Integrating Block Robust Empirical Standardised Influence Function and Block Average to Robustify Seasonal Block Bootstrap Methods

We propose two robust seasonal bootstrap techniques, based on our prior work, the Complex Seasonal Circular Block Bootstrap (XSCBB). These robustifications are implemented through two methods, the Block Robust Empirical Standardised Influence Function (BRESIF or Block RESIF) and the Block Average XSCBB (BA-XSCBB) methods. The BRESIF-XSCBB method employs an adaptive weighting function to adjust the XSCBB technique for time series with heavy-tailed distributions or extreme values. Conversely, the Block-Average/Median XSCBB strategy seeks to reduce the influence of outliers by incorporating either the block average or median to restore the seasonal characteristics. Through simulation studies, we showcase the efficacy of these methods in enhancing the XSCBB's performance when outliers are present. Our results indicate that these robustified versions of XSCBB not only pre-serve the original method's capacity to detect complex seasonal patterns but also significantly enhance resilience and accuracy in challenging data scenarios.