The authors propose the information matrix test to assess the constancy of mean and variance parameters in vector autoregressions (VAR). They additively decompose it into several orthogonal components: conditional heteroskedasticity and asymmetry of the innovations, and their unconditional skewness and kurtosis. Their Monte Carlo simulations explore both its finite size properties and its power against i.i.d. coefficients, persistent but stationary ones, and regime switching. Their procedures detect variation in the autoregressive coefficients and residual covariance matrix of a VAR for the US GDP growth rate and the statistical discrepancy, but they fail to detect any covariation between those two sets of coefficients.
We would like to thank Pablo Cabrales and Jaime de la Vega for able research assistance, as well as participants at the Conference in Honor of Fabio Canova (Hydra, 2021) for helpful comments and suggestions. The first and third authors also acknowledge financial support from the Spanish Ministry of Science and Innovation through grant PID2021-128963 and the Santander CEMFI Research Chair. The second author acknowledges Financial support from MIUR through the PRIN project “High-dimensional time series for structural macroeconomic analysis in times of pandemic”.
Amengual, D., Fiorentini, G. and Sentana, E. (2022), "Tests for Random Coefficient Variation in Vector Autoregressive Models", Dolado, J.J., Gambetti, L. and Matthes, C. (Ed.) Essays in Honour of Fabio Canova (Advances in Econometrics, Vol. 44B), Emerald Publishing Limited, Bingley, pp. 1-35. https://doi.org/10.1108/S0731-90532022000044B001
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