Title: Semi-parametric estimation for the quantile coherence in multivariate time series
Authors: Cristian Felipe Jimenez Varon - King Abdullah University of Science and Technology (Saudi Arabia) [presenting]
Ta-Hsin Li - IBM Watson Research Center (Austria)
Ying Sun - KAUST (Saudi Arabia)
Abstract: In multivariate time series analysis, coherence measures the linear dependency between two-time series at different frequencies; however, real data applications often exhibit nonlinear dependency in the frequency domain. Conventional coherence analysis fails to capture such dependency among the time series. Quantile coherence, on the other hand, characterizes the nonlinear dependency by defining the coherence at a set of quantile levels. Although quantile coherence is a more powerful tool, its estimation remains challenging due to the high level of noise. A new estimation technique is proposed for quantile coherence. The proposed method is semiparametric, which uses the parametric form of the spectrum of the vector autoregressive model (VAR) as an approximation to the quantile spectral matrix, along with nonparametric smoothing across both quantile levels and frequencies. First, the method approximates the matrix-valued quantile partial autocorrelation function (QPACF) as well as the quantile autocovariance function (QACF) with the multivariate version of the Durbin-Levinson algorithm. Then, the QPACF is smoothed across quantile levels by a nonparametric smoother. Finally, quantile coherence is computed from the smoothed QPACF. Numerical results show that the proposed estimation method outperforms other conventional nonparametric methods.