rolling-window bootstrap inference

This work addresses the lack of reliable uncertainty quantification in online trend estimation for nonstationary time series by proposing a general online bootstrap method applicable to trend estimators expressed as time-window-weighted sample means—such as exponential smoothing and moving averages. Built upon asymptotic theory, the method provides the first uniform-in-time coverage guarantees for trend inference under nonstationarity, enabling adaptive anomaly detection and A/B testing in streaming data settings. Empirical evaluations demonstrate that the framework achieves well-calibrated uncertainty estimates and scales effectively across diverse nonstationary scenarios, offering a practical and real-time solution for accurate uncertainty quantification in large-scale online time series analysis.

This study addresses the substantial bias that can afflict long-memory parameter estimation in the presence of strong short-range autocorrelation. To mitigate this issue, the authors propose a bias-correction approach that integrates pre-filtering with sieve bootstrap techniques. The method first obtains an initial estimate using a local polynomial Whittle estimator adapted for noisy observations, then refines this estimate and constructs confidence intervals via the sieve bootstrap. This two-stage procedure effectively reduces estimation bias induced by pronounced short-memory dynamics while delivering reliable interval inference. Simulation experiments demonstrate that the proposed method substantially outperforms conventional local Whittle and detrended fluctuation analysis approaches, achieving superior accuracy in bias correction and markedly improved coverage properties for confidence intervals.

This paper addresses the lack of generality and theoretical foundations in existing bootstrap hypothesis testing frameworks. We propose a unified bootstrap testing framework that accommodates both null-distribution-based resampling and diverse nonstandard bootstrap schemes. We first systematically characterize the exchangeability condition and statistical functional construction criteria, prove the local asymptotic equivalence of different resampling schemes in terms of statistical power, and identify the intrinsic mechanism behind the failure of the naive bootstrap. Leveraging empirical process theory and weak convergence analysis, we rigorously establish the asymptotic exactness and consistency of the test under fixed alternatives. An accompanying open-source R package, *BootstrapTests*, validates the theoretical properties in independence testing, linear regression coefficient testing, and copula model goodness-of-fit testing. Finite-sample simulations demonstrate that the proposed method significantly improves statistical power.

Traditional local projection (LP) bootstrap inference relies on a finite-order VAR assumption, leading to inferential bias when the true data-generating process (DGP) is infinite-order—such as long-memory or high-order dynamic processes. This paper overcomes that limitation by proposing a novel nonparametric bootstrap method grounded in the moving average (MA) representation: it avoids prespecifying VAR order and instead constructs an MA-type resampling scheme directly from LP residuals, asymptotically matching the true DGP. The method substantially improves coverage accuracy and robustness of confidence intervals for multi-step impulse responses. In both simulations and empirical applications, it demonstrates superior finite-sample performance relative to conventional VAR-based bootstraps. The core innovation lies in coupling local projections with an MA structure, enabling adaptive modeling of unknown dynamics. This provides a more reliable nonparametric foundation for causal inference in complex time series settings.

This work proposes a nonparametric kernel-based approach for inference in multivariate or functional time series, addressing problems such as goodness-of-fit testing, change-point detection in marginal distributions, and independence testing. The method avoids both resampling and bandwidth selection by embedding the data into a reproducing kernel Hilbert space (RKHS) and constructing test statistics through sample splitting, projection, and self-normalization. Leveraging a novel conditioning technique, the authors establish that the resulting test statistic admits a pivotal asymptotic null distribution under strong mixing conditions and analyze its power against local alternatives. The proposed procedure achieves high finite-sample accuracy while substantially improving computational efficiency, outperforming existing resampling-based methods.

Traditional bootstrap and conformal prediction methods fail in time series settings due to violations of exchangeability and the absence of a unified framework that supports dependence-aware resampling and adaptive conformal calibration. This work proposes the first typed API integrating block, residual, sieve, and wild resampling schemes with adaptive conformal approaches such as EnbPI and ACI, enabling distribution-free uncertainty quantification. Leveraging compilation-based acceleration and streaming reductions, the method requires only O(B) additional memory, circumventing the O(Bn) tensor duplication typical of conventional implementations. Empirical results demonstrate that the approach substantially mitigates undercoverage under the i.i.d. assumption, with sieve resampling achieving coverage closest to the nominal level for short-memory linear processes, while running several times faster than the arch benchmark.

This study addresses the failure of conventional asymptotic inference for autoregressive conditional duration (ACD) models under a fixed calendar span, where the random number of events and heavy-tailed interarrival times invalidate standard assumptions. To overcome this, the authors propose two recursive bootstrap schemes: one conditioning on a fixed calendar span and the other on a fixed event count. They establish, for the first time, the consistency of the fixed-event-count bootstrap when the tail index κ ≥ 1, and demonstrate that although the estimator converges to a mixed normal limit for 0 < κ < 1, the bootstrap still accurately replicates its conditional Gaussian component, ensuring first-order validity of percentile-based confidence intervals. Drawing on mixed normal limit theory, tail index analysis, and Monte Carlo simulations, the method exhibits strong finite-sample performance under both finite and infinite mean scenarios. An empirical application to cryptocurrency ETF transaction durations reveals pronounced persistence and highlights practical discrepancies between the two inferential frameworks.