Abstract
New results on volatility modeling and forecasting are presented based on the NoVaS transformation approach. Our main contribution is that we extend the NoVaS methodology to modeling and forecasting conditional correlation, thus allowing NoVaS to work in a multivariate setting as well. We present exact results on the use of univariate transformations and on their combination for joint modeling of the conditional correlations: we show how the NoVaS transformed series can be combined and the likelihood function of the product can be expressed explicitly, thus allowing for optimization and correlation modeling. While this keeps the original “model-free” spirit of NoVaS it also makes the new multivariate NoVaS approach for correlations “semi-parametric”, which is why we introduce an alternative using cross validation. We also present a number of auxiliary results regarding the empirical implementation of NoVaS based on different criteria for distributional matching. We illustrate our findings using simulated and real-world data, and evaluate our methodology in the context of portfolio management.
Highlights
Joint modeling of the conditional second moments, volatilities and correlations, of a vector of asset returns is considerably more complicated than individual volatility modeling
With the exception of realized correlation measures, based on high-frequency data, the literature on conditional correlation modeling is plagued with the “curse of dimensionality”: parametric or semi-parametric correlation models are usually dependent on a large number of parameters
The main advantages of using NoVaS transformations for volatility modeling and forecasting, see Politis and Thomakos [8], are that the method is data-adaptable without making any a prior assumptions about the distribution of returns and it can work in a multitude of environments These advantages carry-over to the case of correlation modeling
Summary
Joint modeling of the conditional second moments, volatilities and correlations, of a vector of asset returns is considerably more complicated (and with far fewer references) than individual volatility modeling. The main advantages of using NoVaS transformations for volatility modeling and forecasting, see Politis and Thomakos [8], are that the method is data-adaptable without making any a prior assumptions about the distribution of returns (e.g., their degree of kurtosis) and it can work in a multitude of environments (e.g., global and local stationary models, models with structural breaks etc.) These advantages carry-over to the case of correlation modeling. The NoVaS approach we present in this paper has some similarities with copula-based modeling where the marginal distributions of standardized returns are specified and joined to form a multivariate distribution; for applications in the current context, see Jondeau and Rockinger [26]. The rest of the paper is organized as follows: in Section 2, we briefly review the general development of the NoVaS approach; in Section 3, we present the new results on NoVaS-based modeling and forecasting of correlations; in Section 4, we present a proposal for “model” selection in the context of NoVaS; in Section 5, we present some limited simulation results and a possible application of the methodology in portfolio analysis, while in Section 6, we present an illustrative empirical application; Section 7 offers some concluding remarks
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