Harris, David and Kew, Hsein and Taylor, AM Robert (2020) Level Shift Estimation in the Presence of Non-stationary Volatility with an Application to the Unit Root Testing Problem. Journal of Econometrics, 219 (2). pp. 354-388. DOI https://doi.org/10.1016/j.jeconom.2020.03.008
Harris, David and Kew, Hsein and Taylor, AM Robert (2020) Level Shift Estimation in the Presence of Non-stationary Volatility with an Application to the Unit Root Testing Problem. Journal of Econometrics, 219 (2). pp. 354-388. DOI https://doi.org/10.1016/j.jeconom.2020.03.008
Harris, David and Kew, Hsein and Taylor, AM Robert (2020) Level Shift Estimation in the Presence of Non-stationary Volatility with an Application to the Unit Root Testing Problem. Journal of Econometrics, 219 (2). pp. 354-388. DOI https://doi.org/10.1016/j.jeconom.2020.03.008
Abstract
This paper focuses on the estimation of the location of level breaks in time series whose shocks display non-stationary volatility (permanent changes in unconditional volatility). We propose a new feasible weighted least squares (WLS) estimator, based on an adaptive estimate of the volatility path of the shocks. We show that this estimator belongs to a generic class of weighted residual sum of squares which also contains the ordinary least squares (OLS) and WLS estimators, the latter based on the true volatility process. For fixed magnitude breaks we show that the consistency rate of the generic estimator is unaffected by non-stationary volatility. We also provide local limiting distribution theory for cases where the break magnitude is either local-to-zero at some polynomial rate in the sample size or is exactly zero. The former includes the Pitman drift rate which is shown via Monte Carlo experiments to predict well the key features of the finite sample behaviour of both the OLS and our feasible WLS estimators. The simulations highlight the importance of the break location, break magnitude, and the form of non-stationary volatility for the finite sample performance of these estimators, and show that our proposed feasible WLS estimator can deliver significant improvements over the OLS estimator under heteroskedasticity. We discuss how these results can be applied, by using level break fraction estimators on the first differences of the data, when testing for a unit root in the presence of trend breaks and/or non-stationary volatility. Methods to select between the break and no break cases, using standard information criteria and feasible weighted information criteria based on our adaptive volatility estimator, are also discussed. Simulation evidence suggests that unit root tests based on these weighted quantities can display significantly improved finite sample behaviour under heteroskedasticity relative to their unweighted counterparts. An empirical illustration to U.S. and U.K. real GDP is also considered.
Item Type: | Article |
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Uncontrolled Keywords: | Level break fraction, non-stationary volatility, adaptive estimation, feasible weighted estimator, information criteria, unit root tests and trend breaks |
Divisions: | Faculty of Social Sciences Faculty of Social Sciences > Essex Business School |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 11 Dec 2019 11:35 |
Last Modified: | 16 May 2024 20:06 |
URI: | http://repository.essex.ac.uk/id/eprint/26216 |
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