In contrast to classical econometric approaches which are based on prespecified isotropic weighting schemes, we suggest that the spatial weighting matrix in the presence of directional dependencies should be estimated. We identify this direction based on different candidate neighbourhood sets. In this paper, we consider two different types of processes – namely spatial autoregressive and spatial autoregressive conditional heteroscedastic processes – and derive the consistency of the corresponding maximum likelihood estimates in the presence of directional dependencies. Moreover, Monte Carlo simulation results indicate that the model’s performance improves with sample size and with smaller neighbourhood subset sizes. Finally, we apply this approach to aerosol observations over the North Atlantic region and show that their spatial dependence matches the direction of the trade winds in this area.

与基于预先指定的各向同性加权方案的经典计量经济学方法相反，我们建议应该估计在存在方向性依赖项的情况下的空间加权矩阵。我们根据不同的候选邻域集确定此方向。在本文中，我们考虑了两种不同类型的过程-空间自回归和空间自回归条件异方差过程-并在存在方向依赖性的情况下得出相应最大似然估计的一致性。此外，蒙特卡洛模拟结果表明，模型的性能随样本大小和邻域子集大小的减小而提高。最后，