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Activity Number: 684
Type: Contributed
Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract #317619
Title: Stationary Gaussian Markov Processes That Evolve as Functions of Their Local Derivatives
Author(s): Philip Ernst* and Lawrence D. Brown and Robert Wolpert
Companies: Rice University and University of Pennsylvania and Duke University
Keywords: Continuous Autoregressive Processes ; Gaussian Processes
Abstract:

In many data-driven applications, such as analysis of EEG data, time series data are discritized prior to analysis and are formulated using autoregressive models. The theoretical and applied properties of the convergence of discrete autoregressive processes to their continuous analogs (continuous autoregressive or ``CAR" processes) have been well studied by many mathematicians, statisticians, and economists. However, in departure from the previous literature, we propose a different framework for examining autoregressive processes. Instead of considering a process in which Y_t is a function of Y_{t-1}, Y_{t-2},..., we consider process in which Y_t is a function of its present state and of all of its derivatives up to and including order p-1.

We begin our analysis with a generalized characterization of the zero mean smooth Gaussian processes (on the real line) whose evolution from the current time onward depends only on the current values of the process and its derivatives. We then examine how these processes are limits of stationary AR(p) time series.


Authors who are presenting talks have a * after their name.

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