Random self-decomposability and autoregressive processes

Time-frequency-autoregressive random processes: modeling and fast parameter estimation

We present a novel formulation of nonstationary autoregressive (AR) models in terms of time-frequency (TF) shifts. The parameters of the proposed TFAR model are determined by “TF Yule-Walker equations” that involve the expected ambiguity function and can be solved efficiently due to their block-Toeplitz structure. For moderate model orders, we also propose approximate TF Yule-Walker equations t...

Self-decomposability and Option Pricing

The risk-neutral process is modeled by a four parameter self-similar process of independent increments with a self-decomposable law for its unit time distribution. Six different processes in this general class are theoretically formulated and empirically investigated. We show that all six models are capable of adequately synthesizing European option prices across the spectrum of strikes and mat...

Autoregressive Gaussian Random Vectors of First Order

Autoregressive Negative Binomial Processes

Abstract We start by studying first-order autoregressive negative binomial (NBD) processes. We then compare maximum likelihood and moment based estimators of the parameters of the NBD INAR(1) model and show that the degree of dependence has significant effect on the quality of the estimators. Finally, we construct NBD processes with long-range dependence by using the NBD INAR(1) processes as ba...

Spatially Varying Autoregressive Processes

Spatially Varying Autoregressive Processes Aline A. Nobre, Bruno Sansó and Alexandra M. Schmidt Scientific Computing Program, Oswaldo Cruz Foundation, Rio de Janeiro-RJ CEP:21.045-900, Brazil Department of Applied Mathematics and Statistics, University of California at Santa Cruz, Santa Cruz, CA 95064 Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro-RJ CEP:21.945-...