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 in tegration of ARMA processes and fractional Brownian Motion. A comparis on with usual discrete time ARFIMA models is lead. Some well-known emp irical evidence on macroeconomic and financial time series, such as va riability of forward rates, aggregation of responses across heterogene ous agents, are well-captured by this continuous time modelling. Moreo ver, the usual statistical tools for long memory series and for Stocha stic Differential Equations can be jointly applied in this setting.