A new Combined Bootstrap Method for Long-Memory Time Series

This paper introduces a novel combined bootstrap methodology for the analysis of stationary long-memory time series, addressing the challenges posed by their persistent dependence structures. Unlike existing hybrid approaches that merge algorithms at the procedural level, our method combines independently generated bootstrap samples from a variety of established techniques, including parametric, semi-parametric, and block-based methods, into a unified composite sample. This integration is performed using both simple (mean, median, trimmed mean) and performance-based (correlation, MSE, MAE, regression-based) combination schemes. Through extensive Monte Carlo simulations and empirical applications to the Nile River minima and Microsoft stock returns, we show that the combined bootstrap approach yields improved estimation accuracy for the long-memory parameter d, particularly in terms of root mean squared deviation and confidence interval coverage. The proposed method is shown to mitigate model misspecification risk and improve inference robustness. While our focus is on estimating the long-memory parameter, the approach is general and can be extended to other statistics and dependence structures. This work offers a new perspective on bootstrap methodology and opens avenues for future theoretical and practical advancements.