A semi-parametric estimation method for the quantile spectrum with an application to earthquake classification using convolutional neural network

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