Archive for autoregressive model

generalised Poisson difference autoregressive processes

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , on February 14, 2020 by xi'an

Yesterday, Giulia Carallo arXived the paper on generalised Poisson difference autoregressive processes that is a component of her Ph.D. thesis at Ca’ Foscari Universita di Venezia and to which I contributed while visiting Venezia last Spring. The stochastic process under study is integer valued as a difference of two generalised Poisson variates, made dependent by an INGARCH process that expresses the mean as a regression over past values of the process and past means. Which can be easily simulated as a difference of (correlated) Poisson variates. These two variates can in their turn be (re)defined through a thinning operator that I find most compelling, namely as a sum of Poisson variates with a number of terms being a (quasi-) Binomial variate depending on the previous value. This representation proves useful in establishing stationarity conditions on the process. Beyond establishing various properties of the process, the paper also examines how to conduct Bayesian inference in this context, with specialised Gibbs samplers in action. And comparing models on real datasets via Geyer‘s (1994) logistic approximation to Bayes factors.

Roberto Casarin in Warwick [joint Stats/Econometrics seminar series]

Posted in Statistics with tags , , , , , , , on February 11, 2020 by xi'an

My friend, coauthor and former student Roberto Casarin (da Ca’Foscari Venezia) is giving a talk tomorrow in Warwick:

Bayesian Dynamic Tensor Regression (joint with Billio, M., Iacopini, M., and Kaufmann, S.)

Tensor-valued data (i.e. multidimensional data) are becoming increasingly available and call for suitable econometric tools. We propose a new dynamic linear regression model for tensor-valued response variables and covariates that encompasses some well-known multivariate models as special cases. We exploit the PARAFAC low-rank decomposition for providing a parsimonious parametrization and to incorporate sparsity effects. Our contribution is twofold: first, we extend multivariate econometric models to account for tensor-valued response and covariates; second, we define a tensor autoregressive process (TAR) and the associated impulse response function for studying shock propagation. Inference is carried out in the Bayesian framework combined with Monte Carlo Markov Chain (MCMC). We apply the TAR model for studying time-varying multilayer economic networks concerning international trade and international capital stocks. We provide an impulse response analysis for assessing propagation of trade and financial shocks across countries, over time and between layers.

The seminar will take place on Thursday Feb. 13 at 14:00 in OC0.01 (Oculus), University of Warwick, Coventry, UK.

back to the Bayesian Choice

Posted in Books, Kids, Statistics, University life with tags , , , , , , , , on October 17, 2018 by xi'an

Surprisingly (or not?!), I received two requests about some exercises from The Bayesian Choice, one from a group of students from McGill having difficulties solving the above, wondering about the properness of the posterior (but missing the integration of x), to whom I sent back this correction. And another one from the Czech Republic about a difficulty with the term “evaluation” by which I meant (pardon my French!) estimation.