TY  - JOUR
AU  - Cipollini,Fabrizio
AU  - Engle,Robert F.
AU  - Gallo,Giampiero M.
TI  - Vector Multiplicative Error Models:  Representation and Inference
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 331
PY  - 2006
Y2  - November 2006
UR  - http://www.nber.org/papers/t0331
L1  - http://www.nber.org/papers/t0331.pdf
N1  - Author contact info:
Fabrizio Cipollini
Viale Morgagni
59-50134 Firenze
Italy
E-Mail: cipollin@ds.unifi.it

Robert F. Engle, III
Department of Finance, Stern School of Business
New York University, Salomon Center
44 West 4th Street, Suite 9-160
New York, NY  10012-1126
Tel: 212/998-0710
Fax: 212/995-4220
E-Mail: rengle@stern.nyu.edu

Giampiero M.. Gallo
Dipartimento di Statistica "G.Parenti"
Viale G.B. Morgagni, 59
50134 Firenze – Italy
E-Mail: gallog@ds.unifi.it
AB  - The Multiplicative Error Model introduced by Engle (2002) for positive valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with positive support.  In this paper we propose a multi-variate extension of such a model, by taking into consideration the possibility that the vector innovation process be contemporaneously correlated.  The estimation procedure is hindered by the lack of probability density functions for multivariate positive valued random variables.  We suggest the use of copulafunctions and of estimating equations to jointly estimate the parameters of the scale factors and of the correlations of the innovation processes.  Empirical applications on volatility indicators are used to illustrate the gains over the equation by equation procedure.
ER  -