Forecasting Based on Decomposed Financial Return Series: A Wavelet Analysis

We transform financial return series into its frequency and time domain via wavelet decomposition to separate short‐run noise from long‐run trends and assess the relevance of each frequency to value‐at‐risk (VaR) forecast. Furthermore, we analyze financial assets in calm and turmoil market times and show that daily 95% VaR forecasts are mainly driven by the volatility that is captured by the first scales comprising the short‐run information, whereas more timescales are needed to adequately forecast 99% VaR. As a result, individual timescales linked via copulas outperform classical parametric VaR approaches that incorporate all information available.