Test of Unit Root for Bounded AR (2) Model
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Published
Dec 30, 2020
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14-33
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Sayed Meshaal El-Sayed
Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.
Ahmed Amin EL- Sheikh
Department of Applied Statistics and Econometrics, Faculty of Graduate Studies for Statistical Research, Cairo University, Egypt.
Mohammed Ahmed Farouk Ahmed
High Institute of Computer and Information Technology, Al-Shorouk Academy, Cairo, Egypt.
Abstract
In this paper, the test of unit root for bounded AR (2) model with constant term and dependent errors has been derived. Asymptotic distributions of OLS estimators and t-type statistics under different tests of hypotheses have been derived. A simulation study has been established to compare between different tests of the unit root. Mean squared error (MSE) and Thiel's inequality coefficient (Thiel’s U) have been considered as criteria of comparison.
Keywords:
Bounded AR (2) model, asymptotic distributions, OLS estimators, mean squared error, Thiel's inequality coefficient, t-type statistics
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Original Research Article
References
Dickey DA, Fuller WA. Distribution of the estimators for autoregressive time series with a unit root. JASA. 1979;74(366):427-431.
Dickey DA, Fuller WA. Likelihood ratio statistics for autoregressive time series with a unit. Econometrica. 1981;49(4):1057-1072.
Cavaliere G. A rescaled range statistics approach to unit root tests. Econometric Society World Congress 2000 Contributed Papers 0318; 2000. Available:http://fmwww.bc.edu/RePEc/es2000/0318.pdf.
Cavaliere G. Limited time series with a unit root. Econometric Theory. 2005;21(5):907-945.
Cavaliere G, Xu F. Testing for unit roots in bounded time series. University of Bologna, European University Institute Christian-Albrechts-University of Kiel; 2011. Available:http://www.econ.queensu.ca/files/event/Cavaliere_Xu.pdf.
Schatzman M. Numerical analysis: A mathematical introduction. Clarendon Press, Oxford; 2002.
Sawyer S. Generalized inverses: How to invert a non-invertible. Matrix; 2008. Available:https://www.math.wustl.edu/~sawyer/handouts/GenrlInv.pdf.
Amer GA. Econometrics and time series analysis (Theroy, Methods, Applications) Cairo University; 2015.
Bell J. The weak and strong laws of large numbers. University of Toronto; 2015. Available:https://pdfs.semanticscholar.org/4786/984d97527d81b17ba34bbfdbbb46f1e69f48.pdf
Dickey DA, Fuller WA. Likelihood ratio statistics for autoregressive time series with a unit. Econometrica. 1981;49(4):1057-1072.
Cavaliere G. A rescaled range statistics approach to unit root tests. Econometric Society World Congress 2000 Contributed Papers 0318; 2000. Available:http://fmwww.bc.edu/RePEc/es2000/0318.pdf.
Cavaliere G. Limited time series with a unit root. Econometric Theory. 2005;21(5):907-945.
Cavaliere G, Xu F. Testing for unit roots in bounded time series. University of Bologna, European University Institute Christian-Albrechts-University of Kiel; 2011. Available:http://www.econ.queensu.ca/files/event/Cavaliere_Xu.pdf.
Schatzman M. Numerical analysis: A mathematical introduction. Clarendon Press, Oxford; 2002.
Sawyer S. Generalized inverses: How to invert a non-invertible. Matrix; 2008. Available:https://www.math.wustl.edu/~sawyer/handouts/GenrlInv.pdf.
Amer GA. Econometrics and time series analysis (Theroy, Methods, Applications) Cairo University; 2015.
Bell J. The weak and strong laws of large numbers. University of Toronto; 2015. Available:https://pdfs.semanticscholar.org/4786/984d97527d81b17ba34bbfdbbb46f1e69f48.pdf