Abstract
We develop a new class of dynamic multivariate Poisson count models that allow for fast online updating. We refer to this class as multivariate Poisson-scaled beta (MPSB) models. The MPSB model allows for serial dependence in count data as well as dependence with a random common environment across time series. Notable features of our model are analytic forms for state propagation, predictive likelihood densities, and sequential updating via sufficient statistics for the static model parameters. Our approach leads to a fully adapted particle learning algorithm and a new class of predictive likelihoods and marginal distributions which we refer to as the (dynamic) multivariate confluent hyper-geometric negative binomial distribution (MCHG-NB) and the dynamic multivariate negative binomial (DMNB) distribution, respectively. To illustrate our methodology, we use a simulation study and empirical data on weekly consumer non-durable goods demand.
Highlights
Discrete-valued count data poses a number of statistical modeling challenges with widespread applications in web analytics, epidemiology, economics, finance, operations, and other fields
We develop a class of dynamic multivariate Poisson model together with a particle filtering (PF) and learning (PL) algorithm for sequential online updating (Gordon et al, 1993; Carvalho et al, 2010a)
We term our model the multivariate Poisson-scaled beta (MPSB) and as a by-product, we introduce two new multivariate distributions, the dynamic multivariate negative binomial (DMNB) and the multivariate confluent hyper-geometric negative binomial (MCHG-NB) distributions which correspond to marginal and predictive distributions, respectively
Summary
Discrete-valued count data poses a number of statistical modeling challenges with widespread applications in web analytics, epidemiology, economics, finance, operations, and other fields. We develop a class of dynamic (state space) multivariate Poisson model together with a particle filtering (PF) and learning (PL) algorithm for sequential online updating (Gordon et al, 1993; Carvalho et al, 2010a). A scaled beta state evolution with a random common environment is proposed to account for dependence in counts. The analysis of financial and economic time series includes several series that are affected by the same economic swings in the market To account for such dependence, we assume a Bayesian hierarchical model of the form (Yjt|λj, θt) ∼ P ois(λjθt), for j = 1, . YJ,t−1} represents the sequential arrival of data We refer to this class of models as multivariate Poisson-scaled beta (MPSB) models due to the relationship between the observation and state equations. Following Smith and Miller (1986), the state equation is defined conditional on previous counts unlike the state equations in traditional dynamic linear models
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