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Adaptively varying‐coefficient spatiotemporal models

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  • Zudi Lu
  • Dag Johan Steinskog
  • Dag Tjøstheim
  • Qiwei Yao

Abstract

Summary. We propose an adaptive varying‐coefficient spatiotemporal model for data that are observed irregularly over space and regularly in time. The model is capable of catching possible non‐linearity (both in space and in time) and non‐stationarity (in space) by allowing the auto‐regressive coefficients to vary with both spatial location and an unknown index variable. We suggest a two‐step procedure to estimate both the coefficient functions and the index variable, which is readily implemented and can be computed even for large spatiotemporal data sets. Our theoretical results indicate that, in the presence of the so‐called nugget effect, the errors in the estimation may be reduced via the spatial smoothing—the second step in the estimation procedure proposed. The simulation results reinforce this finding. As an illustration, we apply the methodology to a data set of sea level pressure in the North Sea.

Suggested Citation

  • Zudi Lu & Dag Johan Steinskog & Dag Tjøstheim & Qiwei Yao, 2009. "Adaptively varying‐coefficient spatiotemporal models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 859-880, September.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:4:p:859-880
    DOI: 10.1111/j.1467-9868.2009.00710.x
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    References listed on IDEAS

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    1. Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
    2. Jianqing Fan & Qiwei Yao & Zongwu Cai, 2003. "Adaptive varying‐coefficient linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 57-80, February.
    3. A S Fotheringham & M E Charlton & C Brunsdon, 1998. "Geographically Weighted Regression: A Natural Evolution of the Expansion Method for Spatial Data Analysis," Environment and Planning A, , vol. 30(11), pages 1905-1927, November.
    4. Xia, Yingcun & Li, W. K., 2002. "Asymptotic Behavior of Bandwidth Selected by the Cross-Validation Method for Local Polynomial Fitting," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 265-287, November.
    5. Gérard Biau & Benoît Cadre, 2004. "Nonparametric Spatial Prediction," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 327-349, October.
    6. Kim, T. Y. & Cox, D. D., 1995. "Asymptotic Behaviors of Some Measures of Accuracy in Nonparametric Curve Estimation with Dependent Observations," Journal of Multivariate Analysis, Elsevier, vol. 53(1), pages 67-93, April.
    7. Mammen, Enno, 1990. "A short note on optimal bandwidth selection for kernel estimators," Statistics & Probability Letters, Elsevier, vol. 9(1), pages 23-25, January.
    8. Jones, M. C., 1991. "The roles of ISE and MISE in density estimation," Statistics & Probability Letters, Elsevier, vol. 12(1), pages 51-56, July.
    9. Lu, Zudi & Tjøstheim, Dag & Yao, Qiwei, 2007. "Adaptive varying-coefficient linear models for stochastic processes: asymptotic theory," LSE Research Online Documents on Economics 5411, London School of Economics and Political Science, LSE Library.
    10. Lu, Zudi & Tjøstheim, Dag & Yao, Qiwei, 2008. "Spatial smoothing, Nugget effect and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3145-3151, December.
    11. Marc Hallin & Zudi Lu & Lanh T. Tran, 2004. "Local linear spatial regression," ULB Institutional Repository 2013/2131, ULB -- Universite Libre de Bruxelles.
    12. Lu, Zudi & Lundervold, Arvid & Tjøstheim, Dag & Yao, Qiwei, 2007. "Exploring spatial nonlinearity using additive approximation," LSE Research Online Documents on Economics 5401, London School of Economics and Political Science, LSE Library.
    13. Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models II: spatial processes," LSE Research Online Documents on Economics 5416, London School of Economics and Political Science, LSE Library.
    14. Lu, Zudi & Tjostheim, Dag & Yao, Qiwei, 2008. "Spatial smoothing, Nugget effect and infill asymptotics," LSE Research Online Documents on Economics 24133, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Ting Fung Ma & Fangfang Wang & Jun Zhu & Anthony R. Ives & Katarzyna E. Lewińska, 2023. "Scalable Semiparametric Spatio-temporal Regression for Large Data Analysis," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(2), pages 279-298, June.
    2. Zhang, Lyuou & Zhou, Wen & Wang, Haonan, 2021. "A semiparametric latent factor model for large scale temporal data with heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    3. Kurisu, Daisuke, 2019. "On nonparametric inference for spatial regression models under domain expanding and infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    4. Ren, Xiaohang & Lu, Zudi & Cheng, Cheng & Shi, Yukun & Shen, Jian, 2019. "On dynamic linkages of the state natural gas markets in the USA: Evidence from an empirical spatio-temporal network quantile analysis," Energy Economics, Elsevier, vol. 80(C), pages 234-252.
    5. Amiri, Aboubacar & Dabo-Niang, Sophie, 2018. "Density estimation over spatio-temporal data streams," Econometrics and Statistics, Elsevier, vol. 5(C), pages 148-170.
    6. Sim, Nicholas & Zhou, Hongtao, 2015. "Oil prices, US stock return, and the dependence between their quantiles," Journal of Banking & Finance, Elsevier, vol. 55(C), pages 1-8.
    7. Al-Sulami, Dawlah & Jiang, Zhenyu & Lu, Zudi & Zhu, Jun, 2017. "Estimation for semiparametric nonlinear regression of irregularly located spatial time-series data," Econometrics and Statistics, Elsevier, vol. 2(C), pages 22-35.
    8. Liu, Jialuo & Chu, Tingjin & Zhu, Jun & Wang, Haonan, 2021. "Semiparametric method and theory for continuously indexed spatio-temporal processes," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    9. Lin, Fangzheng & Tang, Yanlin & Zhu, Huichen & Zhu, Zhongyi, 2022. "Spatially clustered varying coefficient model," Journal of Multivariate Analysis, Elsevier, vol. 192(C).

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