Gaussian inference on certain long-range dependent volatility models. (English) Zbl 1027.62074
Summary: For a class of long memory volatility models, we establish the asymptotic distribution theory of Gaussian estimators and the Lagrange multiplier tests. Both the case of estimation of martingale differences and ARMA levels are considered. A Monte Carlo exercise is presented to assess the small sample properties of the Gaussian estimator and the Lagrange multiplier test. An empirical application, using foreign exchange rates and stock index returns, suggests the potential of these models to capture the dynamic features of the data.
MSC:
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62E20 | Asymptotic distribution theory in statistics |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62P20 | Applications of statistics to economics |
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