Essays On Explosive Time Series

In the first chapter of this thesis, we introduce and explore three prominent research areas related to explosive bubbles. We also establish the link between each chapter in the thesis and consequently, these strands of research. In Chapter 2, we introduce a novel test that builds upon the existing WLS-based test proposed by Harvey et al. (2019) to identify explosive bubbles in financial data with the presence of time-varying volatility. Our test outperforms both the conventional supremum bubble test of Phillips and Yu (2011) and Harvey et al. (2019)’s test. Our approach involves replacing the kernel-based volatility function estimator used by Harvey et al. (2019) with our own volatility estimator that is based on an iterative cumulative sum of squares algorithm. Similar to Harvey et al. (2019)’s test, we use the estimated volatility to calculate the WLS-based statistic and employ a wild-bootstrap procedure to control the size of the test and make it robust under various time-varying volatility patterns. We suggest using a union of rejections procedure when the volatility pattern is a late upward shift to capture the better power available from the two constituent tests for a given alternative. Chapter 3 introduces a backward supremum KPSS-based test, which extends the KPSS-based test of Evripidou et al. (2022) to detect short-lived co-explosive behaviour between a pair of asset prices at the end of the sample period. Finite sample simulations show that our test has well-controlled size under most volatility specifications and has higher power than Evripidou et al. (2022)’s test in detecting periods without co-bubbles. As with Evripidou et al. (2022)’s test, our proposed test still employs a wild bootstrap algorithm to deliver a robust test for heteroskedasticity and uses a long-run variance estimate to control the size of the test when serial correlation exists in innovations. By applying both single and double backward supremum tests to the same dataset as Evripidou et al. (2022), we show new findings of co-explosive bubbles in pairs of non-ferrous and precious metals in spot and futures markets. In Chapter 4, we compare the behaviour of common return predictability tests (i.e., IVX, Bonferroni-t, and Bonferroni-Q tests) during bubble periods. Overall, Monte Carlo simulations show that all three tests over-reject the null hypothesis of no predictability. In that regard, the Bonferroni-t test is the least oversized, while the IVX test is badly oversized across different bubble specifications. To conduct the simulations, we introduce a new data generating process that does not require a predetermined variable in the predictive model. Finally, by comparing results obtained from subsamples with and without bubbles, our empirical application shows the over-rejections of the tests to the null using the extended dataset from January 1927 to December 2021 containing 14 financial and macroeconomic predictors of Welch and Goyal (2008). The last chapter of this thesis provides concluding remarks on the significant findings and limitations, as well as presenting suggestions for future research directions.