Conditional correlation estimation and serial dependence identification

TL;DR

This paper explores the estimation of conditional correlations to detect nonlinear dependence and serial dependence in time series, expanding on recent theoretical results and demonstrating practical econometric applications.

Contribution

It introduces methods for estimating conditional correlations in serial dependence contexts and discusses their properties and applications.

Findings

Conditional correlation estimators can detect nonlinear dependence.

The framework effectively identifies serial dependence in econometric data.

Proposed methods are practical for real-world econometric analysis.

Abstract

It has been recently shown in Jaworski, P., Jelito, D. and Pitera, M. (2024), 'A note on the equivalence between the conditional uncorrelation and the independence of random variables', Electronic Journal of Statistics 18(1), that one can characterise the independence of random variables via the family of conditional correlations on quantile-induced sets. This effectively shows that the localized linear measure of dependence is able to detect any form of nonlinear dependence for appropriately chosen conditioning sets. In this paper, we expand this concept, focusing on the statistical properties of conditional correlation estimators and their potential usage in serial dependence identification. In particular, we show how to estimate conditional correlations in generic and serial dependence setups, discuss key properties of the related estimators, define the conditional equivalent of the autocorrelation function, and provide a series of examples which prove that the proposed framework could be efficiently used in many practical econometric applications.