Before revision:  The methodology is illustrated using three real data examples that highlight the differences between simple HP filtering, the data-determined boosted filter, and an alternative autoregressive approach  .
After revision:  The methodology is illustrated using three real data examples that highlight the differences between simple HP filtering, the data-determined boosted filter, and an alternative autoregressive approach . These examples show that the bHP filter is helpful in analyzing a large collection of heterogeneous macroeconomic time series that manifest various degrees of persistence, trend behavior, and volatility .