The sensitivity of unit root tests to the initial condition and to the lag length selection: A Monte Carlo Simulation Study

Abstract

While the recent literature has discussed the effect of the deviation of the initial observation of the economic series from its deterministic component (initial condition) on unit root tests, no studies have examined to date the effect of the selection of the lag length on unit root tests in this setting. Our study aims to fill this gap, and provides a recommendation for the practitioner. The objective is to investigate to what extent the sensitivity of the outcome of unit root tests to the initial condition changes with the use of both standard and modified data-dependent methods to select the lag length in the augmented autoregression, even for those tests that have been considered robust in the presence of uncertainty about the initial condition. To do so, we conduct a Monte Carlo simulation study to analyse the finite sample properties (size and power) of unit root tests based on alternative lag selection criteria and different magnitudes of the initial condition.

Keywords:

• Initial condition
• Lag length
• Monte Carlo simulations
• Sensitivity
• Unit root
• JEL Classifications C12
• C15
• C22

Acknowledgments

This work was supported by the MEC-MICINN under Grants ECO2015-65582 DT and ECO2016-74940 P; Department of Science, Technology and Universities of the Aragonese Government and the European Regional Development Fund under the reference research groups S40_17R and S55_17R.

Notes

1 The focus of this paper has been on unit root tests using OLS and GLS-type detrending procedures (Elliott et al. 1996; Ng and Perron 2001, Perron and Qu 2007) however, there are alternative methods to deal with the deterministic part in unit root hypothesis such as the Weighted Symmetric Least Squares, WSLS (Pantula, Gonzalez-Farias, and Fuller 1994; Park and Fuller 1995), and the Recursive Mean Adjustment (Shin and So 2001; Taylor 2002) among others, for which the study could be extended in the future to provide further insights.

2 Following Harvey and Leybourne (2005), we consider $\widehat{\alpha }=\left(y_1-{\widehat{d}}_1\right)/\widehat{\sigma }$ where ${\widehat{d}}_t$ and $\widehat{\sigma }$ are from the OLS regression of $y_t$ on $d_t.$

3 We only tabulate the results for the model assumed the fixed initial condition, as our results are similar for the random case, and available from authors upon request.