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Title: Non-linear causality test based on partial distance correlation: Application to energy futures Authors:  German Creamer - Stevens Institute of Technology (United States) [presenting]
Chihoon Lee - Stevens Institute of Technology (United States)
Abstract: A nonlinear causality test is proposed by using the partial distance correlation. As an extension of the Brownian distance correlation, partial distance correlation ($R(X_{t-l},Y_t; Y_{t-1})$) calculates the distance correlation between random variables $X$ and $Y$ given a $Z$ random variable. Our test evaluates the non-linear causality of any time series such as the current value of $Y$ ($Y_t$) on the $l$ lagged values of $X$ ($X_{t-1}...X_{t-l}$) given the past values of $Y$ ($Y_{t-1}...Y_{t-l}$) using a modified version of the partial distance correlation $R(X_{t-1}...X_{t-l},Y_t; Y_{t-1}...Y_{t-l})$. Our test uses moving block bootstrap (MBB) to compute the empirical p-values and selects the most relevant variables. The main reason to use MBB is to evaluate the effect of time dependence using variables that are independent and identically distributed.Our method determines relationships similar to those identified by the linear Granger causality test, and it also uncovers additional non-linear lagged relationships among the log prices of oil, coal, and natural gas futures. When these linear and non-linear relationships are used to forecast energy futures with a non-linear regression method such as support vector machine for regression, the forecast of energy futures improves when compared to a forecast based only on Granger causality and by a baseline autoregressive model selected using the Akaike information criterion.