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NONPARAMETRIC PREDICTION WITH SPATIAL DATA

Published online by Cambridge University Press:  23 May 2022

Abhimanyu Gupta  and
Javier Hidalgo
Abhimanyu Gupta*
Affiliation:
University of Essex
Javier Hidalgo
Affiliation:
London School of Economics
*
Address correspondence to Abhimanyu Gupta, Department of Economics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK; e-mail: a.gupta@essex.co.uk.
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Abstract

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We describe a (nonparametric) prediction algorithm for spatial data, based on a canonical factorization of the spectral density function. We provide theoretical results showing that the predictor has desirable asymptotic properties. Finite sample performance is assessed in a Monte Carlo study that also compares our algorithm to a rival nonparametric method based on the infinite $AR$ representation of the dynamics of the data. Finally, we apply our methodology to predict house prices in Los Angeles.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 5 , October 2023 , pp. 950 - 988
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

Research of the first author was supported by the Economic and Social Research Council (ESRC) grant ES/R006032/1. Research of the second author was supported by STICERD, LSE.

References

REFERENCES

Baltagi, B. H., Kelejian, H. H., & Prucha, I. R. (2007) Analysis of spatially dependent data. Journal of Econometrics 140, 1–4.10.1016/j.jeconom.2006.11.001CrossRefGoogle Scholar
Banerjee, S., Gelfand, A.E., Knight, J.R., & Sirmans, C.F. (2004) Spatial modeling of house prices using normalized distance-weighted sums of stationary processes. Journal of Business & Economic Statistics 22, 206–213.CrossRefGoogle Scholar
Batchelor, L. & Reed, H. (1918) Relation of the variability of yields of fruit trees to the accuracy of field trials. Journal of Agricultural Research XII, 245–283.Google Scholar
Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems. Journal of the Royal Statistical Society: Series B 36, 192–236.Google Scholar
Bester, C.A., Conley, T.G., & Hansen, C.B. (2011) Inference with dependent data using cluster covariance estimators. Journal of Econometrics 165, 137–151.CrossRefGoogle Scholar
Bester, C.A., Conley, T.G., Hansen, C.B., & Vogelsang, T.J. (2016) Fixed-b asymptotics for spatially dependent robust nonparametric covariance matrix estimators. Econometric Theory 32, 154–186.CrossRefGoogle Scholar
Bhansali, R.J. (1974) Asymptotic properties of the Wiener–Kolmogorov predictor. I. Journal of the Royal Statistical Society: Series B 36, 61–73.Google Scholar
Bhansali, R.J. (1978) Linear prediction by autoregressive model fitting in the time domain. Annals of Statistics 60, 224–231.Google Scholar
Breidt, F.J., Davis, R.A., & Trindade, A.A. (2001) Least absolute deviation estimation for all-pass time series models. Annals of Statistics 29, 919–946.CrossRefGoogle Scholar
Brillinger, D.R. (1981) Time Series: Data Analysis and Theory. Holden Day.Google Scholar
Cavaliere, G., Nielsen, H.B., & Rahbek, A. (2020) Bootstrapping noncausal autoregressions: With applications to explosive bubble modeling. Journal of Business & Economic Statistics 38, 55–67.CrossRefGoogle Scholar
Conley, T.G. (1999) GMM estimation with cross sectional dependence. Journal of Econometrics 92, 1–45.CrossRefGoogle Scholar
Conley, T.G. & Molinari, F. (2007) Spatial correlation robust inference with imperfect distance information. Journal of Econometrics 140, 76–96.CrossRefGoogle Scholar
Cressie, N. & Huang, H. (1999) Classes of nonseparable, spatio-temporal stationary covariance functions. Journal of the American Statistical Association 94, 1330–1340.CrossRefGoogle Scholar
Cressie, N.A. (1993) Statistics for Spatial Data. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons.CrossRefGoogle Scholar
Dahlhaus, R. & Künsch, H. (1987) Edge effects and efficient parameter estimation for stationary random fields. Biometrika 74, 877–882.CrossRefGoogle Scholar
Davis, R.A., Klüppelberg, C., & Steinkohl, C. (2013) Statistical inference for max-stable processes in space and time. Journal of the Royal Statistical Society: Series B 75, 791–819.CrossRefGoogle Scholar
Fernandez-Casal, R., Gonzalez-Manteiga, W., & Febrero-Bande, M. (2003) Flexible spatio-temporal stationary variogram models. Statistics and Computing 13, 127–136.CrossRefGoogle Scholar
Gao, J., Lu, Z., & Tjøstheim, D. (2006) Estimation in semiparametric spatial regression. The Annals of Statistics 34, 1395–1435.CrossRefGoogle Scholar
Genton, M.G. & Koul, H.L. (2008) Minimum distance inference in unilateral autoregressive lattice processes. Statistica Sinica 18, 617–631.Google Scholar
Gupta, A. (2018) Autoregressive spatial spectral estimates. Journal of Econometrics 203, 80–95.CrossRefGoogle Scholar
Guyon, X. (1982) Parameter estimation for a stationary process on a $d$ -dimensional lattice. Biometrika 69, 95–105.CrossRefGoogle Scholar
Haining, R.P. (1978) The moving average model for spatial interaction. Transactions of the Institute of British Geographers 3, 202–225.CrossRefGoogle Scholar
Helson, H. & Lowdenslager, D. (1958) Prediction theory and Fourier series in several variables. Acta Mathematica 99, 165–202.CrossRefGoogle Scholar
Helson, H. & Lowdenslager, D. (1961) Prediction theory and Fourier series in several variables. II. Acta Mathematica 106, 175–213.CrossRefGoogle Scholar
Hidalgo, J. (2009) Goodness of fit for lattice processes. Journal of Econometrics 151, 113–128.CrossRefGoogle Scholar
Hidalgo, J. & Yajima, Y. (2002) Prediction and signal extraction of strongly dependent processes in the frequency domain. Econometric Theory 18, 584–624.10.1017/S0266466602183022CrossRefGoogle Scholar
Iversen, E. Jr. (2001) Spatially disaggregated real estate indices. Journal of Business & Economic Statistics 19, 341–357.CrossRefGoogle Scholar
Jenish, N. (2016) Spatial semiparametric model with endogenous regressors. Econometric Theory 32, 714–739.CrossRefGoogle Scholar
Jenish, N. & Prucha, I.R. (2012) On spatial processes and asymptotic inference under near-epoch dependence. Journal of Econometrics 170, 178–190.CrossRefGoogle ScholarPubMed
Korezlioglu, H. and Loubaton, P. (1986). Spectral factorization of wide sense stationary processes on ${\mathbb{Z}}^2$ . Journal of Multivariate Analysis 19, 24–47.CrossRefGoogle Scholar
Lanne, M. & Saikkonen, P. (2011) Noncausal autoregressions for economic time series. Journal of Time Series Econometrics 3, 1–30.CrossRefGoogle Scholar
Lanne, M. & Saikkonen, P. (2013) Noncausal vector autoregression. Econometric Theory 29, 447–481.CrossRefGoogle Scholar
Lewis, R. & Reinsel, G.C. (1985) Prediction of multivariate time series by autoregressive model fitting. Journal of Multivariate Analysis 16, 393–411.CrossRefGoogle Scholar
Limaye, B.V. & Zeltser, M. (2009) On the Pringsheim convergence of double series. Proceedings of the Estonian Academy of Sciences 58, 108.CrossRefGoogle Scholar
Majumdar, A., Munneke, H.J., Gelfand, A.E., Banerjee, S., & Sirmans, C.F. (2006) Gradients in spatial response surfaces with application to urban land values. Journal of Business & Economic Statistics 24, 77–90.CrossRefGoogle Scholar
McElroy, T.S. & Holan, S.H. (2014) Asymptotic theory of cepstral random fields. The Annals of Statistics 42, 64–86.CrossRefGoogle Scholar
Mercer, W.B. & Hall, A.D. (1911) The experimental errors of field trials. Journal of Agricultural Science IV, 107–132.CrossRefGoogle Scholar
Mitchell, M.W., Genton, M.G., & Gumpertz, M.L. (2005) Testing for separability of space-time covariances. Environmetrics 16, 819–831.CrossRefGoogle Scholar
Nychka, D., Bandyopadhyay, S., Hammerling, D., Lindgren, F., & Sain, S. (2015) A multiresolution Gaussian process model for the analysis of large spatial datasets. Journal of Computational and Graphical Statistics 24, 579–599.CrossRefGoogle Scholar
Pace, R.K. & Barry, R. (1997) Sparse spatial autoregressions. Statistics & Probability Letters 33, 291–297.CrossRefGoogle Scholar
Robinson, P.M. (2007) Nonparametric spectrum estimation for spatial data. Journal of Statistical Planning and Inference 137, 1024–1034.CrossRefGoogle Scholar
Robinson, P.M. (2011) Asymptotic theory for nonparametric regression with spatial data. Journal of Econometrics 165, 5–19.CrossRefGoogle Scholar
Robinson, P.M. & Vidal Sanz, J. (2006) Modified Whittle estimation of multilateral models on a lattice. Journal of Multivariate Analysis 97, 1090–1120.CrossRefGoogle Scholar
Roknossadati, S.M. & Zarepour, M. (2010) $M$ -estimation for a spatial unilateral autoregressive model with infinite variance innovations. Econometric Theory 26, 1663–1682.CrossRefGoogle Scholar
Serfling, R. (1980) Approximation Theorems of Mathematical Statistics. John Wiley & Sons.CrossRefGoogle Scholar
Solo, V. (1986) Modeling of two-dimensional random fields by parametric Cepstrum. IEEE, Transactions on Information Theory 42, 743–750.CrossRefGoogle Scholar
Stein, M. (1999) Interpolation of Spatial Data: Some Theory for Kriging. Spinger-Verlag.CrossRefGoogle Scholar
Wang, H., Iglesias, E.M., & Wooldridge, J.M. (2013) Partial maximum likelihood estimation of spatial probit models. Journal of Econometrics 172, 77–89.CrossRefGoogle Scholar
Whittle, P. (1954) On stationary processes in the plane. Biometrika 41, 434–449.CrossRefGoogle Scholar