# A Cyclical Model of Exchange Rate Volatility

In this paper, we investigate the long run dynamics of the intraday range of the GBP/USD, JPY/USD and CHF/USD exchange rates. We use a non-parametric filter to extract the low frequency component of the intraday range, and model the cyclical deviation of the range from the long run trend as a sta… tionary autoregressive process. We find that the long run trend is time-varying but highly persistent, while the cyclical component is strongly mean reverting. This has important implications for modelling and forecasting volatility over both short and long horizons. As an illustration, we use the cyclical volatility model to generate out-of-sample forecasts of exchange rate volatility for horizons of up to one year under the assumption that the long run trend is fully persistent. As a benchmark, we compare the forecasts of the cyclical volatility model with those of the two-factor intraday range-based EGARCH model of Brandt and Jones (2006). Not only is the cyclical volatility model significantly easier to estimate than the EGARCH model, but it also offers a substantial improvement in out-of-sample forecast performance.