Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets
Multiresolution Signal Decomposition: Transforms, Subbands, and Wavelets
Robust portfolio selection problems
Mathematics of Operations Research
Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration
SIAM Journal on Scientific Computing
Portfolio Selection with Robust Estimation
Operations Research
Finite Element Approach to Clustering of Multidimensional Time Series
SIAM Journal on Scientific Computing
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This paper presents an application of the recently developed method for simultaneous dimension reduction and metastability analysis of high-dimensional time series in the context of computational finance. Further extensions are included to combine state-specific principal component analysis (PCA) and state-specific regressive trend models to handle the high-dimensional, nonstationary data. The identification of market phases allows one to control the involved phase-specific risk for futures portfolios. The numerical optimization strategy for futures portfolios based on Tikhonov-type regularization is presented. The application of proposed strategies to online detection of the market phases is exemplified first on the simulated data and then on historical futures prices for oil and wheat from 2005-2008. Numerical tests demonstrate the comparison of the presented methods with existing approaches.