Mixture autoregressive (MAR) models have the attractive property that the shape of the conditional distribution of a forecast depends on the recent history of the process. In particular, it may have a varying number of modes over time. We show that the distributions of the multi-step predictors in MAR models are also mixtures and specify them analytically. In the important case when the origina...

While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating structured VAR (vector auto-regressive model), where the structure can be captured by any suitable norm, e.g., Lasso, group Lasso, order weighted Lasso, etc. I...

In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, set of key economic indicators regularly reported different countries every quarter. The at each quarter neatly observed consecutive quarters. Dynamic transport networks with on the edges can be formed as Although it is natural to turn into long vectors, then use standard vecto...

In this paper we extend autoregressive models to fit time series that have three layers of seasonality, i.e. triple seasonal (TSAR) models, and introduce the Bayesian inference for these TSAR models. Assuming model errors are normally distributed employing priors, Jeffreys', g, normal-gamma on parameters, derive marginal posterior distributions parameters. particular, show be multivariate t gam...