分位数-频率分析与频谱度量用于非线性动态时间序列的诊断检验
Quantile-Frequency Analysis and Spectral Measures for Diagnostic Checks of Time Series With Nonlinear Dynamics
AI总结：
本文提出基于分位数周期图的频谱度量，用于检验金融时间序列模型的诊断及基于模型的判别分析，通过模拟研究和S&P 500指数日对数收益率数据验证了方法的有效性。
摘要：
许多金融时间序列表现出非线性动态波动性。最近提出的分位数周期图提供了一种在频域内研究此现象的替代方法。分位数周期图通过不同频率和分位数水平的时间序列数据的三角函数分位数回归构建，使非线性序列依赖的分位数-频率分析（QFA）成为可能。本文介绍了一些基于分位数周期图的频谱度量，用于金融时间序列模型的诊断检验和基于模型的判别分析。采用基于模拟的参数自助法计算频谱度量的p值。通过模拟研究和使用S&P 500指数每日对数收益率数据及GARCH型模型的实证应用，证明了所提方法的实用性。结果表明，QFA方法能够提供传统检验可能遗漏的金融时间序列模型拟合优度的额外见解。此外，结果还表明，QFA方法为检测金融时间序列中的制度转变提供了更有信息量的判别分析方法。
英文摘要：
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.
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