Mathematical Sciences: Long Memory and Infinite Variance

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9404093 Taqqu This research concerns the investigation of the time series with long memory and/or infinite variance. Long memory, in the finite variance case, occurs when the covariances tend to zero like a power and the spectral density diverges at the origin. This behavior has been observed in many real-life phenomena. Sometimes long memory occurs jointly with infinite variance, for example when the underlying process is stable but not Gaussian. In this case it is the tail of the distribution that decays like a power function. The research will focus on the probabilistic and statistical properties of time series with long memory and/or infinite variance. Most of the available statistical techniques assume that the data to be analyzed are not very dependent. However, in a number of areas such as economics and geophysics, the data can display long range dependence and can also sometimes fluctuate significantly from their mean value. The goal of this research is to develop new techniques for modeling and analyzing this type of data.