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Oracally Efficient Estimation and Consistent Model Selection for Spatial ARMA Process With Bivariate Trend

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  • Tong Zhang
  • Yuanyuan Zhang
  • Chen Zhong

Abstract

The analysis of nonlinearity in spatial and spatial‐temporal data continues to be a challenging topic. This article introduces a two‐step estimation procedure for modeling nonstationary spatial processes that comprise a smooth bivariate trend function and a spatial autoregressive and moving average (SRAMA) error term. To remove the bivariate trend from the observed process, we apply the cutting‐edge bivariate penalized spline method. The modified maximum likelihood estimator based on the residuals, as suggested by Yao and Brockwell (2006), is shown to be consistent and oracle efficient, achieving the same efficiency asymptotically as if the true trend function were known and removed to obtain the SARMA errors. Furthermore, we establish the consistency of Bayesian information criteria for model selection concerning the residual sequence. The finite sample performance of the proposed approach is evaluated with simulations and real data.

Suggested Citation

  • Tong Zhang & Yuanyuan Zhang & Chen Zhong, 2026. "Oracally Efficient Estimation and Consistent Model Selection for Spatial ARMA Process With Bivariate Trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 47(4), pages 885-903, July.
    • Handle: RePEc:bla:jtsera:v:47:y:2026:i:4:p:885-903
    DOI: 10.1111/jtsa.12847
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