Semiparametric inference in multivariate fractionally cointegrated systems

• Published in: Journal of econometrics 2010-08, Vol.157 (2), p.492-511
• Main Authors: Hualde, J., Robinson, P.M.
• Format: Article
• Language: English
• Subjects: Applications; Cointegration; Cointegration analysis; Distribution theory; Econometrics; Estimating techniques; Estimation; Exact sciences and technology; Fractional cointegration; Fractional cointegration Semiparametric model Unknown integration orders Standard inference; Insurance, economics, finance; Limit theorems; Linear models; Mathematical analysis; Mathematics; Measure and integration; Monte Carlo simulation; Parameter estimation; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Semiparametric model; Standard inference; Stationarity; Statistical inference; Statistics; Studies; Time series; Unknown integration orders
• ISSN: 0304-4076; 1872-6895
• DOI: 10.1016/j.jeconom.2010.04.002

A semiparametric multivariate fractionally cointegrated system is considered, integration orders possibly being unknown and I ( 0 ) unobservable inputs having nonparametric spectral density. Two estimates of the vector of cointegrating parameters ν are considered. One involves inverse spectral weighting and the other is unweighted but uses a spectral estimate at frequency zero. Both corresponding Wald statistics for testing linear restrictions on ν are shown to have a standard null χ 2 limit distribution under quite general conditions. Notably, this outcome is irrespective of whether cointegrating relations are “strong” (when the difference between integration orders of observables and cointegrating errors exceeds 1/2), or “weak” (when that difference is less than 1/2), or when both cases are involved. Finite-sample properties are examined in a Monte Carlo study and an empirical example is presented.