56,386 research outputs found
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
Penalized Orthogonal Iteration for Sparse Estimation of Generalized Eigenvalue Problem
We propose a new algorithm for sparse estimation of eigenvectors in
generalized eigenvalue problems (GEP). The GEP arises in a number of modern
data-analytic situations and statistical methods, including principal component
analysis (PCA), multiclass linear discriminant analysis (LDA), canonical
correlation analysis (CCA), sufficient dimension reduction (SDR) and invariant
co-ordinate selection. We propose to modify the standard generalized orthogonal
iteration with a sparsity-inducing penalty for the eigenvectors. To achieve
this goal, we generalize the equation-solving step of orthogonal iteration to a
penalized convex optimization problem. The resulting algorithm, called
penalized orthogonal iteration, provides accurate estimation of the true
eigenspace, when it is sparse. Also proposed is a computationally more
efficient alternative, which works well for PCA and LDA problems. Numerical
studies reveal that the proposed algorithms are competitive, and that our
tuning procedure works well. We demonstrate applications of the proposed
algorithm to obtain sparse estimates for PCA, multiclass LDA, CCA and SDR.
Supplementary materials are available online
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Self-organizing linear output map (SOLO): An artificial neural network suitable for hydrologic modeling and analysis
Artificial neural networks (ANNs) can be useful in the prediction of hydrologic variables, such as streamflow, particularly when the underlying processes have complex nonlinear interrelationships. However, conventional ANN structures suffer from network training issues that significantly limit their widespread application. This paper presents a multivariate ANN procedure entitled self-organizing linear output map (SOLO), whose structure has been designed for rapid, precise, and inexpensive estimation of network structure/parameters and system outputs. More important, SOLO provides features that facilitate insight into the underlying processes, thereby extending its usefulness beyond forecast applications as a tool for scientific investigations. These characteristics are demonstrated using a classic rainfall-runoff forecasting problem. Various aspects of model performance are evaluated in comparison with other commonly used modeling approaches, including multilayer feedforward ANNs, linear time series modeling, and conceptual rainfall-runoff modeling
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