On-line trend detection based on ARI modeling

The present paper investigates the recursive adaptive algorithms for rapidly detecting various stochastic trends in signals by modeling them as the autoregressive integrated (ARI) process. Two kinds of new criteria are presented for determining the degree of differencing which represents the changing rate of nonstationary trend components; one is derived by extending the concept of the AIC and the other is based on hypothesis testing. The parameter coefficients of the ARI model are identified by use of the least squares adaptive lattice filters. The effectiveness of the algorithms is examined through numerical simulation data.