Speaker: Farzad Sabzikar, Iowa State University
Abstract: Stochastic processes with long-range dependence correlation have proven helpful in many areas, from engineering to science in 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 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. This talk presents 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, a tempered fractional Gaussian noise, and a tempered 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 theoretical contributions and applications of these new models in finance and geophysics will be presented.