Wavelet Multiresolution Analysis of High-Frequency FX Rates, Summer 1997

FX pricing processes are nonstationary and their frequency characteristics are time-dependent. Most do not conform to geometric Brownian motion, since they exhibit a scaling law with a Hurst exponent between zero and 0.5 and fractal dimensions between 1.5 and 2. This paper uses wavelet multiresolution analysis, with Haar wavelets, to analyze the nonstationarity (time-dependence) and self-similarity (scale-dependence) of intra-day Asian currency spot exchange rates.foreign exchange, anti-persistence, multi-resolution analysis, wavelets, Asia

Persistence Characteristics of the Chinese Stock Markets

This paper identifies such fundamental characteristics as the lack of ergodicity, stationarity, and independence, and it identifies the degree of initial persistence of the Chinese stock markets when they were more regulated. The index series are from the Shanghai (SHI) stock market and Shenzhen A-shares (SZI) and B-shares (SZBI) stock markets, before and after the various deregulations and reregulations. Accurate and complete signal processing methods are applied to the complete series and to their sub-periods. The evidence of lack of stationarity and ergodicity can be ascribed to two causes: (1) the initial interventions in these stock markets by the Chinese government by imposing various daily price change limits, and (2) the changing trading styles in the course of the development of these emerging stock markets, after the Chinese government left these equity markets to develop by themselves. By computing the markets' monofractal Hurst exponents (and its accuracy range with a new statistic), using wavelet multiresolution analysis (MRA), we identify the markets' subsequent degrees of persistence. The empirical evidence shows that SHI, SZI, and SZBI are moderately persistent with Hurst exponents slightly greater than the Fickian 0.5 of the Geometric Brownian Motion. It also shows that these stock markets were considerably more persistent before the deregulations, but that they now move much more like geometric Brownian motions, i.e., efficiently. Our results also show that the Chinese stock markets are gradually and properly integrating into one Chinese stock market. Our results are consistent with similar empirical findings from Latin American, European, and other Asian emerging financial markets.Long-term dependence, degrees of persistence, Hurst exponent, wavelet multiresolution analysis, Chinese equity markets

Quantum-coherent dynamics in photosynthetic charge separation revealed by wavelet analysis

Experimental/theoretical evidence for sustained vibration-assisted electronic (vibronic) coherence in the Photosystem II Reaction Center (PSII RC) indicates that photosynthetic solar-energy conversion might be optimized through the interplay of electronic and vibrational quantum dynamics. This evidence has been obtained by investigating the primary charge separation process in the PSII RC by two-dimensional electronic spectroscopy (2DES) and Redfield modeling of the experimental data. However, while conventional Fourier transform analysis of the 2DES data allows oscillatory signatures of vibronic coherence to be identified in the frequency domain in the form of static 2D frequency maps, the real-time evolution of the coherences is lost. Here we apply for the first time wavelet analysis to the PSII RC 2DES data to obtain time-resolved 2D frequency maps. These maps allow us to demonstrate that i) coherence between the excitons initiating the two different charge separation pathways is active for more than 500 fs, and ii) coherence between exciton and charge-transfer states, the reactant and product of the charge separation reaction, respectively, is active for at least 1 ps. These findings imply that the PSII RC employs coherence i) to sample competing electron transfer pathways, and ii) to perform directed, ultrafast and efficient electron transfer.Comment: Scientific reports 201

Wavelet analysis of the seismograms of the 2004 Sumatra-Andaman earthquake and its application to tsunami early warning

We applied the wavelet transform in an attempt to detect long-period components early in a seismogram. We analyzed the displacement seismograms of the 26 December 2004 Sumatra-Andaman earthquake (Mw = 9.2) and the 28 March 2005 Nias earthquake (Mw = 8.7). Wavelet analysis is able to clearly distinguish the amplitudes of the long-period W phase between the seismograms of the two earthquakes before the S wave reaches the station. It shows that the 2004 earthquake generates a W phase of significantly greater amplitude. This facility has potential application to the rapid identification of truly great earthquakes with high tsunami potential

Wavelet Multiresolution Analysis of High-Frequency Asian FX Rates, Summer 1997

FX pricing processes are nonstationary and their frequency characteristics are time-dependent. Most do not conform to geometric Brownian motion, since they exhibit a scaling law with a Hurst exponent between zero and 0.5 and fractal dimensions between 1.5 and 2. This paper uses wavelet multiresolution analysis, with Haar wavelets, to analyze the nonstationarity (time-dependence) and self-similarity (scale-dependence) of intra-day Asian currency spot exchange rates. These are the ask and bid quotes of the currencies of eight Asian countries (Japan, Hong Kong, Indonesia, Malaysia, Philippines, Singapore, Taiwan, Thailand), and of Germany for comparison, for the crisis period May 1, 1998 - August 31, 1997, provided by Telerate (U.S. dollar is the numeraire). Their time-scale dependent spectra, which are localized in time, are observed in wavelet based scalograms. The FX increments can be characterized by the irregularity of their singularities. This degrees of irregularity are measured by homogeneous Hurst exponents. These critical exponents are used to identify the fractal dimension, relative stability and long term dependence of each Asian FX series. The invariance of each identified Hurst exponent is tested by comparing it at varying time and scale (frequency) resolutions. It appears that almost all FX markets show anti-persistent pricing behavior. The anchor currencies of the D-mark and Japanese Yen are ultra-efficient in the sense of being most anti-persistent. The Taiwanese dollar is the most persistent, and thus unpredictable, most likely due to administrative control. FX markets exhibit these non- linear, non-Gaussian dynamic structures, long term dependence, high kurtosis, and high degrees of non-informational (noise) trading, possibly because of frequent capital flows induced by non-synchronized regional business cycles, rapidly changing political risks, unexpected informational shocks to investment opportunities, and, in particular, investment strategies synthesizing interregional claims using cash swaps with different duration horizons.foreign exchange markets, anti-persistence, long-term dependence, multi-resolution analysis, wavelets, time-scale analysis, scaling laws, irregularity analysis, randomness, Asia

Laser Scanning and the Continuous Wavelet Transform for Flatness Control

Current methods for surface flatness control in construction are based on sparse measurements and therefore may lead to inaccurate and imprecise results. Previous research has shown that Terrestrial Laser Scanning (TLS), with the accuracy and density of 3D point clouds it can provide, could support more complete and reliable control of surface flatness in construction. However, these previous works have only applied to existing methods based on sparse measurements, or used defect detection methods that are not based on the analysis of surface waviness (i.e. the frequencies in the floor surface profile), although this generally constitutes the key information sought after in surface flatness assessment. In this paper, we investigate the application of a frequency analysis technique, more particularly the Continuous Wavelet Trans-form (CWT), to TLS point clouds associated to surfaces. The aim is to make full use of the density of points provided by TLS and provide detailed results frequency-wise. We provide the reasoning behind employing the CWT for analyzing frequencies in this context, and report results obtained using data acquired from actual slabs. The CWT results are also compared with those obtained when applying the Waviness Index method. The encouraging preliminary results lead us to suggest a path forward for future development and testing with a view on possibly establishing a new standard test method for floor flatness

Temporal and Periodic Variations of Sunspot Counts in Flaring and Non-flaring Active Regions

We analyzed temporal and periodic behavior of sunspot counts (SSCs) in flaring (C, M, or X class flares), and non-flaring active regions (ARs) for the almost two solar cycles (1996 through 2016). Our main findings are as follows: i) The temporal variation of monthly means of daily total SSCs in flaring and non-flaring ARs are different and these differences are also varying from cycle to cycle; temporal profile of non-flaring ARs are wider than the flaring ones during the solar cycle 23, while they are almost the same during the current cycle 24. The second peak (second maximum) of flaring ARs are strongly dominate during current cycle 24, while this difference is not such a remarkable during cycle 23. The amplitude of SSCs in the non-flaring ARs are comparable during the first and second peaks (maxima) of the current solar cycle, while the first peak is almost not existent in case of the flaring ARs. ii) Periodic variations observed in SSCs of flaring and non-flaring ARs are quite different in both MTM spectrum and wavelet scalograms and these variations are also different from one cycle to another; the largest detected period in the flaring ARs is 113 days, while there are much higher periodicities (327, 312, and 256 days) in non-flaring ARs. There are no meaningful periodicities in MTM spectrum of flaring ARs exceeding 45 days during solar cycle 24, while a 113 days periodicity detected from flaring ARs of solar cycle 23. For the non-flaring ARs the largest period is 72 days during solar cycle 24, while the largest period is 327 days during current cycle.Comment: Submitted to Solar Physics, 17 pages, 5 figure

Persistence Characteristics of Latin American Financial Markets

The financial rates of return from Latin American stock and currency markets are found to be non-normal, non-stationary, non-ergodic and long-term dependent, i.e., they have long memory. The degree of long- term dependence is measured by monofractal (global) Hurst exponents from wavelet multiresolution analysis (MRA). Scalograms and scalegrams provide the respective visualizations of these wavelet coefficients and the power spectrum of the rates of return. The slope of the power spectrum identifies the Hurst exponent and thereby the degree of scaling dependence that cannot be determined by Box-Jenkins type time series analysis. Our dependency and time and frequency scaling results are consistent with similar empirical findings from American, European, and Asian financial markets, extending the domain of the empirical investigation of the dynamics and risk characteristics of financial markets and refuting the hypothesis of perfectly efficient markets.financial markets, long memory, Hurst exponent, scalegram, wavelets, multiresolution analysis, measurement accuracy