The stationary bootstrap

By Dimitris Nicolas Politis, Joseph P. Romano. 1994

Abstract This article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations. Previously, a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m-dimensional joint distribution of m consecutive observations, where m is fixed. This procedure has been generalized by constructing a “blocks of blocks” resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole (i.e., infinite-dimensional) joint distribution of the stationary sequence of observations. These methods share the construction of resampling blocks of observations to form a pseudo-time series, so that the statistic of interest may be recalculated based on the resampled data set. But in the context of applying this method to stationary data, it is natural...

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Citations in the corpus

The Double Power Law in Consumption and Implications for Testing Euler Equations (2015, methodology): “The bootstrap standard errors are based on the stationary bootstrap of Politis and Romano (1994), which also account for the sampling error in the cross-section as well as the time series.”
A bivariate Markov regime switching GARCH approach to estimate time varying minimum variance hedge ratios (2007, methodology): “3 To apply the stationary bootstrap method of Politis and Romano (1994), we set the smoothing parameter q to 0.5 and we resample 1000 times for each application.”
Forecasting the Yield Curve in a Data-Rich Environment: A No-Arbitrage Factor-Augmented VAR Approach (2008, unknown): “4 As discussed in Rudebusch et al. (2006a), this assumption is consistent with the predictions of standard New-Keynesian models in which aggregate output is determined by a forward-looking IS curve and therefore only depends on expected future short-term real interest rates.”
Forecasting The Path of U.S. CO2 Emissions Using State-Level Information (2012, unknown): “We used the stationary bootstrap of Politis and Romano (1994) with a block length of 4 and B = 500 resamples.”
Parameter uncertainty in portfolio selection: Shrinking the inverse covariance matrix (2012, methodology): “To test the null hypothesis “H0 : σ̂2s − σ̂2p = 0” or “H0 : CERs − CERp = 0” for two strategies s and p, we employ the circular studentized bootstrap of Politis and Romano (1994) assuming an expected block size of 5.”
Statistical arbitrage pairs trading strategies: Review and outlook (2017, unknown): “It may be an enhancement to consider a stationary bootstrap, following Politis and Romano (1994) in this time series context.”
A general nonparametric bootstrap test for Granger causality (2001, methodology): “The stationary bootstrap proposed by Politis and Romano [11] is simple to apply to univariate time series.”
Predictability of Currency Carry Trades and Asset Pricing Implications (2013, unknown): “The confidence intervals are based on the stationary bootstrap (Politis and Romano, 1994), with optimal block size determined according to the algorithm of Politis and White (2004), which accounts for conditional heteroskedasticity (Goncalves and White, 2002), as well as nonnormality.”
A Transaction-Cost Perspective on the Multitude of Firm Characteristics (2020, unknown): “Nevertheless, to gauge the importance of the iid assumption, we have repeated the tests using the stationary bootstrap in Politis and Romano (1994), which takes serial dependence into account, and we have found that the results are robust.”