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Exchange rate fluctuations significantly impact forex market participants, making it crucial to understand the asymmetrical responses and spillover effects across different time horizons. This study examines the multiscale properties of Indian exchange rate returns for the Indian Rupee (INR) against the US Dollar (USD), Euro (EUR), British Pound (GBP), and Japanese Yen (JPY) from January 6, 1999, to September 5, 2023. Using wavelet multiresolution analysis combined with non-linear methods, we identify significant volatility spillovers and persistent long-term effects. Wavelet and spectral variance analyses reveal notable fluctuations during financial crises, such as the taper tantrum, while wavelet coherence and phase difference reveal INR-USD's leading influence on other currency pairs. Hurst exponent analysis highlights long memory at broader scales and mean-reversion over shorter intervals (2–32 days), while chaos is found to be statistically insignificant. . The presence of volatility spillovers and long memory suggests inefficiencies in price discovery, particularly for more volatile currency pairs like INRJPY and INREUR, while stable pairs like INRUSD and INRGBP exhibit relatively efficient market behavior.Traditional models like ARMA and GARCH provide superior forecasts for stable pairs (INRUSD, INRGBP), while wavelet-augmented models, especially Hybrid LSTM-Wavenet, outperform for volatile currencies like INRJPY and INREUR by capturing complex, multiscale patterns. These results offer critical insights for risk management and policy formulation, highlighting the importance of multiscale analysis and machine learning techniques in enhancing the exchange rate forecasting and understanding market dynamics in globally integrated financial systems.
