Bootstrap-Based Unit Root Tests for Higher Order Autoregressive Models with GARCH(1, 1) Errors


Bootstrap-based unit root tests are a viable alternative to asymptotic distribution-based procedures and, in some cases, are preferable because of the serious size distortions associated with the latter tests under certain situations. While several bootstrap-based unit root tests exist for autoregressive moving average processes with homoskedastic errors, only one such test is available when the innovations are conditionally heteroskedastic. The details for the exact implementation of this procedure are currently available only for the first order autoregressive processes. Monte-Carlo results are also published only for this limited case. In this paper we demonstrate how this procedure can be extended to higher order autoregressive processes through a transformed series used in augmented Dickey-Fuller unit root tests. We also investigate the finite sample properties for higher order processes through a Monte-Carlo study. Results show that the proposed tests have reasonable power and size properties.


Mathematics and Statistics

Keywords and Phrases

Conditional volatility; Non-stationarity tests; Random walk; Residual bootstrap; Time series

International Standard Serial Number (ISSN)

0094-9655; 1563-5163

Document Type

Article - Journal

Document Version


File Type





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Publication Date

01 Oct 2016