In this paper we introduce a bootstrap procedure to test parameter restrictions in vector autoregressive models which is robust in cases of conditionally heteroskedastic error terms. The adopted wild bootstrap method does not require any parametric specification of the volatility process and takes contemporaneous error correlation implicitly into account. Via a Monte Carlo investigation empiric...

We show that the order of integration of a vector autoregressive process is equal to the difference between the multiplicity of the unit root in the characteristic equation and the multiplicity of the unit root in the adjoint matrix polynomial. The equivalence with the standard I(1) and I(2) conditions (Johansen, 1996) is proved and polynomial cointegration discussed in the general setup.

This paper generalizes the cointegrated vector autoregressive model of Johansen (1988) to allow for structural changes. Estimation under various hypotheses is made possible by a new estimation technique, that makes it simple to derive a number of interesting likelihood ratio tests. E.g., the test for m structural changes against m+ k structural changes (occurring at fixed points in time), m ∈ N...

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...

Seasonal and periodic vector autoregressions are two common approaches to modeling vector time series exhibiting cyclical variations. The total number of parameters in these models increases rapidly with the dimension and order of the model, making it difficult to interpret the model and questioning the stability of the parameter estimates. To address these and other issues, two methodologies f...

Vector Auto-regressive (VAR) models are useful for analyzing temporal dependencies among multivariate time series, known as Granger causality. There exist methods for learning sparse VAR models, leading directly to causal networks among the variables of interest. Another useful type of analysis comes from clustering methods, which summarize multiple time series by putting them into groups. We d...

The authors investigate a sea surface temperature anomaly (SSTA)-only vector autoregressive (VAR) model for prediction of El Niño–Southern Oscillation (ENSO). VAR generalizes the linear inverse method (LIM) framework to incorporate an extended state vector including many months of recent prior SSTA in addition to the present state. An SSTA-only VARmodel implicitly captures subsurface forcing ob...

This paper proposes a Vector Autoregressive (VAR) model as a new technique for missing feature reconstruction in ASR. We model the spectral features using multiple VAR models. A VAR model predicts missing features as a linear function of a block of feature frames. We also propose two schemes for VAR training and testing. The experiments on AURORA-2 database have validated the modeling methodolo...

Order-selection criteria for vector autoregressive (AR) modeling are discussed. The performance of an order-selection criterion is optimal if the model of the selected order is the most accurate model in the considered set of estimated models: here vector AR models. Suboptimal performance can be a result of underfit or overfit. The Akaike information criterion (AIC) is an asymptotically unbiase...

A distance between pairs of sets of autoregressive moving average (ARMA) processes is proposed. Its main properties are discussed. The paper also shows how the proposed distance finds application in time series analysis. In particular it can be used to evaluate the distance between portfolios of ARMA models or the distance between vector autoregressive (VAR) models.