Gaussian pseudo-maximum likelihood estimation of fractional time series models

By J. Hualde, Peter M. Robinson. 2011

84 citations recorded by the source corpus.

We consider the estimation of parametric fractional time series models in which not only is the memory parameter unknown, but one may not know whether it lies in the stationary/invertible region or the nonstationary or noninvertible regions. In these circumstances, a proof of consistency (which is a prerequisite for proving asymptotic normality) can be difficult owing to nonuniform convergence of the objective function over a large admissible parameter space. In particular, this is the case for the conditional sum of squares estimate, which can be expected to be asymptotically efficient under Gaussianity. Without the latter assumption, we establish consistency and asymptotic normality for this estimate in case of a quite general univariate model. For a multivariate model, we establish asymptotic normality of a one-step estimate based on an initial √n-consistent estimate.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/117c6cffdd514b7f09c40b2702feec531dde8789

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Citations in the corpus

Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model (2010, methodology): “2In independent and concurrent work, Hualde and Robinson (2011) prove consistency for a large set of admissible values in a fractional model with one fractional parameter and initial values equal to zero, i.e. both X−n = 0 and X̃−n = 0 for n ≥ 0.”
Estimation of fractionally integrated panels with fixed effects and cross-section dependence (2015, unknown): “…defined and entail optimization Though the aim in this type of problems is to cover a wide range of values of δ i ∈ D i in the asymptotics, c.f. Hualde and Robinson (2011) and Nielsen (2014), in our framework there are interactions with other model parameters that require to restrict the…”
THE ROLE OF INITIAL VALUES IN CONDITIONAL SUM-OF-SQUARES ESTIMATION OF NONSTATIONARY FRACTIONAL TIME SERIES MODELS (2015, methodology): “This can be formulated as choosing μ = C in the likelihood function (10) and defining d̂c = arg min d∈D Lc(d), (14)”