Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean
By Valentin Patilea
IRMAR-INSA and CREST ENSAI (2010)
Abstract Paper

Hamdi  Raïssi

IRMAR-INSA

France

The code provides Wald tests results for testing linear Granger causality in mean in the framework of VAR models with non constant variance. A summary on bandwidth selection and the minimum eigenvalues of the estimated volatilities is displayed. The series have to be centered before proceeding to the tests. Note that the adequacy of the VAR model has to be tested before using the modified portmanteau tests available on this companion website.
Created
March 01, 2012
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Fortan absoft
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October 08, 2012
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Abstract
Linear Vector AutoRegressive (VAR) models where the innovations could be unconditionally heteroscedastic and serially dependent are considered. The volatility structure is deterministic and quite general, including breaks or trending variances as special cases. In this framework we propose Ordinary Least Squares (OLS), Generalized Least Squares (GLS) and Adaptive Least Squares (ALS) procedures. The GLS estimator requires the knowledge of the time-varying variance structure while in the ALS approach the unknown variance is estimated by kernel smoothing with the outer product of the OLS residuals vectors. Different bandwidths for the different cells of the time-varying variance matrix are also allowed. We derive the asymptotic distribution of the proposed estimators for the VAR model coefficients and compare their properties. In particular we show that the ALS estimator is asymptotically equivalent to the infeasible GLS estimator. This asymptotic equivalence is obtained uniformly with respect to the bandwidth(s) in a given range and hence justifies data-driven bandwidth rules. Using these results we build Wald tests for the linear Granger causality in mean which are adapted to VAR processes driven by errors with a non stationary volatility. It is also shown that the commonly used standard Wald test for the linear Granger causality in mean is potentially unreliable in our framework (incorrect level and lower asymptotic power). Monte Carlo and real-data experiments illustrate the use of the different estimation approaches for the analysis of VAR models with time-varying variance innovations.
Patilea, V., "Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean", IRMAR-INSA and CREST ENSAI.
number of observations
number of observations
dimension of the process
dimension of the process
dimension of the first subvector X1
dimension of the first subvector X1
dimension of the subvector X2
dimension of the subvector X2
autoregressive order
autoregressive order
number of grid points
number of grid points
sup bound for the grid
sup bound for the grid
min bound for the grid
min bound for the grid
data
data
Waiting time

Please cite the publication as :

Patilea, V., "Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean", IRMAR-INSA and CREST ENSAI.

Please cite the companion website as :

Patilea, V., "Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean", RunMyCode companion website, http://www.execandshare.org/CompanionSite/Site62

number of observations
number of observations
dimension of the process
dimension of the process
dimension of the first subvector X1
The tests determine if X2 Granger-causes X1 linearly in mean.
dimension of the subvector X2
The tests determine if X2 Granger-causes X1 linearly in mean.
autoregressive order
The lag length of the VAR model. It have to be tested by using portmanteau tests developed in Patilea and Raïssi (2011).
number of grid points
The number of grid points corresponds to the number of candidate bandwidths for the non parametric estimation of the volatility structure.
sup bound for the grid
The input 'ma' serves to compute a sup bound of the grid in regard to the 'long run' variance of the ordinary least squares residuals and the sample size.
min bound for the grid
The input 'mi' serves to compute a min bound of the grid in regard to the 'long run' variance of the ordinary least squares residuals and the sample size.
data
Data
Variable/Parameters Description Visualisation
number of observations
dimension of the process
dimension of the first subvector X1
dimension of the subvector X2
autoregressive order
number of grid points
sup bound for the grid
min bound for the grid
data The first column corresponds to the first differences of the U.S. balance on merchandise trade in billions dollars. The second column corresponds to the first differences of the U.S. balance on services in billions dollars. The linear Granger causality in mean from the from the balance on services to the balance on merchandise trade is tested. Data source: http://research.stlouisfed.org/
Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean
H. Raïssi (2012)
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Coder:
• Hamdi Raïssi

IRMAR-INSA

France

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Adaptive Estimation of Vector Autoregressive Models with Time-Varying Variance: Application to Testing Linear Causality in Mean

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