Are These Shocks for Real? Sensitivity Analysis of the Significance of the Wavelet Response to Some CKLS Processes

The CKLS process (introduced by Chan, Karolyi, Longstaff, and Sanders) is a typical example of a mean-reverting process. It combines random fluctuations with an elastic attraction force that tends to restore the process to a central value. As such, it is widely used to model the stochastic behaviour of various financial assets. However, the calibration of CKLS processes can be problematic, resulting in high levels of uncertainty on the parameter estimates. In this paper we show that it is still possible to draw solid conclusions about certain qualitative aspects of the time series, as the corresponding indicators are relatively insensitive to changes in the CKLS parameters.

Improved SURF Descriptor Based on Triangle Partition

In order to improve the robustness and real time performance of SURF based image matching algorithms, a new descriptor is proposed. We compute the new descriptor in a rectangle local region (the side set to 20s). Firstly, the local region is divided into 8 equal triangle subregion. Secondly, local region location grid is rotated to align its dominate orientation to a canonical direction. The keypoint dominate orientation and its orthogonalorientation is defined as the x and y directions of the descriptors local coordinate system.Thirdly, compute the Haar wavelet response in x and y directions within the keypoint local region. In order to reduce the boundary effect and outer noise, Haar wavelet response in the same Grid of different triangle is both assigned to each triangle in different weight, and then a gaussian weighting function is used. Compute the histogram of Haar wavelet response and absolute Haar wavelet response, so each triangle subregion constitutes a vector with 4 dimensions. Finally, a descriptor with 32 dimensions is constituted and the descriptor is normalized to achieve illumination invariance. The experimental results show that the performance of the new descriptor is even better than SURF descriptor.

SYMMETRIZATION AND ENHANCEMENT OF THE CONTINUOUS MORLET TRANSFORM FOR SPECTRAL DENSITY ESTIMATION

The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the wavelet based on power. The spectral density has physical units which may be related to the squared amplitude of the signal, as do its margins the mean wavelet power and the integrated instant power, giving a quantitative estimate of the power density with temporal resolution. Deconvolution with the wavelet response matrix reduces the spectral leakage and produces an enhanced wavelet spectrum providing maximum resolution of the harmonic content of a signal. Applications to data analysis are discussed.