Open AccessA Simple Integration Order Test: An Alternative to Unit Root Testing
Author(s) -
Chibuzo G. Amaefula
Publication year - 2021
Publication title -
european journal of mathematics and statistics
Language(s) - English
Resource type - Journals
ISSN - 2736-5484
DOI - 10.24018/ejmath.2021.2.3.22
Subject(s) - unit root test , unit root , mathematics , augmented dickey–fuller test , order of integration (calculus) , series (stratigraphy) , null hypothesis , autoregressive model , simple (philosophy) , test statistic , logarithm , statistics , statistical hypothesis testing , econometrics , cointegration , mathematical analysis , paleontology , philosophy , epistemology , biology
The paper introduces order of integration test (OIT) which serves as a simple alternative to unit root test built generally using auxiliary autoregressive AAR(3) model. The parametric boundary conditions necessary and sufficient for testing the null hypothesis that the non-stationary variable under test is integrated order zero I(0) were estimated via generalized least squares (GLS). The decision on the hypothesis is evaluated using t-statistic. The test procedure was applied to a simulated non-stationary series (y1) of sample size n = 2000 and a known non-stationary time series data (y2) with two unit roots. The results showed that y1 is integrated order one (I(1)) and y2 is I(2). These results were confirmed by Augmented Dickey Fuller (ADF); Phillips-Perron (PP); Kwiatkowski, Phillips, Schmidt, and Shin (KPSS); Elliot, Rothenberg, and Stock Point Optimal (ERS) and Ng and Perron (NP) unit root tests. For logarithm transformed variable, the divergent opinions of other unit root tests in clear-cut solution of the integrated order of such variable makes the new test procedure a better alternative. Nevertheless, the simplicity and aptness of the integration order test give it leverage over conventional methods of unit root test.