Hualde Bilbao, Javier
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Hualde Bilbao
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Javier
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Economía
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INARBE. Institute for Advanced Research in Business and Economics
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Publication Open Access A simple test for the equality of integration orders(2012) Hualde Bilbao, Javier; Economía; EkonomiaA necessary condition for two time series to be nontrivially cointegrated is the equality of their respective integration orders. Thus, it is standard practice to test for order homogeneity prior to testing for cointegration. Tests for the equality of integration orders are particular cases of more general tests of linear restrictions among memory parameters of different time series, for which asymptotic theory has been developed in parametric and semiparametric settings. However, most tests have been developed in stationary and invertible settings, and, more importantly, many of them are invalid when the observables are cointegrated, because they usually involve inversion of an asymptotically singular matrix. We propose a general testing procedure which does not suffer from this serious drawback, and, in addition, it is very simple to compute, it covers the stationary/nonstationary and invertible/noninvertible ranges, and, as we show in a Monte Carlo experiment, it works well in finite samples.Publication Open Access Fixed bandwidth inference for fractional cointegration(Wiley, 2019) Hualde Bilbao, Javier; Iacone, Fabrizio; Economía; EkonomiaIn a fractional cointegration setting we derive the fixed bandwidth limiting theory of a class of estimators of the cointegrating parameter which are constructed as ratios of weighted periodogram averages. These estimators offer improved limiting properties over those of more standard approaches like ordinary least squares or narrow band least squares estimation. These advantages have been justified by means of traditional asymptotic theory and here we explore whether these improvements still hold when considering the alternative fixed bandwidth theory and, more importantly, whether this latter approach provides a more accurate approximation to the sampling distribution of the corresponding test statistics. This appears to be relevant, especially in view of the typical oversizing displayed by Wald statistics when confronted to the standard limiting theory. A Monte Carlo study of finite-sample behaviour is included.Publication Open Access Small‐b and fixed‐b asymptotics for weighted covariance estimation in fractional cointegration(Wiley, 2015) Hualde Bilbao, Javier; Iacone, Fabrizio; Economía; EkonomiaIn 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.