Multivariate Return Decomposition: Theory and Implications

Stanislav Anatolyev and Nikolay Gospodinov

Working Paper 2015-7
August 2015

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In this paper, we propose a model based on multivariate decomposition of multiplicative—absolute values and signs—components of several returns. In the m-variate case, the marginals for the m absolute values and the binary marginals for the m directions are linked through a 2m-dimensional copula. The approach is detailed in the case of a bivariate decomposition. We outline the construction of the likelihood function and the computation of different conditional measures. The finite-sample properties of the maximum likelihood estimator are assessed by simulation. An application to predicting bond returns illustrates the usefulness of the proposed method.

JEL classification: C13, C32, C51, G12

Key words: multivariate decomposition, multiplicative components, volatility and direction models, copula, dependence

The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.
Please address questions regarding content to Stanislav Anatolyev, New Economic School, 100A Novaya Street, Skolkovo, Moscow, 143026, Russia,, or Nikolay Gospodinov, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree St. NE, Atlanta, GA 30309, 404-498-7892,
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