Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach

TY - JOUR

T1 - Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach

AU - Nielsen, Morten Ørregaard

AU - Shimotsu, Katsumi

N1 - Funding Information: We are grateful to P.M. Robinson and two anonymous referees for constructive and very useful suggestions and comments. This work was initiated in the spring of 2002 when both authors were visiting Yale University and the Cowles Foundation. We are very grateful for their hospitality. The first author is also grateful for research support from the Danish Social Sciences Research Council (grant no. FSE 275-05-0220).

PY - 2007/12

Y1 - 2007/12

N2 - We propose to extend the cointegration rank determination procedure of Robinson and Yajima [2002. Determination of cointegrating rank in fractional systems. Journal of Econometrics 106, 217-242] to accommodate both (asymptotically) stationary and nonstationary fractionally integrated processes as the common stochastic trends and cointegrating errors by applying the exact local Whittle analysis of Shimotsu and Phillips [2005. Exact local Whittle estimation of fractional integration. Annals of Statistics 33, 1890-1933]. The proposed method estimates the cointegrating rank by examining the rank of the spectral density matrix of the dth differenced process around the origin, where the fractional integration order, d, is estimated by the exact local Whittle estimator. Similar to other semiparametric methods, the approach advocated here only requires information about the behavior of the spectral density matrix around the origin, but it relies on a choice of (multiple) bandwidth(s) and threshold parameters. It does not require estimating the cointegrating vector(s) and is easier to implement than regression-based approaches, but it only provides a consistent estimate of the cointegration rank, and formal tests of the cointegration rank or levels of confidence are not available except for the special case of no cointegration. We apply the proposed methodology to the analysis of exchange rate dynamics among a system of seven exchange rates. Contrary to both fractional and integer-based parametric approaches, which indicate at most one cointegrating relation, our results suggest three or possibly four cointegrating relations in the data.

AB - We propose to extend the cointegration rank determination procedure of Robinson and Yajima [2002. Determination of cointegrating rank in fractional systems. Journal of Econometrics 106, 217-242] to accommodate both (asymptotically) stationary and nonstationary fractionally integrated processes as the common stochastic trends and cointegrating errors by applying the exact local Whittle analysis of Shimotsu and Phillips [2005. Exact local Whittle estimation of fractional integration. Annals of Statistics 33, 1890-1933]. The proposed method estimates the cointegrating rank by examining the rank of the spectral density matrix of the dth differenced process around the origin, where the fractional integration order, d, is estimated by the exact local Whittle estimator. Similar to other semiparametric methods, the approach advocated here only requires information about the behavior of the spectral density matrix around the origin, but it relies on a choice of (multiple) bandwidth(s) and threshold parameters. It does not require estimating the cointegrating vector(s) and is easier to implement than regression-based approaches, but it only provides a consistent estimate of the cointegration rank, and formal tests of the cointegration rank or levels of confidence are not available except for the special case of no cointegration. We apply the proposed methodology to the analysis of exchange rate dynamics among a system of seven exchange rates. Contrary to both fractional and integer-based parametric approaches, which indicate at most one cointegrating relation, our results suggest three or possibly four cointegrating relations in the data.

KW - Cointegration rank

KW - Exact local Whittle estimator

KW - Fractional cointegration

KW - Fractional integration

KW - Long memory

KW - Nonstationarity

KW - Semiparametric estimation

UR - http://www.scopus.com/inward/record.url?scp=34848827390&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2006.10.008

DO - 10.1016/j.jeconom.2006.10.008

M3 - Journal article

AN - SCOPUS:34848827390

SN - 0304-4076

VL - 141

SP - 574

EP - 596

JO - Journal of Econometrics

JF - Journal of Econometrics

IS - 2

ER -