Nonlinear dynamic volatility has been observed in many financial time series. The recently proposed quantile periodogram offers an alternative way to examine this phenomena in the frequency domain. The quantile periodogram is constructed from trigonometric quantile regression of time series data at different frequencies and quantile levels, enabling the quantile‐frequency analysis (QFA) of nonlinear serial dependence. This paper introduces some spectral measures based on the quantile periodogram for diagnostic checks of financial time series models and for model‐based discriminant analysis. A simulation‐based parametric bootstrapping technique is employed to compute the p‐values of the spectral measures. The usefulness of the proposed method is demonstrated by a simulation study and a motivating application using the daily log returns of the S&P 500 index together with GARCH‐type models. The results show that the QFA method is able to provide additional insights into the goodness of fit of these financial time series models that may have been missed by conventional tests. The results also show that the QFA method offers a more informative way of discriminant analysis for detecting regime changes in financial time series.

中文翻译：

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具有非线性动力学的时间序列诊断检查的分位数频率分析和频谱测量

在许多金融时间序列中都观察到了非线性动态波动。最近提出的分位数周期图提供了一种在频域中检查此现象的替代方法。分位数周期图是根据时间序列数据在不同频率和分位数级别下的三角分位数回归而构建的，从而实现了非线性序列相关性的分频分析（QFA）。本文介绍了基于分位数周期图的一些频谱度量，用于金融时间序列模型的诊断检查和基于模型的判别分析。采用基于仿真的参数自举技术来计算p光谱测量值。通过使用S＆P 500指数的日对数收益率以及GARCH类型的模型进行的模拟研究和激励性应用，证明了该方法的有效性。结果表明，QFA方法能够为传统测试可能遗漏的这些金融时间序列模型的拟合优度提供更多的见解。结果还表明，QFA方法为判别金融时间序列中的政权变化提供了更多信息的判别分析方法。