ALTERNATIVES TO LARGE VAR, VARMA AND MULTIVARIATE
STOCHASTIC VOLATILITY MODELS
Mike G. Tsionas
Athens University of Economics and Business
ABSTRACT
In this paper, our proposal is to combine univariate ARMA models to produce a variant of the VARMA model that is much more easily implementable and does not involve certain complications. The original model is reduced to a series of univariate problems and a copula – like term (a mixture-of-normals densities) is introduced to handle dependence. Since the univariate problems are easy to handle by MCMC or other techniques, computations can be parallelized easily, and only univariate distribution functions are needed, which are quite often available in closed form. The results from parallel MCMC or other posterior simulators can then be taken together and use simple sampling - resampling to obtain a draw from the exact posterior which includes the copula - like term. We avoid optimization of the parameters entering the copula mixture form as its parameters are optimized only once before MCMC begins. We apply the new techniques in three types of challenging problems. Large time-varying parameter vector autoregressions (TVP-VAR) with nearly 100 macroeconomic variables, multivariate ARMA models with 25 macroeconomic variables and multivariate stochastic volatility models with 100 stock returns. Finally, we perform impulse response analysis in the data of Giannone, Lenza, and Primiceri (2015) and compare, as they proposed with results from a dynamic stochastic general equilibrium model.
Keywords: Vector Autoregressive Moving Average models; Multivariate Stochastic Volatility models; Copula models; Bayesian analysis.
JEL Classifications: C11, C13.
Acknowledgements: The author is grateful to the Bank of Greece for its hospitality and funding the research in this paper. Excellent research assistance by Xingzhi Yao is gratefully acknowledged. The views of the paper are of the author and do not necessarily reflect those of the Bank of Greece.
Correspondence:
E. G. Tsionas
Athens University of Economics and Business
76 Patission Str.,10434
Athens,Greece
email: tsionas@otenet.gr