Exchange rate volatility modeling: ARIMAX-FIGARCH with wavelet-based outlier detection for USD/PEN

Introduction Exchange rate volatility in partially dollarized emerging economies poses persistent challenges for financial risk management and monetary policy. Short-memory GARCH specifications provide inferior fit relative to long-memory alternatives under managed floating regimes with recurrent political disruptions. Methods This study proposes a two-stage framework: a wavelet-dummy operator maps the return series into a binary indicator of atypical observations incorporated as an exogenous regressor in an ARIMAX(2,0) model; filtered residuals serve as input for five conditional variance specifications-ARCH(1), GARCH(1,1), GJR-GARCH(1,1,1), EGARCH(1,1,1), and FIGARCH(1,d,1)-applied to 2,803 daily log-returns of the USD/PEN (January 2015-March 2026). Results The operator identifies 36 atypical observations concentrated in the 2020-2023 sub-period. FIGARCH(1,d,1) dominates under the Akaike Information Criterion with d = 0.553 ( p < 0.001) under Skewed Student-t innovations, extending long-memory evidence for USD/PEN conditional variance to 2015-2026 and resolving prior ambiguity in the Peruvian Forex literature. Ljung-Box tests confirm white noise in both standardized residuals ( p = 0.4846) and squared residuals ( p = 0.9921). Predictive evaluation across three validation windows yields Theil's U between 0.93 and 1.02, indicating mean-forecast accuracy comparable to the random-walk benchmark, while expanding-window volatility forecasts consistently outperform the constant-variance benchmark. Discussion These findings demonstrate that wavelet-based outlier detection combined with long-memory GARCH estimation substantially improves volatility modeling for emerging-market currencies under managed floating regimes, institutional fragility and partial dollarization.