Model Free Inference on Multivariate Time Series with Conditional Correlations

Dimitrios Thomakos, Johannes Klepsch and Dimitris N. Politis
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Johannes Klepsch: Department of Mathematical Statistics, Technische Universität München, 85748 Munich, Germany
Dimitris N. Politis: Department of Mathematics and Halicioglu Data Science Institute, University of California, San Diego, CA 92093, USA

Stats, 2020, vol. 3, issue 4, 1-26

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.

Keywords: conditional correlation; forecasting; NoVaS transformations; volatility (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2020
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