Consistency of Long Autoregressive Model Parameter Estimates

• Activity Number: 489
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Sreenivas Konda*+
• Companies: University of Waterloo
• Keywords: Time Series ; Regularization ; Consistency

Abstract

We consider an Autoregressive (AR) process of large unknown order p in this research. Model selection and asymptotics of the parameter estimates of these long AR processes of unknown order p are difficult but useful. So we propose a regularization method to estimate the AR model parameters using the smoothness priors in the form of the integrated squared derivatives of a function of the AR model spectrum. We then derive the consistency of the long AR parameter estimates using the popular procedure, banding of covariance matrices. We show that the derived estimates are consistent in the operator norm as long as (log p)/n goes to 0 and under suitable conditions on the regularized parameter. Simulated and real examples are considered to prove whether the proposed method can be applied to online business forecasting and biomedical applications. Extensions of this method to derive the consistent parametric spectral estimate of a linear process and applications of this method to locally stationary processes are briefy described.