Farzad Sabzikar
Department of Statistics
Iowa State University

Stochastic processes with semi-long range dependence

 Stochastic processes with long range dependence correlation have been proven useful in many areas from engineering to science in both theory and applications. This class includes fractional Brownian motion, fractional Gaussian noise, and fractional ARIMA time series. One of the main properties of long range dependence is the fact that the spectral density is unbounded at the origin. However, in many applications, data fit with this spectral density model only up to a low frequency cutoff, after which the observed spectral density remains bounded. In this talk, we present a novel modification of these models that involves tempering the power law correlation function with an exponential. This results in a tempered fractional Brownian motion, tempered fractional Gaussian noise, and tempered fractional ARIMA time series.  These processes have semi-long range dependence:  Their autocovariance function resembles that of a long memory model for moderate lags but eventually diminishes exponentially fast according to the presence of a decay factor governed by a tempering parameter. Several applications of these new models in finance, geophysics, turbulence will be presented. Finally, some theoretical problems related to tempered processes will be discussed.

Refreshments at 3:45pm in Snedecor 2101.