Nonparametric Tests of Conditional Independence for Time Series

TL;DR

This paper introduces consistent nonparametric tests for conditional independence in time series, utilizing differences in joint and product of conditional CDFs, with proven asymptotic properties and bootstrap implementation.

Contribution

It develops a novel testing procedure based on conditional moment restrictions for assessing conditional independence in time series data.

Findings

Tests perform well in finite samples according to simulations.

Application reveals nonlinear predictability of equity risk premium.

Method detects various degrees of dependence at different horizons.

Abstract

We propose consistent nonparametric tests of conditional independence for time series data. Our methods are motivated from the difference between joint conditional cumulative distribution function (CDF) and the product of conditional CDFs. The difference is transformed into a proper conditional moment restriction (CMR), which forms the basis for our testing procedure. Our test statistics are then constructed using the integrated moment restrictions that are equivalent to the CMR. We establish the asymptotic behavior of the test statistics under the null, the alternative, and the sequence of local alternatives converging to conditional independence at the parametric rate. Our tests are implemented with the assistance of a multiplier bootstrap. Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed tests. We apply our tests to examine the predictability of equity risk premium using variance risk premium for different horizons and find that there exist various degrees of nonlinear predictability at mid-run and long-run horizons.