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Nielsen, Morten Ørregaard
Year of Publication: 
Series/Report no.: 
Queen's Economics Department Working Paper 1259
This paper proves consistency and asymptotic normality for the conditional-sum-of-squares (CSS) estimator in fractional time series models. The models are parametric and quite general. The novelty of the consistency result is that it applies to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probablity thus making the proof much more challenging than usual. The neighborhood around the critical point where uniform convergence fails is handled using a truncation argument. The only other consistency proof for such models that applies to an arbitrarily large set of admissible parameter values appears to be Hualde and Robinson (2010), who require all moments of the innovation process to exist. In contrast, the present proof requires only a few moments of the innovation process to be finite (four in the simplest case). Finally, all arguments, assumptions, and proofs in this paper are stated entirely in the time domain, which is somewhat remarkable for this literature.
asymptotic normality
conditional-sum-of-squares estimator
fractional integration
fractional time series
likelihood inference
long memory
uniform convergence
Document Type: 
Working Paper

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