A Semi-Parametric Estimation Method for the Quantile Spectrum with an Application to Earthquake Classification Using Convolutional Neural Network

TL;DR

This paper introduces a semi-parametric method for estimating the quantile spectrum of time series data, combining AR models with nonparametric smoothing, and applies it to earthquake classification using CNNs, outperforming traditional methods.

Contribution

The paper develops a novel semi-parametric estimation technique for the quantile spectrum that integrates AR modeling with smoothing, and demonstrates its effectiveness in earthquake data classification with CNNs.

Findings

Proposed method outperforms conventional smoothing techniques.

CNN trained on quantile periodograms achieves higher accuracy.

Effective application to earthquake classification.

Abstract

In this paper, a new estimation method is introduced for the quantile spectrum, which uses a parametric form of the autoregressive (AR) spectrum coupled with nonparametric smoothing. The method begins with quantile periodograms which are constructed by trigonometric quantile regression at different quantile levels, to represent the serial dependence of time series at various quantiles. At each quantile level, we approximate the quantile spectrum by a function in the form of an ordinary AR spectrum. In this model, we first compute what we call the quantile autocovariance function (QACF) by the inverse Fourier transformation of the quantile periodogram at each quantile level. Then, we solve the Yule-Walker equations formed by the QACF to obtain the quantile partial autocorrelation function (QPACF) and the scale parameter. Finally, we smooth QPACF and the scale parameter across the quantile levels using a nonparametric smoother, convert the smoothed QPACF to AR coefficients, and obtain the AR spectral density function. Numerical results show that the proposed method outperforms other conventional smoothing techniques. We take advantage of the two-dimensional property of the estimators and train a convolutional neural network (CNN) to classify smoothed quantile periodogram of earthquake data and achieve a higher accuracy than a similar classifier using ordinary periodograms.