Class of Modified Two-Stage Procedure in a Autoregressive Process

Soudabe Sajjadipanah, Sayyed Mahmoud Mirjalili, Sayyedeh Maryam Mousavialiabadi

Abstract


In this paper, we first discuss the class of modified two-stage procedure for estimation of the autoregressive parameter in a first-order autoregressive model ( AR(1)).

 

We prove the significant properties of the modified two-stage procedure, including asymptotic efficiency, asymptotic risk efficiency, and asymptotic consistency for the point and the interval estimation based on least-squares estimators.

Then, the introduced class is generalized to the p-order autoregressive model ( AR(p)) and is checked their asymptotic properties of which.

Also, we conduct comprehensive Monte Carlo simulation studies to test the properties of the proposed procedure in practice.

Finally, a real-time series is provided to investigate the applicability of the class of modified two-stage variables.


Keywords


Modified two-stage procedure, Autoregressive process, Asymptotic risk efficiency, Asymptotic efficiency, Asymptotic consistency.

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