A Simple Integer-Valued AR(p) Process

• Activity Number: 101
• Type: Invited
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: SSC
• Author(s): Keith Freeland*+
• Companies: University of Waterloo
• Keywords: Pegram operator ; Skellam distribution ; Negative correlations ; integer-valued

Abstract

We construct a simple AR(p) process using the Pegram operator. The distribution of the innovations can follow any discrete distribution, and include Poisson and Binomial distributions. However, we focus on innovations from the differenced Poisson distribution, or Skellam distribution. These innovations have many nice properties, including: infinitely divisibility, convolution closed and symmetric. While the model includes the usual AR(p) correlation structure, it can be made more general. In fact, the operator can be extended in a way where it is possible to have components which contribute to positive correlation, while at the same time have components which contribute to negative correlation. We illustrate the process by using it to model the price change of a stock at each transaction time.