Modelación de series de tiempo, estacionariedad y métodos Bayesianos no paramétricos - Juan Carlos Martínez-Ovando; Stephen G. Walker (Banco de México, 2011)
– In this paper we introduce two general non-parametric first-order stationary time-series models for which marginal (invariant) and transition distributions are expressed as infinite-dimensional mixtures. That feature makes them the first Bayesian stationary fully non-parametric models developed so far. We draw on the discussion of using stationary models in practice, as a motivation, and advocate the view that exible (non-parametric) stationary models might be a source for reliable inferences and predictions. It will be noticed that our models adequately fit in the Bayesian inference framework due to a suitable representation theorem. A stationary scale-mixture model is developed as a particular case along with a computational strategy for posterior inference and predictions. The usefulness of that model is illustrated with the analysis of Euro/USD exchange rate log-returns.
Keywords: C11; C14; C15; C22; C51; 330; Stationarity; Markov processes; Dynamic mixture models; Random probability measures; Conditional random probability measures; Latent processes