Identifying shifts in spread using the Cauchy CUSUM: An application to the Japanese yen/US dollar exchange rate

It is well known that the log price relative of floating exchange rates, as well as a variety of other commodities and securities, does not follow a normal distribution but instead tends to be characterized by a heavy-tailed stable Paretian distribution. Specifically, we illustrate this property of floating exchange rates with the Japanese yen/US dollar exchange rate. Furthermore, we show that the distribution itself changes from time to time, with periods of sustained shifts in volatility. To capture the heavy-tailed nature of the distribution, we develop a Cumulative Sum (CUSUM) chart based on the Cauchy distribution to identify these periods of differing volatility.