Modified Whittle Estimation of Multilateral Models on a Lattice
AbstractIn 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /2005/492.
Date of creation: Jun 2005
Date of revision:
Contact details of provider:
Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp
spatial data; multilateral modelling; Whittle estimation; edge effect; consistent variance estimation;
Other versions of this item:
- Robinson, P.M. & Vidal Sanz, J., 2006. "Modified Whittle estimation of multilateral models on a lattice," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1090-1120, May.
- Robinson, P.M. & Vidal-Sanz, Jose M., 2006. "Modified Whittle estimation of multilateral models on a lattice," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/7249, Universidad Carlos III de Madrid.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ma, Chunsheng, 2004. "Spatial autoregression and related spatio-temporal models," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 152-162, January.
- Heyde, C. C. & Gay, R., 1993. "Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 169-182, March.
- Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May.
- Hannan, E. J. & Dunsmuir, W. T. M. & Deistler, M., 1980. "Estimation of vector ARMAX models," Journal of Multivariate Analysis, Elsevier, vol. 10(3), pages 275-295, September.
- Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
- Jose Vidal-Sanz, 2009.
"Automatic spectral density estimation for random fields on a lattice via bootstrap,"
TEST: An Official Journal of the Spanish Society of Statistics and Operations Research,
Springer, vol. 18(1), pages 96-114, May.
- Vidal-Sanz, Jose M., 2007. "Automatic spectral density estimation for random fields on a lattice via bootstrap," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/7344, Universidad Carlos III de Madrid.
- Jose M. Vidal-Sanz, 2007. "Automatic spectral density estimation for Random fields on a lattice via bootstrap," Business Economics Working Papers wb072606, Universidad Carlos III, Departamento de Economía de la Empresa.
- Sándor Baran & Gyula Pap, 2011. "Asymptotic inference for a one-dimensional simultaneous autoregressive model," Metrika, Springer, vol. 74(1), pages 55-66, July.
- Hidalgo, Javier, 2009. "Goodness of fit for lattice processes," Journal of Econometrics, Elsevier, vol. 151(2), pages 113-128, August.
- Peter M Robinson, 2011. "Inference on Power Law Spatial Trends (Running Title: Power Law Trends)," STICERD - Econometrics Paper Series /2011/556, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Javier Hidalgo & Myung Hwan Seo, 2013. "Specification For Lattice Processes," STICERD - Econometrics Paper Series /2013/562, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Robinson, P.M., 2008. "Correlation testing in time series, spatial and cross-sectional data," Journal of Econometrics, Elsevier, vol. 147(1), pages 5-16, November.
- Peter Robinson, 2007. "Correlation testing in time series, spatial and cross-sectional data," CeMMAP working papers CWP01/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Peter M Robinson, 2006. "Nonparametric Spectrum Estimation for SpatialData," STICERD - Econometrics Paper Series /2006/498, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Beran, Jan & Ghosh, Sucharita & Schell, Dieter, 2009. "On least squares estimation for long-memory lattice processes," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2178-2194, November.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.