Goodness of fit for lattice processes
The paper discusses tests for the correct specification of a model when data is observed in a d-dimensional lattice, extending previous work when the data is collected in the real line. As it happens with the latter type of data, the asymptotic distributions of the tests are functionals of a Gaussian sheet process, say , [nu][set membership, variant][0,[pi]]d. Since it is not easy to find a time transformation h([nu]) such that becomes the standard Brownian sheet, a consequence is that the critical values are difficult, if at all possible, to obtain. So, to overcome the problem of its implementation, we propose employing a bootstrap approach, showing its validity in our context.
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- Peter M Robinson & J Vidal Sanz, 2005.
"Modified Whittle Estimation of Multilateral Models on a Lattice,"
STICERD - Econometrics Paper Series
492, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- 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.
- Peter M. Robinson & J. Vidal Sanz, 2005. "Modified whittle estimation of multilateral models on a lattice," LSE Research Online Documents on Economics 4545, London School of Economics and Political Science, LSE Library.
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- Hidalgo, J. & Kreiss, J.-P., 2006. "Bootstrap specification tests for linear covariance stationary processes," Journal of Econometrics, Elsevier, vol. 133(2), pages 807-839, August.
- An, Hong-Zhi & Chen, Zhao-Guo & Hannan, E. J., 1983. "The maximum of the periodogram," Journal of Multivariate Analysis, Elsevier, vol. 13(3), pages 383-400, September.
- Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
- Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," Journal of Econometrics, Elsevier, vol. 117(2), pages 369-399, December.
- Efstathios Paparoditis, 2000. "Spectral Density Based Goodness-of-Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 143-176.
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