A semi-parametric estimation method for quantile coherence with an application to bivariate financial time series clustering

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In multivariate time series analysis, spectral coherence traditionally measures linear dependencies between time series across different frequencies but often fails to capture nonlinear dependencies. In contrast, quantile coherence detects these nonlinear relationships across various quantile levels using trigonometric quantile regression. A new semi-parametric technique for estimating quantile coherence is introduced, combining the parametric spectrum of a vector autoregressive (VAR) model with nonparametric smoothing across quantiles. For each quantile level, the quantile autocovariance function (QACF) is obtained by applying the Fourier inverse transform to quantile periodograms. The multivariate Durbin-Levinson algorithm is then used to estimate the VAR parameters, which are subsequently applied to derive the quantile coherence estimate. A nonparametric smoother is applied across quantiles to enhance the initial estimate. Numerical results demonstrate that this method outperforms traditional nonparametric approaches. Moreover, clustering bivariate time series based on quantile coherence shows advantages over using ordinary VAR coherence. For instance, when applied to financial stocks, quantile coherence identifies clusters with a more informative structure, providing insights into diversified investment portfolios, which could help investors make better decisions.