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

By Morten Ørregaard Nielsen, Per Frederiksen. 2011

67 citations recorded by the source corpus.

We 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.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/64beb100b6de98e2a728d21e0ff217c8092af84a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

In Finance

In Statistics and Probability

Katsumi Shimotsu

Citations in the corpus

Exact local Whittle estimation of fractionally cointegrated systems (2012, methodology): “2 of Phillips and Shimotsu (2004) and using the definition of cn, we have Re{T1n} = m−1 ∑m j=1 Re{(1− ej)0}(Iu2j − ω22) +Op(n0m). Therefore, using Lemma 3(b) of Shimotsu (2010b), summation by parts, and (1 − eiλj)−ν0 − (1 − eiλj+1)−ν0 = O(nν0j−ν0−1), and noting ν0 > 1/2, we obtain Re{T1n} = m−1 ∑m j”