Long memory continuous time models

This paper presents a new family of long memory models: the continuous time moving average fractional process. The continuous time framework allows to reconcile two competitive types of modelling: fractional integration of ARMA processes and fractional Brownian Motion. A comparison with usual discrete time ARFIMA models is lead. Some well-known empirical evidence on macroeconomic and financial time series, such as variability of forward rates, aggregation of responses across heterogeneous agents, are well-captured by this continuous time modelling. Moreover, the usual statistical tools for long memory series and for Stochastic Differential Equations can be jointly applied in this setting.