Boundary and Sign Problems of Parameters along with its Solutions of the Augmented Dickey-Fuller Test

Abstract

Usual test of testing unit root such as Dickey-Fuller (DF), Augmented Dickey-Fuller (ADF), Phillips Perron etc ignores sign and boundary of parameters. In this paper, we demonstrated the ignorance of sign and boundary of parameters and consequences of this ignorance in estimation and testing by Monte Carlo Simulation. Our main objective is to develop a method to capture the non-stationarity keeping in mind the boundary and sign problem and to develop the restricted ADF test based on ESS using the constraint estimate of parameters. We compare the power properties of the usual ADF test and ADF test with restricted error sum of squares using the constraint estimate of parameters by Monte Carlo Simulation and we find that the proposed ADF test gives better result than the usual ADF test in terms of power properties.