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.
X. Zhong and V. A. Samaranayake, "Bootstrap-Based Unit Root Tests for Higher Order Autoregressive Models with GARCH(1, 1) Errors," Journal of Statistical Computation and Simulation, vol. 86, no. 15, pp. 3025 - 3037, Taylor & Francis, Oct 2016.
The definitive version is available at https://doi.org/10.1080/00949655.2016.1146720
Mathematics and Statistics
Keywords and Phrases
Conditional volatility; Non-stationarity tests; Random walk; Residual bootstrap; Time series
International Standard Serial Number (ISSN)
Article - Journal
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01 Oct 2016