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Gaussian Semi‐parametric Estimation of Fractional Cointegration
Author(s) -
Velasco Carlos
Publication year - 2003
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00311
Subject(s) - mathematics , series (stratigraphy) , parametric statistics , long memory , bivariate analysis , gaussian , cointegration , rate of convergence , univariate , convergence (economics) , asymptotic distribution , random variate , statistics , econometrics , multivariate statistics , estimator , random variable , volatility (finance) , paleontology , channel (broadcasting) , physics , quantum mechanics , economic growth , economics , biology , electrical engineering , engineering
. We analyse consistent estimation of the memory parameters of a nonstationary fractionally cointegrated vector time series. Assuming that the cointegrating relationship has substantially less memory than the observed series, we show that a multi‐variate Gaussian semi‐parametric estimate, based on initial consistent estimates and possibly tapered observations, is asymptotically normal. The estimates of the memory parameters can rely either on original (for stationary errors) or on differenced residuals (for nonstationary errors) assuming only a convergence rate for a preliminary slope estimate. If this rate is fast enough, semi‐parametric memory estimates are not affected by the use of residuals and retain the same asymptotic distribution as if the true cointegrating relationship were known. Only local conditions on the spectral densities around zero frequency for linear processes are assumed. We concentrate on a bivariate system but discuss multi‐variate generalizations and show the performance of the estimates with simulated and real data.