We develop theory leading to testing procedures for the presence of a change point in the intraday volatility pattern. The new theory is developed in the framework of Functional Data Analysis. It is based on a model akin to the stochastic volatility model for scalar point-to-point returns. In our context, we study intraday curves, one curve per trading day. After postulating a suitable model for such functional data, we present three tests focusing, respectively, on changes in the shape, the magnitude and arbitrary changes in the sequences of the curves of interest. We justify the respective procedures by showing that they have asymptotically correct size and by deriving consistency rates for all tests. These rates involve the sample size (the number of trading days) and the grid size (the number of observations per day). We also derive the corresponding change point estimators and their consistency rates. All procedures are additionally validated by a simulation study and an application to US stocks.

翻译：我们发展了用于检测日内波动率模式是否存在突变点的检验理论。该新理论在函数型数据分析框架下构建，基于一种类似标量点对点收益随机波动模型的设定。研究对象为日内收益率曲线（每个交易日对应一条曲线）。在建立此类函数型数据的适当模型后，我们提出了三种检验方法，分别聚焦于感兴趣曲线序列的形状变化、幅度变化及任意形式变化。通过证明各检验具有渐近正确尺寸并推导其一致性收敛速率，我们验证了相应方法的有效性。这些收敛速率涉及样本量（交易日数）与网格密度（每日观测点数）。同时推导了对应的变点估计量及其收敛速率。所有方法还通过模拟研究及美股实例进行了验证。