On Explosive Time Series

The first chapter of this thesis, discusses the characteristics of an asset bubble episode outlining the reasons these episodes have attracted so much interest nowadays and provides an overview of historical bubble episodes motivating the testing procedures proposed in Chapters 2-4. The second chapter proposes a right-tailed bootstrap implementation of the covariate Augmented Dickey-Fuller (CADF) unit root test of Hansen (1995), motivated by the work of Chang, Sickles and Song (2017). We apply the right-tailed bootstrap BCADF test in a recursive manner and provide evidence that the inclusion of relevant covariates offers significant power gains. An empirical application of the proposed methodology is conducted, utilising the Moody's Seasoned Aaa and Baa Corporate Bond Yields, the Ten-Year Treasury Rate and the Volatility Index (VXO) as covariates. The third chapter intends to examine the size and power properties of right-tailed Dickey-Fuller unit root test processes when testing for market efficiency in the commodity markets by applying a wild bootstrap approach to Phillips et al. (2015) tests. The simulations results show that the proposed wild bootstrap test offers better size control and power performance in finite samples. In the empirical exercise, our proposed test suggests periods of market inefficiency prior to the existence of the bubble episode as identified by the conventional tests during two periods of oil crises. The fourth chapter studies the hypothesis of an asset bubble in a rational expectations framework using a bivariate coexplosive vector autoregression as in Nielsen (2010). Firstly, we apply a co-explosive vector autoregression to model whether the WTI crude oil price run-up of 2007-2008 can be attributed to the existence of a bubble as well as whether the WTI crude oil collapse of 2014-2015 exhibits characteristics of bubble implosion. In the fifth and final chapter, concluding remarks are made regarding and directions for future research are proposed.