In this article, we propose a Bayesian non‐parametric model for the analysis of multiple time series. We consider an autoregressive structure of order p for each of the series and borrow strength across the series by considering a common error population that is also evolving in time. The error populations (distributions) are assumed non‐parametric whose law is based on a series of dependent Polya trees with zero median. This dependence is of order q and is achieved via a dependent beta process that links the branching probabilities of the trees. We study the prior properties and show how to obtain posterior inference. The model is tested under a simulation study and is illustrated with the analysis of the economic activity index of the 32 states of Mexico.
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Luis Enrique Nieto Barajas has a BSc in Actuarial Science from ITAM, an MSc in Statistics from IIMAS-UNAM and PhD in Statistics from the University of Bath in the UK. Worked in a marketing research company for two years and from 2001 to date is full time Professor of Statistics at ITAM. Has been statistical consultant for IFE (now INE) is diverse projects such as district formation, quick count and verification of the electoral pattern, and external consultant for several companies. Received two international awards for his PhD thesis, the "Savage Award 2001" and the "Francisco Aranda Ordaz Award 2002-2004". Currently is a member of the national system of researchers and has published more than 34 papers in peer reviewed journals. Is a member of the Mexican Statistical Association and has been member of the board as a vocal from 2005 to 2009, as a vice-president from 2017 to 2019 and future president from 2019 to 2021.