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Bayesian Model Selection for Beta Autoregressive Processes
We deal with Bayesian inference for Beta autoregressive processes. We
restrict our attention to the class of conditionally linear processes. These
processes are particularly suitable for forecasting purposes, but are difficult
to estimate due to the constraints on the parameter space. We provide a full
Bayesian approach to the estimation and include the parameter restrictions in
the inference problem by a suitable specification of the prior distributions.
Moreover in a Bayesian framework parameter estimation and model choice can be
solved simultaneously. In particular we suggest a Markov-Chain Monte Carlo
(MCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm and
solve the model selection problem following a reversible jump MCMC approach
Rank-based estimation for all-pass time series models
An autoregressive-moving average model in which all roots of the
autoregressive polynomial are reciprocals of roots of the moving average
polynomial and vice versa is called an all-pass time series model. All-pass
models are useful for identifying and modeling noncausal and noninvertible
autoregressive-moving average processes. We establish asymptotic normality and
consistency for rank-based estimators of all-pass model parameters. The
estimators are obtained by minimizing the rank-based residual dispersion
function given by Jaeckel [Ann. Math. Statist. 43 (1972) 1449--1458]. These
estimators can have the same asymptotic efficiency as maximum likelihood
estimators and are robust. The behavior of the estimators for finite samples is
studied via simulation and rank estimation is used in the deconvolution of a
simulated water gun seismogram.Comment: Published at http://dx.doi.org/10.1214/009053606000001316 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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