A Long Memory Stochastic Parameter Regression

• Activity Number: 235
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Jaechoul Lee*+ and Rose Ocker
• Companies: Boise State University and Boise State University
• Keywords: Autoregressive fractionally integrated moving-average ; Dynamic linear model ; Heteroscedasticity ; Innovations algorithm ; Kalman filter

Abstract

Allowing for time-varying parameters in a regression model has become popular in analyzing data, but the best way to estimate the parameters of the time-varying parameter is still in discussion. These parameters can be appreciably autocorrelated with their past for a long time, but most of the existing models for parameters are of the short memory type, leaving the error process to account for any long memory behavior in the response variable. As an alternative, we propose a long memory stochastic parameter regression model, using a fractionally integrated noise model to take into account long memory autocorrelations in the parameter process. Use of this stochastic model for the time-varying parameter consequently deals with heteroscedasticity without using transformation techniques. We then develop estimation methods using the Innovations Algorithm and the Kalman Filter, including truncated versions of each to aid faster estimation without a noticeable loss of accuracy. Based on simulation results, our methods satisfactorily estimate the model parameters and we illustrate a real data application in climatology and/or economics.