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...

We introduce the new time series analysis features of scikits.statsmodels. This includes descriptive statistics, statistical tests and several linear model classes, autoregressive, AR, autoregressive moving-average, ARMA, and vector autoregressive models VAR.

This paper reviews the analysis of the threshold autoregressive, smooth threshold autoregressive, and Markov switching autoregressive models from the Bayesian perspective. For each model we start by describing a baseline model and discussing possible extensions and applications. Then we review the choice of prior, inference, tests against the linear hypothesis, and conclude with models selectio...

The vector autoregressive model is very popular for modeling multiple time series. Estimation of its parameters is typically done by a least squares procedure. However, this estimation method is unreliable when outliers are present in the data, and therefore we propose to estimate the vector autoregressive model by using a multivariate least trimmed squares estimator. We also show how the order...

We present a model for representing stationary multivariate time series with arbitrary marginal distributions and autocorrelation structures and describe how to generate data quickly and accurately to drive computer simulations. The central idea is to transform a Gaussian vector autoregressive process into the desired multivariate time-series input process that we presume as having a VARTA (Vec...

Bayesian networks have become one of the major models used for statistical inference. We study the question whether the decisions computed by a Bayesian network can be represented within a low-dimensional inner product space. We focus on two-label classification tasks over the Boolean domain. As main results we establish upper and lower bounds on the dimension of the inner product space for Bay...

In this paper we propose a class of time-domain models for analyzing possibly nonstationary time series. This class of models is formed as a mixture of time series models, whose mixing weights are a function of time. We consider specifically mixtures of autoregressive models with a common but unknown lag. To make the methodology work we show that it is necessary to first partition the data into...

We study cross-country differences in monetary policy transmission across the largest euro area economies (France, Germany, Italy, and Spain) using a large Bayesian vector autoregressive (BVAR) model with endogenous prior selection. Drawing on posterior distributions of impulse responses other tests, we find real output money supply to respond more strongly Germany than countries. Whereas, pric...