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Estimation for autoregressive processes with positive innovations

Paul D. Feigin, Sidney I. Resnick

Open publisher page 40 citations

Abstract

We consider stationary autoregressive processes of order p which have positive parameters and positive innovations. The main results concern the rate of consistency of parameter estimators for the case p = 2. These estimators are defined in terms of estimating equations. Relevant asymptotic theory is developed in the wider context of vector autoregressive processes with positive innovations having a distribution with regularly varying left or right tails. These weak convergence results may be of independent interest.

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What this paper is about

We consider stationary autoregressive processes of order p which have positive parameters and positive innovations. The main results concern the rate of consistency of parameter estimators for the case p = 2. These estimators are defined in terms of estimating equations. Relevant asymptotic theory is developed in the wider context of vector autoregressive processes with positive innovations having a distribution with regularly varying left or right tails. These weak convergence results may be of independent interest.

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Available abstract

We consider stationary autoregressive processes of order p which have positive parameters and positive innovations. The main results concern the rate of consistency of parameter estimators for the case p = 2. These estimators are defined in terms of estimating equations. Relevant asymptotic theory is developed in the wider context of vector autoregressive processes with positive innovations having a distribution with regularly varying left or right tails. These weak convergence results may be of independent interest.

Key concepts: Autoregressive model, Estimator, Asymptotic distribution, Mathematics, Strong consistency, Context (archaeology), STAR model, Consistency (knowledge bases)

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