Two improved generalized extended stochastic gradient algorithms for CARARMA systems

Abstract

The paper innovatively proposes two improved generalized extended stochastic gradient (GESG) algorithms for the controlled autoregressive autoregressive moving average (CARARMA) system with autoregressive moving average (ARMA) model noise. Firstly, we propose a latest estimation based weighted generalized extended stochastic gradient (LE-WGESG) algorithm, which introduces multiple momentary corrections in the traditional parameter estimation process. By carefully adjusting the weighting coefficients of the correction quantities at different moments, the algorithm has a rapid and greater efficient convergence property. More importantly, utilizing the theory of moving data window, this paper also proposes a multi-innovation based latest estimated weighted generalized extended stochastic gradient (MI-LE-WGESG) algorithm, which can better capture the interactions among multiple correction terms and further improve the predictive ability of the model.