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

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.Comment: 29 pages, 5 figures, To appear at the Annals of Operations Researc

Estimation of AR and ARMA models by stochastic complexity

In this paper the stochastic complexity criterion is applied to estimation of the order in AR and ARMA models. The power of the criterion for short strings is illustrated by simulations. It requires an integral of the square root of Fisher information, which is done by Monte Carlo technique. The stochastic complexity, which is the negative logarithm of the Normalized Maximum Likelihood universal density function, is given. Also, exact asymptotic formulas for the Fisher information matrix are derived.Comment: Published at http://dx.doi.org/10.1214/074921706000000941 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Methodology and theory for partial least squares applied to functional data

The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares estimator of slope is either used to construct linear predictive models, or as a tool to project the data onto a one-dimensional quantity that is employed for further statistical analysis. Although the partial least squares approach is often viewed as an attractive alternative to projections onto the principal component basis, its properties are less well known than those of the latter, mainly because of its iterative nature. We develop an explicit formulation of partial least squares for functional data, which leads to insightful results and motivates new theory, demonstrating consistency and establishing convergence rates.Comment: Published in at http://dx.doi.org/10.1214/11-AOS958 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Built to Last or Built Too Fast? Evaluating Prediction Models for Build Times

Automated builds are integral to the Continuous Integration (CI) software development practice. In CI, developers are encouraged to integrate early and often. However, long build times can be an issue when integrations are frequent. This research focuses on finding a balance between integrating often and keeping developers productive. We propose and analyze models that can predict the build time of a job. Such models can help developers to better manage their time and tasks. Also, project managers can explore different factors to determine the best setup for a build job that will keep the build wait time to an acceptable level. Software organizations transitioning to CI practices can use the predictive models to anticipate build times before CI is implemented. The research community can modify our predictive models to further understand the factors and relationships affecting build times.Comment: 4 paged version published in the Proceedings of the IEEE/ACM 14th International Conference on Mining Software Repositories (MSR) Pages 487-490. MSR 201