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Identifying the start and end dates of explosive bubble regimes has become a prominent issue in the econometric literature. Recent research has demonstrated the advantage of a model-based minimum sum of squared residuals estimator, combined with Bayesian Information Criterion model selection, over recursive unit root testing methods in providing accurate date estimates for a single explosive regime. However, in the context of multiple bubbles, a large number of models are possible, making such a model-based method unappealing. In this paper, we propose a two-step procedure for dating multiple explosive regimes. First, recursive unit root tests are used to identify a ‘date window’ in which an explosive episode starts and ends. Second, a model-based BIC approach is used to precisely estimate the regime change points within each date window. In addition, our method allows us to distinguish between different types of explosive episode, such as whether or not each explosive regime crashes before reverting back to a unit root process, and date any crash regimes. Monte Carlo simulations highlight the effectiveness of our procedure when compared to existing methods of dating. The value of the new methodology is also demonstrated through an empirical application to housing markets.

Recent research has proposed a method of detecting explosive processes that is based on forward recursions of OLS, right‐tailed, Dickey–Fuller [DF] unit root tests. In this paper, an alternative approach using GLS DF test statistics is considered. We derive limiting distributions for both mean‐invariant and trend‐invariant versions of OLS and GLS‐based Phillips, Wu and Yu (2011, International Economic Review 52, 201–226) [PWY] test statistics under a temporary, locally explosive alternative. These limits are shown to be dependent on both the value of the initial condition and the start and end points of the temporary explosive regime. Local asymptotic power simulations show that a GLS version of the PWY statistic offers superior power when a large proportion of the data is explosive, but that the OLS approach is preferred for explosive periods of short duration as a proportion of the total sample. These power differences are magnified by the presence of an asymptotically non‐negligible initial condition. We propose a union of rejections procedure that capitalizes on the respective power advantages of both OLS and GLS‐based approaches. This procedure achieves power close to the effective envelope provided by the two individual PWY tests across all settings of the initial condition and length of the explosive period considered in this paper. These results are shown to be robust to the point in the sample at which the temporary explosive regime occurs. An application of the union procedure to NASDAQ prices confirms the empirical value of this testing strategy.

In this paper, we show that when computing standard Diebold-Mariano-type tests for equal forecast accuracy and forecast encompassing, the long-run variance can frequently be negative when dealing with multi-step-ahead predictions in small, but empirically relevant, sample sizes. We subsequently consider a number of alternative approaches to dealing with this problem, including direct inference in the problem cases and use of long-run variance estimators that guarantee positivity. The finite sample size and power of the different approaches are evaluated using extensive Monte Carlo simulation exercises. Overall, for multi-step-ahead forecasts, we find that the recently proposed Coroneo and Iacone (2016) test, which is based on a weighted periodogram long-run variance estimator, offers the best finite sample size and power performance.

In this paper we examine the local power of unit root tests against globally stationary exponential smooth transition autoregressive [ESTAR] alternatives under two sources of uncertainty: the degree of nonlinearity in the ESTAR model, and the presence of a linear deterministic trend. First, we show that the KSS test (Kapetanios, G., Y. Shin, and A. Snell. 2003. “Testing for a Unit Root in the Nonlinear STAR Framework.” Journal of Econometrics 112: 359–379) for nonlinear stationarity has local asymptotic power gains over standard Dickey-Fuller [DF] tests for certain degrees of nonlinearity in the ESTAR model, but that for other degrees of nonlinearity, the linear DF test has superior power. Second, we derive limiting distributions of demeaned, and demeaned and detrended KSS and DF tests under a local ESTAR alternative when a local trend is present in the DGP. We show that the power of the demeaned tests outperforms that of the detrended tests when no trend is present in the DGP, but deteriorates as the magnitude of the trend increases. We propose a union of rejections testing procedure that combines all four individual tests and show that this captures most of the power available from the individual tests across different degrees of nonlinearity and trend magnitudes. We also show that incorporating a trend detection procedure into this union testing strategy can result in higher power when a large trend is present in the DGP.