Intraday forecasts of a volatility index: functional time series methods with dynamic updating

Abstract

As a forward-looking measure of future equity market volatility, the VIX index has gained immense popularity in recent years to become a key measure of risk for market analysts and academics. We consider discrete reported intraday VIX tick values as realisations of a collection of curves observed sequentially on equally spaced and dense grids over time and utilise functional data analysis techniques to produce one-day-ahead forecasts of these curves.The proposed method facilitates the investigation of dynamic changes in the index over very short time intervals as showcased using the 15-second high-frequency VIX index values. With the help of dynamic updating techniques, our point and interval forecasts are shown to enjoy improved accuracy over conventional time series models.

Is the Group Structure Important in Grouped Functional Time Series?

“…Functional depth-based outlier detection methods of Hyndman and Shang (2010), and the recently developed novel multivariate functional outlier detection methods of Dai and Genton (2018) and Dai et al (2020) can be adopted to check if a particular curve is an outlying observation. Among other methods, the robust functional principal component analysis method and the robust regularized singular value decomposition method of Shang et al (2019) can be applied to mitigate influences of functional outliers in modeling and forecasting age-specific morality rates (see also Zhang et al, 2013;Bali et al, 2011).…”

Granger causality of bivariate stationary curve time series

“…that is, r j t ðu i Þ is the log-return for the jth company at the middle of time interval i at day t (e.g., see Li et al 2020;Shang et al 2019). In a given day, there are 96 5-minute price observations from 9:30 to 17:20 Eastern time, resulting in 95 values of the logreturns.…”

“…In these time series, the data frequency is high enough to model itself as a curve time series and gives rise to the analysis of functional time series (see, e.g., Horváth & Kokoszka, 2012;Kokoszka & Reimherr, 2017). Examples of functional time series include intraday stock price curves, with each functional observation defined as a pricing function of time points within a day (e.g., see Horváth, Kokoszka, & Rice, 2014;Li, Robinson, & Shang, 2020), and intraday volatility curves, with each functional observation defined as a volatility function of time points within a day (e.g., see Shang, Yang, & Kearney, 2019).…”

Granger causality of bivariate stationary curve time series

“…that is, r j t (u i ) is the log return for j th company at the middle of time interval i at day t (e.g., see , Shang et al 2019, Li et al 2020. In a given day, there are 96 5-minute price observations from 9:30 to 17:20 Eastern time, resulting in 95 values of the log returns.…”

“…In these time series, the data frequency is high enough to model itself as a curve time series and gives rise to the analysis of functional time series (see, e.g., Horváth & Kokoszka 2012, Kokoszka & Reimherr 2017. Examples of functional time series include intraday stock price curves with each functional observation defined as a pricing function of time points within a day (e.g., see Horváth et al 2014, Li et al 2020, and intraday volatility curves with each functional observation defined as a volatility function of time points within a day (e.g., see Shang et al 2019).…”