Nonparametric Directional Dependence Estimation and Its Application to Cryptocurrency

Abstract

This paper proposes a nonparametric directional dependence by using the local polynomial regression technique. With data generated from a bivariate copula having a nonmonotone regression structure, we show that our nonparametric directional dependence is superior to the copula directional dependence method in terms of the root-mean-square error. To validate the directional dependence with real data, we use the log returns of daily prices of Bitcoin, Ethereum, Ripple, and Stellar. We conclude that our nonparametric directional dependence, by using the local polynomial regression technique with asymmetric-threshold GARCH models for marginal distributions, detects the directional dependence better than the copula directional dependence method by an asymmetric GARCH model.