Parameters Estimations for Autoregressive Process

Hai Long Chen; Jing Yang; Chun Li Liu; Jun Ting Wang

doi:10.4028/www.scientific.net/AMM.543-547.1711

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 543-547Parameters Estimations for Autoregressive Process

Parameters Estimations for Autoregressive Process

Abstract:

Autoregressive process is better than other stochastic processes, which models flexibility, and simulates some other stochastic processes by setting the parameters of model. This paper firstly describes in detail the basic definition of autoregressive process and its stationary conditions, and then studies estimation autoregressive process parameters with residuals briefly in order to research Hubors М-estimation for autoregressive process with symmetric stable residuals. Secondly, prove autoregressive processes with residuals, which are-stable random variables, are also stationary processes, and use Markov's inequality and related theories to discuss Hubors М-estimation for autoregressive process with symmetric stable residuals. Finally, prove the consistency and asymptotic normality of this estimate further.