A copula-VAR-X approach for industrial production modelling and forecasting

Abstract

World economies, and especially European ones, have become strongly interconnected in the last decade and a joint modelling is required. We propose here the use of copulae to build flexible multivariate distributions, since they allow for a rich dependence structure and more flexible marginal distributions that better fit the features of empirical data, such as leptokurtosis. We use our approach to forecast industrial production series in the core European Monetary Union (EMU) countries and we provide evidence that the copula-Vector Autoregression (VAR) model outperforms or at worst compares similarly to normal VAR models, keeping the same computational tractability of the latter approach.

Notes

¹ See Cherubini et al. (2004) for more details.

² Industrial production forecasts can be subsequently translated into more meaningful and operationally useful Gross Domestic Product (GDP) forecasts by using bridge models; see Baffigi et al. (2004).

³ As well known, these three countries account for about three-fourths of the industrial production of the whole Euro area.

⁴ We use the Augmented Dickey–Fuller and Dickey–Fuller test with Generalized Least Squares (GLS) detrending (DF–GLS) by Elliott et al. (1996).

⁵ See Lütkepohl (1991) for a detailed discussion of the argument.

⁶ See, as an example of this result, Bodo et al. (2000).

⁷ The last letter at the end of each variable indicates the country to which we are referring; thus F, G and I stand, respectively, for France, Germany and Italy. All data used in the empirical application have been retrieved from the Eurostat online database.

⁸ Excess returns are more significant than simple share price indices in the estimates; see also Bradley and Jansen (2004).

⁹ We also tried adding other lagged variables as well as exogenous variables. None of these changes affected the final conclusion.

¹⁰ The first test can be used only with bivariate copulas.

¹¹ The authors would like to thank Peter Hansen for supplying the Ox code that calculates the SPA test statistics and associated p-values.