ON THE RECURSIVE FITTING OF SUBSET AUTOREGRESSIONS

Abstract

Abstract. In fitting a vector autoregressive process which may include lags up to and including lag K , we may wish to search for the subset vector autoregressive process of size k (where k is the number of lags with non‐zero coefficient matrices, k = 1, 2, K ) which has the minimum generalized residual variance. This paper provides a recursive procedure, which is initialized by evaluating all ‘forwardand’‘backward’ autoregressions in which k = 1. The recursion then allows one to develop successively all subsets of size k = 2, k = 3 up to k = K . The optimum subset vector autoregression is found by employing the proposed recursive procedures in conjunction with model selection criteria. This approach is used on simulated data to assess its performance and to re‐examine the annual trappings of the Canadian lynx investigated by Tong (1977).