Estimation of possibly non-stationary first-order auto-regressive processes

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: EERI Research Paper Series ; No. 21/2016

Classification and Topics

• Classification: Wirtschaft ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Estimation: General ; Hypothesis Testing: General ; Computational Techniques; Simulation Modeling
• Subject: Nonlinear Estimation ; Grid Search Methods ; AR(1) Processes ; Integrated Series ; Differenced Processes ; Factored AR(1) Processes ; Unit Roots

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Martins, Ana Paula
• Event: Veröffentlichung
• (who): Economics and Econometrics Research Institute (EERI)
• (where): Brussels
• (when): 2016

Further information

• Handle: http://hdl.handle.net/10419/179399
• Last update: 10.03.2025, 11:41 AM CET