On the sequential space lattice fitting of two-dimensional subset autoregressions

The space lattice recursive fitting algorithm to select the optimum two-dimensional (2-D) full-order autoregressive models (AR) is generalised to apply to 2-D subset ARs, including full-order models. It is initiated by fitting all 'forward' and 'backward' one-lag 2-D ARs. The method thus allows us to develop successively all 2-D subset ARs of size κ (the number of lags with nonzero coefficient matrices) from 1 to K. Finally, the best subsets of each size with the minimum generalised residual power for that size are compared to a modified 2-D model selection criterion to find the optimum 2-D subset AR.