Statistical Methodologies for Non-Gaussian Noisy Environments
Abstract
The research focused on long-range dependence, high variability and non-linear filtering in time series. Long-range dependence occurs when the low frequencies have a fundamental impact on the dependence structure of the data. There is high variability when the data is non-Gaussian and takes large values with high probability, for example when it is Pareto or has a stable distribution. The data can also be the output of a non-linear filter and hence possess non-linear characteristics. We studied the behavior of symmetric statistics, e.g. U and Von Mises statistics, and the asymptotoc behavior of quadratic forms, when the data has finite variance with long-range dependence. The results are non-standard. We also focused on situations where the data has a stable distribution and hence exhibits high-variability. We studied joint moments and conditional moments, and linear regression problems. Linear Fractional Levy Motions are important models when the data exhibit both high variability and long-range dependence. We found that there are many such models and we investigated their asymptotic dependence structure. We studied the tail behavior of probability distributions of multiple integrals with respect to stable noise and the sample paths behavior of related stochastic processes. We also developed a technique for approximating both the information structure and the paths behavior of stochastic processes.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 09, 1990
- Accession Number
- ADA222137
Entities
People
- Murad S. Taqqu
Organizations
- Boston University