8 Conclusions
In this paper a simple multivariate non-stationary paradigm for modeling and forecasting the distribution of returns on financial instruments is discussed.
Unlike most of the multivariate econometric models for financial returns, our approach supposes the volatility to be exogenous. The vectors of returns are assumed to be independent and to have a changing unconditional covariance structure. The methodological frame is that of non-parametric regression with fixed equidistant design points where the regression function is the evolving unconditional covariance. The vectors of standardized innovations have independent coordinates and asymmetric heavy tails and are modeled parametrically. The use of the non-stationary paradigm is exemplified on a trivariate sample of risk factors consisting of a foreign exchange rate Euro/Dollar (EU), an index, FTSE 100 index, and an interest rate, the 10 year US T-bond. The paradigm provides both a good description of the changes in the dynamic of the three risk factors and good multivariate distributional forecasts.
We believe that the careful parametric modeling of the extremal behavior of the standardized innovations makes our approach amenable for precise VaR calculations. Evaluating its behavior in these settings is, however, subject of further research.
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Herzel, S., Stărică, C., Tütüncüc, R. (2006). A non-stationary paradigm for the dynamics of multivariate financial returns. In: Bertail, P., Soulier, P., Doukhan, P. (eds) Dependence in Probability and Statistics. Lecture Notes in Statistics, vol 187. Springer, New York, NY . https://doi.org/10.1007/0-387-36062-X_18
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