Mixing Times and Structural Inference for Bernoulli Autoregressive Processes

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non...

Innnite Order Cointegrated Vector Autoregressive Processes: Estimation and Inference

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992). The asymptotic properties of the estimated coeecients of the autoregressive ECM (error correction model) and the pure VAR (vector autoregressive) representations are derived under the assumption that the autoregressive order goes to innnity with the sample size. Thes...

Bounds on Mixing Times in the Bernoulli-Laplace Diffusion Model - Elementary proofs for variation distance and first passage times

The Bernoulli-Laplace model describes a diffusion process of two types of particles. To analyze the finite-size dynamics of this process, we apply a generating function method for diagonalizing the corresponding transition matrix. The method is a generalization of the generating function approach of Mark Kac [1] to diagonalize the Ehrenfest model. We then apply this solution to provide elementa...

Bayesian Structural Inference for Hidden Processes

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological ...

Statistics and Error Terms of Occurrence Times in Mixing Processes