Estimation of Possibly Non-Stationary First-Order Auto-Regressive Processes

Ana Paula Martins

EERI Research Paper Series from Economics and Econometrics Research Institute (EERI), Brussels

Abstract: This paper inspects a grid search algorithm to estimate the AR(1) process, based on the joint estimation of the canonical AR(1) equation along with its reverse form. The method relies on the GLS principle, accounting for the covariance error structure of the special estimable system. Nevertheless, it stands as potentially improving to rely on across-equation-restricted system estimation with free covariance structure. The algorithm is (computationally) implemented and applied to inference of the AR(1) parameter of simulated – some stationary, others non-stationary - series. Additionally, it is argued - and illustrated by simulation - that non-stationary AR(1) processes appear to be consistently estimable by OLS. Also, it is suggested that the parameter of a stationary AR(1) process is estimable by OLS from the AR(2) representation of its non-stationary “first-integrated” series; or from the joint estimate of the canonical and reverse form of the AR(1) process by OLS. Importance of further study of differenced, D(p) – stationary after being integrated p times - processes is concluded.

Keywords: Nonlinear Estimation; Grid Search Methods; AR(1) Processes; Integrated Series; Differenced Processes; Factored AR(1) Processes; Unit Roots. (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 C63 (search for similar items in EconPapers)
Date: 2016-11-21
New Economics Papers: this item is included in nep-ecm and nep-ets
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Journal Article: Estimation of Possibly Non-Stationary First-Order Auto-Regressive Processes (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:eei:rpaper:eeri_rp_2016_21

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