Modified Whittle Estimation of Multilateral Models on a Lattice
Peter M Robinson and
STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE
In the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d >= 2, the achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the "edge effect", which worsens with increasing d. The other is the possible difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, due mainly to the Jacobian term. This is especially a problem in "multilateral" models, which are naturally expressed in terms of lagged values in both directions for one or more of the d dimensions. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the computational problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally convenient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. The asymptotic regime allows increase in both directions of all d dimensions, with the central limit theorem established after re-ordering as a triangular array. However our work offers something new for "unilateral" models also. When the data are non-Gaussian, asymptotic variances of all parameter estimates may be affected, and we propose consistent, non-negative definite estimates of the asymptotic variance matrix.
Keywords: spatial data; multilateral modelling; Whittle estimation; edge effect; consistent variance estimation (search for similar items in EconPapers)
JEL-codes: C13 (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
Journal Article: Modified Whittle estimation of multilateral models on a lattice (2006)
Working Paper: Modified whittle estimation of multilateral models on a lattice (2005)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:492
Access Statistics for this paper
More papers in STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE
Bibliographic data for series maintained by ().