Analysis of Nongaussian, Nonlinear Time Series with Long-Memory

摘要

The project has been concerned with statistical analysis of certain time seriesand stochastic signals that are unusual, in that they have long memory and are nonGuassian. Standard statistical procedures, such as the Box Jenkins procedure which presumes Guassianity and short range dependence, when applied to these series will certainly produce inferior and suboptimal results. The PI pursued two approaches to address the twin problems of long memory and nonGuassianity. The first approach is rather general and it uses the setup of the Kolmogorov Wiener prediction theory of stationary processes. The second approach is more specific and it uses a random coefficient stochastic difference equation, which has a stationary solution with long memory and nonGuassian marginal simulating time series data with aforementioned properties. Such simulated data are used in verifying empirically the more general results obtained via the first approach.