model and is invariant to short-run dynamics. Nor does it require the choice of any smoothing parameters that change the test statistic without being re ‡ected in the asymptotic distribution. Furthermore, a consistent estimator of the cointegration space can be obtained from the procedure. The asymptotic distribution theory for the proposed test is non-standard but easily tabulated or simulated. Monte Carlo simulations demonstrate excellent …nite sample properties, even rivaling those of well-speci…ed parametric tests. The proposed methodology is applied to the term structure of interest rates, where, contrary to both fractional and integer-based parametric approaches, evidence in favor of the expectations hypothesis is found using the nonparametric approach. Terms of use: Documents inJEL Classi…cation: C32.

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Root--consistent estimation of weak fractional cointegration

Cited by 43 publications

References 38 publications

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

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

Fractional integration and cointegration in US financial time series data

Nonparametric cointegration analysis of fractional systems with unknown integration orders

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