Simulation and estimation of long memory continuous time models. (English) Zbl 0836.62060
Summary: Some general properties of long memory continuous time processes are recalled or proved. Methods of simulation are studied. A comparison with the usual discrete time autoregressive fractionally integrated moving- average filter is made and illustrations are provided. Then, two methods of estimation of the parameters of such a model from a discrete sample are studied, both theoretically and empirically, with Monte Carlo experiments.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62M20 | Inference from stochastic processes and prediction |
| 65C05 | Monte Carlo methods |
| 62F10 | Point estimation |
Keywords:
long memory continuous time processes; simulation; discrete time autoregressive fractionally integrated moving-average filter; Monte CarloReferences:
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