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Small‐ b and Fixed‐ b Asymptotics for Weighted Covariance Estimation in Fractional Cointegration
Author(s) -
Hualde Javier,
Iacone Fabrizio
Publication year - 2015
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/jtsa.12113
Subject(s) - mathematics , estimator , asymptotic distribution , covariance , asymptotic analysis , central limit theorem , limit (mathematics) , monte carlo method , cointegration , statistics , mathematical analysis
In a standard cointegrating framework, Phillips (1991) introduced the weighted covariance (WC) estimator of cointegrating parameters. Later, Marinucci (2000) applied this estimator to fractional circumstances and, like Phillips (1991), analysed the so‐called small‐ b asymptotic approximation to its sampling distribution. Recently, an alternative limiting theory (fixed‐ b asymptotics) has been successfully employed to approximate sampling distributions. With the purpose of comparing both approaches, we derive here the fixed‐ b limit of WC estimators in a fractional setting, filling also some gaps in the traditional (small‐ b ) theory. We also provide some Monte Carlo evidence that suggests that the fixed‐ b limit is more accurate.