Approximating a harmonizable isotropic random field.
The problem of asymmetry appears in various aspects of time series modelling. Typical examples are asymmetric time series, asymmetric error distributions and asymmetric loss functions in estimating and predicting. The paper deals with asymmetric modifications of some recursive time series methods including Kalman filtering, exponential smoothing and recursive treatment of Box-Jenkins models.
In this paper, the filtering problem is revisited in the basic Gaussian homogeneous linear system driven by fractional Brownian motions. We exhibit a simple approximate filter which is asymptotically optimal in the sense that, when the observation time tends to infinity, the variance of the corresponding filtering error converges to the same limit as for the exact optimal filter.