Lee Sangyeol, Kim Chang Kyeom, Lee Sangjo
Department of Statistics, Seoul National University, Seoul 08826, Korea.
Entropy (Basel). 2020 May 20;22(5):578. doi: 10.3390/e22050578.
This study considers the problem of detecting a change in the conditional variance of time series with time-varying volatilities based on the cumulative sum (CUSUM) of squares test using the residuals from support vector regression (SVR)-generalized autoregressive conditional heteroscedastic (GARCH) models. To compute the residuals, we first fit SVR-GARCH models with different tuning parameters utilizing a time series of training set. We then obtain the best SVR-GARCH model with the optimal tuning parameters via a time series of the validation set. Subsequently, based on the selected model, we obtain the residuals, as well as the estimates of the conditional volatility and employ these to construct the residual CUSUM of squares test. We conduct Monte Carlo simulation experiments to illustrate its validity with various linear and nonlinear GARCH models. A real data analysis with the S&P 500 index, Korea Composite Stock Price Index (KOSPI), and Korean won/U.S. dollar (KRW/USD) exchange rate datasets is provided to exhibit its scope of application.
本研究基于支持向量回归（SVR）-广义自回归条件异方差（GARCH）模型的残差，利用平方和累积和（CUSUM）检验，考虑了检测具有时变波动率的时间序列条件方差变化的问题。为了计算残差，我们首先利用训练集的时间序列拟合具有不同调优参数的SVR-GARCH模型。然后，通过验证集的时间序列获得具有最优调优参数的最佳SVR-GARCH模型。随后，基于所选模型，我们获得残差以及条件波动率的估计值，并利用这些来构建残差平方和CUSUM检验。我们进行蒙特卡罗模拟实验，以说明其在各种线性和非线性GARCH模型中的有效性。提供了对标准普尔500指数、韩国综合股价指数（KOSPI）和韩元/美元（KRW/USD）汇率数据集的实际数据分析，以展示其应用范围。
