Bootstrap Sequential Tests to Determine the Order of Integration of Individual Units in A Time Series Panel

Abstract

We propose an approach to investigate the unit root properties of individual units in a time series panel or large multivariate time series, based on testing user‐defined increasing proportions of hypothesized I(0) units sequentially. Asymptotically valid critical values are obtained using the block bootstrap. This sequential approach has an advantage over multiple testing approaches as it can exploit the (cross‐sectional) dimension of the system, which the multiple testing approaches cannot do effectively. A simulation study and an empirical application are conducted to analyse the relative performance of the approach in comparison with multiple testing approaches. These demonstrate the usefulness of our method, in particular in systems with a relatively small time dimension.

A sequential purchasing power parity test for panels of large cross-sections and implications for investors

“…As Smeekes (2011) shows, the above procedure is asymptotically (as T → ∞) valid in the sense that if q is among the quantiles to be tested, then…”

“…. , c 4 are set as in Smeekes (2011) to the negative inverse of the α-level critical values for each test statistic, which are obtained in a preliminary bootstrap step.…”

“…Specifically, the bootstrap sequential quantile test (BSQT) approach of Smeekes (2011) is used, which has the advantage that it not only allows one to estimate the proportion of stationary real exchange rates in panels with large cross-sections, but also that it allows one to identify the countries for which PPP holds. This feature makes BSQT one of the most flexible approaches that has been used so far.…”

Multiple Inference and Market Integration: An Application to Swedish Fish Markets

“…The BST described above is asymptotically valid (see Smeekes, ). More specifically, as T → ∞, it can be shown that: (i) FWER ≥ α ; and (ii) if γ i < 0, then the null hypothesis that the LOP does not hold will be rejected with probability tending to 1.…”

Identifying stationary series in panels: A Monte Carlo evaluation of sequential panel selection methods

“…Other approaches have been recently proposed in the literature to determine the stationarity of individual time series in panels (see, e.g., Ng, 2008;Hanck, 2009;Moon and Perron, 2012;Smeekes, 2015); however, these procedures cannot be strictly labelled as spsm (in the sense used by Chortareas and Kapetanios, 2009) and cannot be analyzed using our simulation method, specifically tailored on Chortareas and Kapetanios (2009).…”