Residual-Based Block Bootstrap for Unit Root Testing

Abstract

A nonparametric, residual-based block bootstrap procedure is proposed in the context of testing for integrated (unit root) time series. The resampling procedure is based on weak assumptions on the dependence structure of the stationary process driving the random walk and successfully generates unit root integrated pseudo-series retaining the important characteristics of the data. It is more general than previous bootstrap approaches to the unit root problem in that it allows for a very wide class of weakly dependent processes and it is not based on any parametric assumption on the process generating the data. As a consequence the procedure can accurately capture the distribution of many unit root test statistics proposed in the literature. Large sample theory is developed and the asymptotic validity of the block bootstrap-based unit root testing is shown via a bootstrap functional limit theorem. Applications to some particular test statistics of the unit root hypothesis, i.e., least squares and Dickey-Fuller type statistics are given. The power properties of our procedure are investigated and compared to those of alternative bootstrap approaches to carry out the unit root test. Some simulations examine the finite sample performance of our procedure.

Combining non-cointegration tests

“…However, as Paparoditis and Politis (2003) show for unit-root tests, imposing such a restriction may lead to a power loss.…”

Detrending Bootstrap Unit Root Tests

“…The tests proposed by Chang and Park (2003) are very similar, except they consider the ADF test. Paparoditis and Politis (2003) propose a block bootstrap test based on residuals, for both the DF and ADF coefficient test. Swensen (2003a) considers two DF (coefficient and t) bootstrap tests based on differences; one uses the sieve bootstrap, and one the stationary bootstrap.…”

“…However, when conducting unit root tests in practice, one will often want to include an intercept and possibly a linear time trend in the regression. Psaradakis (2001), Paparoditis and Politis (2003) and Parker et al (2006) explicitly discuss deterministic components and show the validity of their tests for these situations.…”

Tapered Block Bootstrap for Unit Root Testing

“…There are many such tests in the literature; see for example Fuller (1996), Dickey and Fuller (1979), Dickey, Bell, and Miller (1986) and Phillips and Perron (1988). More recently in Swensen (2003), Paparoditis and Politis (2003) and Parker, Paparoditis, and Politis (2006), bootstrap-based tests for a unit root were proposed. The latter two papers use a bootstrap procedure (block and stationary bootstraps respectively) on the residuals, while the former applies the stationary bootstrap on the differenced series.…”