Fully Modified Narrow-Band Least Squares Estimation of Weak Fractional Cointegration
AbstractWe consider estimation of the cointegrating relation in the weak fractional cointegration model, where the strength of the cointegrating relation (difference 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 financial 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 modified 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 different 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.
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Bibliographic InfoPaper provided by Queen's University, Department of Economics in its series Working Papers with number 1226.
Length: 35 pages
Date of creation: May 2010
Date of revision:
Fractional cointegration; frequency domain; fully modified estimation; long memory; semiparametric;
Other versions of this item:
- Morten Ørregaard Nielsen & Per Frederiksen, 2011. "Fully modified narrow‐band least squares estimation of weak fractional cointegration," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 77-120, February.
- Morten Ørregaard Nielsen & Per Frederiksen, 2010. "Fully Modified Narrow-Band Least Squares Estimation of Weak Fractional Cointegration," CREATES Research Papers 2010-31, School of Economics and Management, University of Aarhus.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-01-10 (All new papers)
- NEP-ECM-2010-01-10 (Econometrics)
- NEP-ETS-2010-01-10 (Econometric Time Series)
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