Principal component and second generation wavelet analysis of treasury yield curve evolution

Porous rock deformation has important implications for fluid flow in a range of crustal settings as compaction can increase fluid pressure and alter permeability. The onset of inelastic strain for porous materials is typically defined by a yield curve plotted in differential stress (Q) versus effective mean stress (P) space. Empirical studies have shown that these curves are broadly elliptical in shape. Here conventional triaxial experiments are first performed to document (a) the yield curve of porous bassanite (porosity ≈ 27–28%), a material formed from the dehydration of gypsum, and (b) the postyield behavior, assuming that P and Q track along the yield surface as inelastic deformation accumulates. The data reveal that after initial yield, the yield surface cannot be perfectly elliptical and must evolve significantly as inelastic strain is accumulated. To investigate this further, a novel stress‐probing methodology is developed to map precisely the yield curve shape and subsequent evolution for a single sample. These measurements confirm that the high‐pressure side of the curve is partly composed of a near‐vertical limb. Yield curve evolution is shown to be dependent on the nature of the loading path. Bassanite compacted under differential stress develops a heterogeneous microstructure and has a yield curve with a peak that is almost double that of an equal porosity sample that has been compacted hydrostatically. The dramatic effect of different loading histories on the strength of porous bassanite highlights the importance of understanding the associated microstructural controls on the nature of inelastic deformation in porous rock.

The article examines the application of the Principal Component Analysis (PCA) and machine learning method, the Long Short-Term Memory (LSTM), in the prediction of the yield curve for Poland. The PCA was applied to decompose the yield curve, forecast its components using the LSTM, and obtain the yield curve predictions upon recomposition. The results from the PCA-LSTM model were compared to predictions generated directly by the LSTM model, simple autoregression and random walk, which serves as a benchmark. Overall, LSTM predictions are the most accurate with PCA-LSTM being a close second, nonetheless PCA-LSTM is more accurate in short-term forecasting of interest rates at long maturities. Both methods outperform the benchmark, while autoregression usually underperforms. For these reasons, the PCA-LSTM as well as the LSTM can be useful in interest rate management or building trading strategies. The PCA-LSTM has the advantage that it can focus on particular components of the yield curve, such as variability of the yield curve’s level or steepness.

This paper presents a fault diagnosis method for rolling bearings working in non-stationary running conditions. The proposed approach is based on an improved version of the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), the multivariate denoising using wavelet analysis and principal component analysis (PCA), the spectral kurtosis, and the order tracking analysis (OTA). The results show that the improved CEEMDAN has completely decomposed the raw signal into different intrinsic mode functions (IMFs) representing the natural oscillatory modes embedded into the signal. The most relevant IMF from which the defect was extracted is selected by the kurtogram plot which allows locating the optimal frequency band having the highest kurtosis value. Multivariate denoising based on wavelet analysis and PCA is used to increase the signal-to-noise ratio (SNR) of the selected IMF. The results show the great contribution of the denoising approach when comparing the selected denoised IMF with the original one. Finally, order tracking analysis is applied on the denoised IMF’s envelope to remove the effect of speed variation, and an envelope order spectrum is obtained. The proposed approach is first applied on theoretical signal simulating rolling bearing defect in variable regime including three different phases. The final order spectrum shows exactly the simulated defect order and several of its harmonics. For the experimental validation, several signals of defective rolling bearings have been measured on the Machine Fault Simulator test rig in variable regime. Despite the combined variable regime including acceleration-constant regime-deceleration, at the same time, the obtained results indicate the efficiency of the proposed method to extract the fault order with high accuracy. The maximum error between the theoretical order and the experimentally obtained one was 1.3% for outer race defect and 1% for inner race defect. Finally, the performances of the proposed method are compared to those of another diagnosis method designed for variable regime conditions. Both outer race and inner race defects are considered in acceleration regime. The results show the superiority of the proposed method to highlight the defect order with highest clarity.

Changes in soft tissue profile following mandibular set back were investigated with lateral cephalograms of 40 patients initially having mandibular prognathism. Soft tissue profiles were evaluated using the analysis methods reported by Legan and Burstone, Ricketts, and Merrifield. Differences of the measurements before and after surgery were calculated as changes in profile produced by surgery, and following studies were made.1. The average changes in profile were analysed and the results were as follows: 1) Facial convexity improved, 2) Mandibular prognathism decreased, 3) No change in maxillary prognathism, 4) Posterior displacement of the upper lip with elongation and increase in upper lip protrusion, 5) Nasolabial angle increased, 6) Decrease in lower lip protrusion, 7) Lower facial height decreased, 8) Vertical lip-chin ratio improved, 9) Labiomental sulcus depth increased.2. The principal component analysis was employed in order to qualify the changes in profile as composition of several patterns.The analysis resulted in four principal components having 85% of accumulated contribution ratio.1) The first component (37.9%) is indicative of over-all quantitative change in profile by surgery.2) The second (23%) is indicative of displacement of the upper lip and change in lower lip protrusion.3) The third (14%) is indicative of changes in height of the lower lip and lower facial height and in the nasolabial angle.4) The fourth (10%) is indicative of change in the depth of the labiomental sulcus.Since there is no correlation among components in a principal component analysis, the second and third components in this study suggest the qualitative patterns of profile change. Therefore, changes in profile vary in the height of the lips and lower face and lower lip protrusion, based upon the averaged over-all changes.

This paper characterizes an approach to data compression and defect isolation for the multi-variable process by introducing the wavelet principal component analysis (PCA) and the genetic algorithms. In the defect analysis process, data compression is a critical phase. In our case of study, this can be achieved through the wavelet PCA. We can, through the use of such a technique, filter the data noise and the measurement errors by combining the PCA and the wavelet analysis. The genetic algorithm optimization feature is then employed in structuring the residues of the defect isolation. We present the principle of the PCA as well as the wavelet compression property. Then, we describe both the defect isolation classical method by structuring the residues and the principle of optimizing a problem by the genetic algorithms. The proposed approach is implemented on a statistic system and the Tennessee Eastman process. In comparison with other previous methods, the obtained results mirror the performance of the approach to defect isolation.

The human brain is a complex system able to continuously adapt. How and where brain activity is modulated by behavior can be studied with functional magnetic resonance imaging (fMRI), a non-invasive neuroimaging technique with excellent spatial resolution and whole-brain coverage. FMRI scans of healthy adults completing a variety of behavioral tasks have greatly contributed to our understanding of the functional role of individual brain regions. However, by statistically analyzing each region independently, these studies ignore that brain regions act in concert rather than in unison. Thus, many studies since have instead examined how brain regions interact. Surprisingly, structured interactions between distinct brain regions not only occur during behavioral tasks but also while a subject rests quietly in the MRI scanner. Multiple groups of regions interact very strongly with each other and not only do these groups bear a striking resemblance to the sets of regions co-activated in tasks, but many of these interactions are also progressively disrupted in neurological diseases. This suggests that spontaneous fluctuations in activity can provide novel insights into fundamental organizing principles of the human brain in health and disease. Many techniques to date have segregated regions into spatially distinct networks, which ignores that any brain region can take part in multiple networks across time. A more natural view is to estimate dynamic brain networks that allow flexible functional interactions (or connectivity) over time. The estimation and analysis of such dynamic functional interactions is the subject of this dissertation. We take the perspective that dynamic brain networks evolve in a low-dimensional space and can be described by a small number of characteristic spatiotemporal patterns. Our proposed approaches are based on well-established statistical methods, such as principal component analysis (PCA), sparse matrix decompositions, temporal clustering, as well as a multiscale analysis by novel graph wavelet designs. We adapt and extend these methods to the analysis of dynamic brain networks. We show that PCA and its higher-order equivalent can identify co-varying functional interactions, which reveal disturbed dynamic properties in multiple sclerosis and which are related to the timing of stimuli for task studies, respectively. Further we show that sparse matrix decompositions provide a valid alternative approach to PCA and improve interpretability of the identified patterns. Finally, assuming an even simpler low-dimensional space and the exclusive temporal expression of individual patterns, we show that specific transient interactions of the medial prefrontal cortex are disturbed in aging and relate to impaired memory.

We present a pricing kernel that summarizes well the main features of the dynamics of interest rates and risk in postwar U.S. data and use it to uncover how the pricing kernel has moved with the short rate in this data. Our findings imply that standard monetary models miss an essential link between the central bank instrument and the economic activity that monetary policy is intended to affect, and thus we call for a new approach to monetary policy analysis. We sketch a new approach using an economic model based on our pricing kernel. The model incorporates the key relationships between policy and risk movements in an unconventional way: the central bank's policy changes are viewed as primarily intended to compensate for exogenous business cycle fluctuations in risk that threaten to push inflation off target. This model, while an improvement on standard models, is considered just a starting point for their revision. It leads to critical questions that researchers need to answer as they continue to revise their approach to monetary policy analysis. Copyright © 2009 by the National Bureau of Economic Research.

Image fusion is one of the important techniques for image information enhancing. In order to utilize respective information from different remote sensing images, we propose a new image fusion method based on the Principal Component Analysis (PCA) and feature product of wavelet transform. Firstly, the multi-spectral image is transformed with PCA. Secondly, the histogram-matched panchromatic image and the first principal component are decomposed into wavelet coefficients respectively. Thirdly, the first principal component of the multi-spectral image and the panchromatic image are merged with feature product of wavelet based fusion method, and the former is replaced with the merged data. Finally, the new multi-spectral image is obtained by inverse PCA. Some evaluation parameters are suggested and applied to compare the new method with those of PCA method, the combined PCA and traditional wavelet method and the combined PCA and local deviation of wavelet method. Subjective visual effect and objective statistical results indicate that the performance of the new method is better than those methods. It not only preserves spectral information of the original multi-spectral image well, but also enhances spatial detail information greatly.

Principal Component Analysis (PCA) is one of the most widely used tools for the representation of high-dimensional data. Many different versions have been proposed to enhance the robustness of the model. Most of these ideas are not median based formulation, which is always a robust estimator in statistics. In this paper, we attempt to design a new median based PCA model based on k-medians clustering, for which each principal component is always the spatial median of the projected space. We prove that the proposed method converges. We also compare the proposed method with several state-of-the-art methods including l 1 -PCA, RPCA and RPCA-OM. Experimental results show that the proposed k-medians clustering based PCA performs the best in many cases.

In this study, we propose an implementation of the multifactor Heath-Jarrow-Morton (HJM) interest rate model using an approach that integrates principal component analysis (PCA) and Monte Carlo simulation (MCS) techniques. By integrating PCA and MCS with the multifactor HJM model, we successfully capture the principal factors driving the evolution of short-term interest rates in the US market. Additionally, we provide a framework for deriving spot interest rates through parameter calibration and forward rate estimation. For this, we use daily data from the US yield curve from June 2017 to December 2019. The integration of PCA, MCS with multifactor HJM model in this study represents a robust and precise approach to characterizing interest rate dynamics and compared to previous approaches, this method provided greater accuracy and improved understanding of the factors influencing US Treasury Yield interest rates.

Robust principal component analysis via ES-algorithm

Face detection is the first step in the face recognition system. The Neural network as well as Gabor wavelet based face detection is proposed in this paper. The proposed system applies neural network algorithm to make the slanting face upright and Gabor wavelet is used to extract the invariable features from the selected window. The principal component analysis is applied to identify the person from the data base. The Proposed system gives very high detection efficiency with low number of false alarms. We have shown the results on different test sets with different degrees of variability of the face patterns. In this paper, we present a new approach for determining the orientation of face in the selected window and then use this information to rotate the face upright

Enhanced chiller sensor fault detection, diagnosis and estimation using wavelet analysis and principal component analysis methods

Research into network anomaly detection has become crucial as a result of a significant increase in the number of computer attacks. Many approaches in network anomaly detection have been reported in the literature, but data or solutions typically are not freely available. Recently, a labeled network traffic flow dataset, Kyoto2006+, has been created and is publicly available. Most existing approaches using Kyoto2006+ for network anomaly detection apply various clustering techniques. This paper leverages existing well known statistical analysis and spectral analysis techniques for network anomaly detection. The first popular approach is a statistical analysis technique called Principal Component Analysis (PCA). PCA describes data in a new dimension to unlock otherwise hidden characteristics. The other well known spectral analysis technique is Haar Wavelet filtering analysis. It measures the amount and magnitude of abrupt changes in data. Both approaches have strengths and limitations. In response, this paper proposes a Hybrid PCA–Haar Wavelet Analysis. The hybrid approach first applies PCA to describe the data and then Haar Wavelet filtering for analysis. Based on prototyping and measurement, an investigation of the Hybrid PCA–Haar Wavelet Analysis technique is performed using the Kyoto2006+ dataset. The authors consider a number of parameters and present experimental results to demonstrate the effectiveness of the hybrid approach as compared to the two algorithms individually.

Thermal power estimation by fouling phenomena compensation using wavelet and principal component analysis