129,103 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
Model estimation of cerebral hemodynamics between blood flow and volume changes: a data-based modeling approach
It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV
A group-based approach to the least squares regression for handling multicollinearity from strongly correlated variables
Multicollinearity due to strongly correlated predictor variables is a
long-standing problem in regression analysis. It leads to difficulties in
parameter estimation, inference, variable selection and prediction for the
least squares regression. To deal with these difficulties, we propose a
group-based approach to the least squares regression centered on the collective
impact of the strongly correlated variables. We discuss group effects of such
variables that represent their collective impact, and present the group-based
approach through real and simulated data examples. We also give a condition
more precise than what is available in the literature under which predictions
by the least squares estimated model are accurate. This approach is a natural
way of working with multicollinearity which resolves the difficulties without
altering the least squares method. It has several advantages over alternative
methods such as ridge regression and principal component regression.Comment: 36 pages, 1 figur
- …