Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in Michael McAleer Department of Economics University of Western Australia Revised: June 2001Abstract Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition α+β < 1. The former has the usual unit root distribution and the latter is a functional of a bivariate Brownian motion, as in Ling and Li (1998). Several unit root tests based on LS estimators, ML estimators, and mixing LS and ML estimators, are constructed. Simulation results show that tests based on mixing LS and ML estimators perform better than Dickey-Fuller tests which are based on LS estimators, and that tests based on the ML estimators perform better than the mixed estimators.

Assessing the anchoring of inflation expectations

“…With regard to the impact of neglected GARCH on the (augmented) Dickey-Fuller (ADF, Dickey and Fuller 1979) test, see, e.g., Kim and Schmidt (1993), Ling and McAleer (2003) and the literature they refer to. Due to the invariance principle, the ADF test proves to be asymptotically robust to covariance stationary GARCH errors.…”

Adaptive Wild Bootstrap Tests for a Unit Root With Non‐Stationary Volatility

“…This implies that conventional DF tests for a unit root will be asymptotically valid, even though more powerful tests can be obtained by explicitly modelling the volatility process; see, e.g., Seo (1999) and Ling et al (2003).…”

“…This was illustrated using Monte Carlo simulations by Kim and Schmidt (1993). However, subsequent research has indicated that in such cases more powerful tests for a unit root may be obtained from a likelihood analysis of a model with GARCH innovations; see Seo (1999) and Ling et al (2003), based on Ling and Li (1998), inter alia.…”

Estimation for nearly unit root processes with GARCH errors

“…Many theories for inference for unit root models with GARCH errors are readily available. For example, [10] considers the least squares and maximum likelihood estimation for unit root processes with GARCH(1,1) errors; [9] investigates the one-step local quasi-maximum likelihood estimator for the unit root processes with GARCH(1,1) errors. The asymptotic distributions of the estimators in both papers are derived under the condition that Eu 2 t < ∞ and Ez 4 t < ∞.…”