The problem of test of fit for Vector AutoRegressive (VAR) processes with unconditionally heteroscedastic errors is studied. The volatility structure is deterministic but time-varying and allows for changes that are commonly observed in economic or financial multivariate series such as breaks or smooth transitions. Our analysis is based on the residual autocovariances and autocorrelations obtai...

Vector autoregressive (VAR) models assume linearity between the endogenous variables and their lags. This assumption might be overly restrictive could have a deleterious impact on forecasting accuracy. As solution we propose combining VAR with Bayesian additive regression tree (BART) models. The resulting vector (BAVART) model is capable of capturing arbitrary nonlinear relations covariates wit...

We consider Johansen’s (1988, 1991) cointegration tests when a Vector AutoRegressive (VAR) process of order k is used to approximate a more general linear process with a possibly infinite VAR representation. Traditional methods to select the lag order, such as Akaike’s (AIC) or the Bayesian information criteria, often lead to too parsimonious a model with the implication that the cointegration ...

The dynamic Boltzmann machine (DyBM) has been proposed as a stochastic generative model of multi-dimensional time series, with an exact, learning rule that maximizes the log-likelihood of a given time series. The DyBM, however, is defined only for binary valued data, without any nonlinear hidden units. Here, in our first contribution, we extend the DyBM to deal with real valued data. We present...

Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) ina multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated...

We consider a class of semi-parametric dynamic models with strong white noise errors. This processes includes the standard Vector Autoregressive (VAR) model, nonfundamental structural VAR, mixed causal-noncausal models, as well nonlinear such (multivariate) ARCH-M model. For estimation in this class, we propose Generalized Covariance (GCov) estimator, which is obtained by minimizing residual-ba...

Nowadays one of the most important issues in our economy, both from economic and political view is the link between monetary policy and business cycle fluctuations. Amongst the shocks related to the supply side, the shock of oil price is the important factor that has affected the world economy since the 1970s. This paper examines the effects of monetary policy and oil price shocks on the busine...

Level vector autoregressive (VAR) models are used extensively in empirical macroeconomic research. However, estimated level VAR models may contain explosive roots, which is at odds with the widespread consensus among macroeconomists that roots are at most unity. This paper investigates the frequency of explosive roots in estimated level VAR models in the presence of stationary and nonstationary...

Abstract Time series data commonly show are interconnected behaviour and non-stationer interrelated variables, so a model that able to obtain good forecasting result from non-stationary multivariate variables time needed. Vector Error Correction Model (VECM) is one of which vector form Autoregressive Boundary (VAR) for has cointegration relationship. The purpose this study identify the VECM in ...