When data exhibit high volatility and jumps, which are common features in most high frequency financial time series, forecasting becomes even more challenging. Using high frequency exchange rate data, we show that wavelets, which are robust to high volatility and jumps, are useful forecasters in high frequency settings when high volatility is a dominant feature that affects estimation zones, forecasting zones or both. The results indicate that decomposing the time series into homogeneous components that can then be used in time series forecast models is critical. Different components become more useful than others for different data features associated with a volatility regime. We cover a wide range of linear and nonlinear time series models for forecasting high frequency exchange rate return series. Our results indicate that when data display nonstandard features with high volatility, nonlinear models outperform linear alternatives. However, when data are in low volatility ranges for both estimations and forecasts, simple linear autoregressive models prevail, although considerable denoising of the data via wavelets is required.