1/2, in particular =consistent-n and asymptotically normal estimation of the cointegrating vector ? is possible when ß < 1/2, as we explore in a simple bivariate model. The estimate depends on ? and d or, more realistically, on estimates of unknown ? and d. These latter estimates need to be consistent-n, and the asymptotic distribution of the estimate of ? is sensitive to their precise form. We propose estimates of ? and d that are computationally relatively convenient, relying on only univariate nonlinear optimization. Finite sample performance of the methods is examined by means of Monte Carlo simulations, and several applications to empirical data included.">
Empirical evidence has emerged of the possibility of fractional cointegration such that the gap, ß, between the integration order d of observable time series, and the integration order ? of cointegrating errors, is less than 0.5. This includes circumstances when observables are stationary or asymptotically stationary with long memory (so d < 1/2), and when they are nonstationary (so d 1/2). This "weak cointegration" contrasts strongly with the traditional econometric prescription of unit root observables and short memory cointegrating errors, where ß = 1. Asymptotic inferential theory also differs from this case, and from other members of the class ß > 1/2, in particular =consistent-n and asymptotically normal estimation of the cointegrating vector ? is possible when ß < 1/2, as we explore in a simple bivariate model. The estimate depends on ? and d or, more realistically, on estimates of unknown ? and d. These latter estimates need to be consistent-n, and the asymptotic distribution of the estimate of ? is sensitive to their precise form. We propose estimates of ? and d that are computationally relatively convenient, relying on only univariate nonlinear optimization. Finite sample performance of the methods is examined by means of Monte Carlo simulations, and several applications to empirical data included.
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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number
/06/499.
Find related papers by JEL classification: C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models
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