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

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  • Ana Paula Martins

Abstract

This paper inspected 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 was (computationally) implemented and applied to inference of the AR(1) parameter of simulated – some stationary, others non-stationary - series. Additionally, it was argued - and illustrated by simulation - that non-stationary AR(1) processes appear to be consistently estimable by OLS. Also, it was 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 was concluded.

Suggested Citation

  • Ana Paula Martins, 2017. "Estimation of Possibly Non-Stationary First-Order Auto-Regressive Processes," Journal of Economics and Econometrics, Economics and Econometrics Society, vol. 60(1), pages 52-73.
    • Handle: RePEc:eei:journl:v:60:y:2017:i:1:p:52-73
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    Keywords

    Nonlinear Estimation; Grid Search Methods; AR(1) Processes; Integrated Series; Differenced Processes; “Factored” AR(1) Processes; Unit Roots.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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