Cointegration of stochastic multifractals with application to foreign exchange rates

The existing concept of cointegration applies to integrated processes (in the Box–Jenkins ARIMA framework) or processes with long-range dependence. These processes are assumed to display a monoscaling behaviour (such as that of a fractional Brownian motion). On the other hand, many turbulent processes are known to be intermittent, hence possess multiscaling characteristics. This paper develops a concept of cointegration for these stochastic multifractals. A model is suggested for testing for cointegration and applied to the exchange rates of three major currencies.