Vector Multiplicative Error Models: Representation and Inference

54 Pages Posted: 7 Nov 2008

See all articles by Fabrizio Cipollini

Fabrizio Cipollini

Universita di Firenze, DiSIA (Dipartimento di Statistica, Informatica, Applicazioni)

Robert F. Engle

New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER); New York University (NYU) - Volatility and Risk Institute

Giampiero M. Gallo

Corte dei Conti - Italian Court of Audits; University of Bologna - Rimini Center for Economic Analysis (RCEA); Universita' di Firenze - Dipartimento di Statistica, Informatica, Applicazioni "G.Parenti"

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Date Written: October 2006

Abstract

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 multivariate 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 copula functions 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.

Suggested Citation

Cipollini, Fabrizio and Engle, Robert F. and Gallo, Giampiero M., Vector Multiplicative Error Models: Representation and Inference (October 2006). NYU Working Paper No. SC-CFE-06-01, Available at SSRN: https://ssrn.com/abstract=1297099

Fabrizio Cipollini (Contact Author)

Universita di Firenze, DiSIA (Dipartimento di Statistica, Informatica, Applicazioni) ( email )

Viale Morgagni, 59
Florence, Florence 50134
Italy
+39 055 2751592 (Phone)
+39 055 4223560 (Fax)

Robert F. Engle

New York University (NYU) - Department of Finance

Stern School of Business
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New York, NY 10012-1126
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
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New York University (NYU) - Volatility and Risk Institute ( email )

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New York, NY 10012
United States

Giampiero M. Gallo

Corte dei Conti - Italian Court of Audits ( email )

viale Mazzini
Roma, Roma 00195
Italy

University of Bologna - Rimini Center for Economic Analysis (RCEA) ( email )

Via Patara, 3
Rimini (RN), RN 47900
Italy

Universita' di Firenze - Dipartimento di Statistica, Informatica, Applicazioni "G.Parenti" ( email )

Viale G.B. Morgagni, 59
Florence, 50134
Italy
0039 055 2751 591 (Phone)
0039 055 4223560 (Fax)

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