7,634 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
EVALUATION OF THE NORMAL APPROXIMATION FOR THE PAIRED TWO SAMPLE PROBLEM WITH MISSING DATA
Previous authors have combined tests for pairs and unpaired data so that population means can be compared using a paired study design with incomplete data. The primary object of my thesis is to determine the appropriate sample size and the appropriate proportion and configuration of complete data and incomplete data so that a normal approximation can be used to calculate p-values. The test statistic studied is one due to Wilson (1992) in which the sign test and rank sum test are combined to form of composite test statistic. To fulfill these objectives, the following approach is adopted:(1)Choose different data scenarios in terms of different sample sizes of paired data and different proportions of complete data.(2)Obtain the exact sampling distribution of the test statistic under each data scenario we study.(3)Obtain the normal approximation distribution under each data scenario we study.(4)Compare the exact and approximate cumulate distribution by their difference on each possible test statistic value. The results show that when the study groups are approximately balanced with respect to incomplete data, and have at least 9 observations in each group, the normal approximation appears to be useful when the number of complete pairs is as low as 5. However, when the groups are highly unbalanced with respect to incomplete data, using the normal approximation seems not to be appropriate, at least when the total sample size is 70 or less. These results may make public health studies easier to carry out when the data include both complete and incomplete pairs
Design and fabrication of robust broadband extreme ultraviolet multilayers
The random layer thickness variations can induce a great deformation of the
experimental reflection of broadband extreme ultraviolet multilayer. In order
to reduce this influence of random layer thickness fluctuations, the
multiobjective genetic algorithm has been improved and used in the robust
design of multilayer with a broad angular bandpass. The robust multilayer with
a lower sensitivity to random thickness errors have been obtained and the
corresponding multilayer mirrors were fabricated. The experimental results of
robust Mo/Si multilayer with a wide angular band were presented and analyzed,
and the advantage of robust multilayer design was demonstrated
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