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Long memory continuous time models. (English) Zbl 0856.62104

Summary: 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 made. 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.

MSC:

62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91B84 Economic time series analysis
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