3rd Moments Research Articles

Stock and currency market linkages: New evidence from realized spillovers in higher moments

We examine the linkages both within and between stock and foreign exchange (FX) markets via three higher moments of return distributions (volatility, skewness and kurtosis). We find that FX market linkages (in the 2nd and 4th moments) are relatively more prominent in developed markets. Cross-asset markets in emerging countries are more likely to be negatively linked through the 3rd moment but they are positively associated via the 2nd and 4th moments in developed markets indicating common concerns regarding tail risks in the former. Finally, cross-asset market linkages are of a similar magnitude to intra-asset-market linkages within emerging markets but the latter are stronger in developed markets.

Theoretical geodesy

Abstract The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011-2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-Msplit estimation, which allows to estimate a vector of parameter differences and the Shift-Msplit(+) that is a generalisation of Shift-Msplit estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2nd, 3rd and 4th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.

Cluster stability as a new method to assess changes in performance and its determinant factors over a season in young swimmers.

To apply a new method to identify, classify, and follow up young swimmers based on their performance and its determinant factors over a season and analyze the swimmers' stability over a competitive season with that method. Fifteen boys and 18 girls (11.8±0.7 y) part of a national talent-identification scheme were evaluated at 3 different moments of a competitive season. Performance (ie, official 100-m freestyle race time), arm span, chest perimeter, stroke length, swimming velocity, speed fluctuation, coefficient of active drag, propelling efficiency, and stroke index were selected as variables. Hierarchical and k-means cluster analysis were computed. Data suggested a 3-cluster solution, splitting the swimmers according to their performance in all 3 moments. Cluster 1 was related to better performances (talented swimmers), cluster 2 to poor performances (nonproficient swimmers), and cluster 3 to average performance (proficient swimmers) in all moments. Stepwise discriminant analysis revealed that 100%, 94%, and 85% of original groups were correctly classified for the 1st, 2nd, and 3rd evaluation moments, respectively (0.11≤Λ≤0.80; 5.64≤χ2≤63.40; 0.001<P≤.68). Membership of clusters was moderately stable over the season (stability range 46.1-75% for the 2 clusters with most subjects). Cluster stability is a feasible, comprehensive, and informative method to gain insight into changes in performance and its determinant factors in young swimmers. Talented swimmers were characterized by anthropometrics and kinematic features.

Retrievals of vertical profiles of stratus cloud properties from combined oxygen A‐band and radar observations

A synergetic algorithm of retrieving vertical distribution of cloud drop effective radius (Re), liquid water content (LWC), and optical depth has been developed by combining oxygen A‐band spectral measurements with radar reflectivity. The underlying physics is to utilize the photon path length information from oxygen A‐band measurements to constrain the retrievals of cloud microphysical properties from radar reflectivity. Through a radiation closure of the rotating shadowband spectrometer (RSS) diffuse‐horizontal irradiances in the oxygen A‐band (which is sensitive to vertical distribution of the 2nd moment of particle size distribution), vertical distributions of cloud microphysical property (the 3rd moment of particle size distribution) are optimized and retrieved from Millimeter Wave Cloud Radar (MMCR) reflectivity (the 6th moment of particle size distribution). The critical issues in the synergetic cloud retrievals of combining passive and active instruments are discussed and carefully taken into account. Evaluation and validation through case studies show that the retrieved column mean values of cloud optical depth, effective radius, and liquid water path agree well with independent measurements from the microwave radiometer (MWR) and independent retrievals from a combined algorithm of multifilter rotating shadowband radiometer (MFRSR) and MWR and the column physical characterization (CPC) of MMCR. These studies demonstrate that this active‐passive synergetic retrieval algorithm is feasible and accurate for retrievals of vertical distribution of cloud Re and LWC for stratus clouds.

Two-soliton interaction as an elementary act of soliton turbulence in integrable systems

Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of these interactions to the dynamical and statistical characteristics of the nonlinear wave field of soliton turbulence we study properties of the spatial moments of the two-soliton solution of the Korteweg–de Vries (KdV) equation. While the first two moments are integrals of the KdV evolution, the 3rd and 4th moments undergo significant variations in the dominant interaction region, which could have strong effect on the values of the skewness and kurtosis in soliton turbulence. ► Two-soliton interactions define the structure of the KdV soliton turbulence. ► The 3rd and 4th moments of the KdV two-soliton are not conserved. ► Their variations lead to the decrease of the skewness and kurtosis.

221 卓越振動数を有する非白色励振を受ける非対称非線形系の非ガウス応答特性 : 入力の帯域幅による影響

Non-Gaussian response characteristics of an asymmetric nonlinear system subjected to nonwhite random excitation are investigated. Applying a previously developed analytical method, which contains moment equations method and non-Gaussian equivalent linearization technique, stationary responses are numerically computed. Non-Gaussian indicators i.e. skewness, kurtosis and equivalent linear coefficients which are defined by the 3rd and 4th order moments are considered. Responses in a family of the asymmetric parameter of the system and the dominant frequency of the excitation are plotted onto a diagram as the map of non-Gaussianity. Numerical results demonstrate the effects of bandwidth and amplitude of the excitation, as well as the asymmetric properties of the system and the dominant frequencies of the excitation, upon the non-Gaussian response characteristics.

Evaluation of Non-Gaussian Response Characteristics of an Asymmetric Nonlinear System Subjected to Nonwhite Excitation Using Higher Order Statistical Values

Non-Gaussian response characteristics of an asymmetric nonlinear system subjected to nonwhite random excitation are investigated. Applying a previously developed analytical method, which contains moment equations method and non- Gaussian equivalent linearization technique, stationary responses are numerically computed. Non-Gaussian indicators i.e. skewness, kurtosis and equivalent linear coefficients which are defined by the 3rd and 4th order moments are considered to evaluate the non-Gaussianity of the responses. Skewness and kurtosis of the response in a family of the asymmetric parameter of the system and the dominant frequency of the excitation are plotted onto a diagram as the map of non- Gaussianity. The non-Gaussian map indicates the variation of the shape of probability density function. The equivalent linear coefficients are illustrated in the same way. These numerical results demonstrate the effects of the asymmetric properties of the system and the dominant frequencies of the excitation upon the non-Gaussian response characteristics.

Problematic standard errors and confidence intervals for skewness and kurtosis

Many statistics packages print skewness and kurtosis statistics with estimates of their standard errors. The function most often used for the standard errors (e.g., in SPSS) assumes that the data are drawn from a normal distribution, an unlikely situation. Some textbooks suggest that if the statistic is more than about 2 standard errors from the hypothesized value (i.e., an approximate value for the critical value from the t distribution for moderate or large sample sizes when α = 5%), the hypothesized value can be rejected. This is an inappropriate practice unless the standard error estimate is accurate and the sampling distribution is approximately normal. We show distributions where the traditional standard errors provided by the function underestimate the actual values, often being 5 times too small, and distributions where the function overestimates the true values. Bootstrap standard errors and confidence intervals are more accurate than the traditional approach, although still imperfect. The reasons for this are discussed. We recommend that if you are using skewness and kurtosis statistics based on the 3rd and 4th moments, bootstrapping should be used to calculate standard errors and confidence intervals, rather than using the traditional standard. Software in the freeware R for this article provides these estimates.

Comparison of three different methods of moments for derivation of probability distribution parameters

Offshore structures are exposed to random wave loading in the ocean environment and hence the probability distribution of their response to wave loading is a minimum requirement for the efficient probabilistic analysis of these structures. Even if the structural system can be assumed to be linear, due to nonlinearity of the wave loading mechanism and also due to the intermittency of wave loading on members in the splash zone, the response is often non-Gaussian. The (conventional) method of moments is one of the methods which is frequently used to determine the parameters of the adopted probability model from a simulated or measured record of response. However, when higher order moments (e.g. 3rd or 4th order moments) are required for the derivation of distribution parameters, the parameter values obtained from this method show considerable scatter due to sampling variability. The purpose of this investigation was to compare the efficiency of the conventional form of the method of moments with two alternative forms of the method, i.e. with linear and the (new) low-order methods of moments. As a method of demonstration, the three different methods of moments have been applied to symmetric Pierson–Holmes distributions. The results show that in most cases the sampling variability of the parameter values determined from the two alternative forms of the method of moments is much smaller than their corresponding values derived from the conventional method of moments.

SHAPE SLOPE PARAMETER DISTRIBUTION MODELLING OF ELECTROMAGNETIC SCATTERING BY RAIN DROPS

Gamma model parameters using 2nd, 3rd and 4th moments are calculated from the drop size data of Singapore. The gamma model is simplifled into two parameter model by flnding a relation between the shape and slope parameters, and ⁄. Due to the poor correlation found between and ⁄, the drop size data is flltered based on their rain rates before a good correlation between the two parameters can be found. The -⁄ relations are then fltted for the difierent ranges of rain rate flltering. Scatter plots of and ⁄ are plotted with constant median volume diameter (D0) lines. The -⁄ relations for the difierent rain types for the tropical island of Singapore are proposed and compared with the -⁄ relations from three other countries of difierent climatic zones. T-Matrix calculations are performed to flnd the polarimetric variables at S-band by using the gamma DSD calculated from the Singapore's drop size data. The calculated difierential re∞ectivity and horizontal re∞ectivity are used along with the best -⁄ relations to flnd the gamma model parameters. The retrieved rain rate using polarimetric variables is compared with the distrometer's measured rain rate. Results show a good agreement between the retrieved rain rate and the measured rain rate. Therefore, the proposed shape slope relationship is found to be suitable for rain rate retrieval.

CHARACTERIZING MAGNETOHYDRODYNAMIC TURBULENCE IN THE SMALL MAGELLANIC CLOUD

We investigate the nature and spatial variations of turbulence in the Small Magellanic Cloud (SMC) by applying several statistical methods on the neutral hydrogen (HI) column density image of the SMC and a database of isothermal numerical simulations. By using the 3rd and 4th statistical moments we derive the spatial distribution of the sonic Mach number (M_s) across the SMC. We find that about 90% of the HI in the SMC is subsonic or transonic. However, edges of the SMC `bar' have M_s=4 and may be tracing shearing or turbulent flows. Using numerical simulations we also investigate how the slope of the spatial power spectrum depends on both sonic and Alfven Mach numbers. This allows us to gauge the Alfven Mach number of the SMC and conclude that its gas pressure dominates over the magnetic pressure. The super-Alfvenic nature of the HI gas in the SMC is also highlighted by the bispectrum, a three-point correlation function which characterizes the level of non-Gaussianity in wave modes. We find that the bispectrum of the SMC HI column density displays similar large-scale correlations as numerical simulations, however it has localized enhancements of correlations. In addition, we find a break in correlations at a scale of 160 pc. This may be caused by numerous expanding shells of a similar size.

Temporal characteristics and variability of point rainfall: a statistical and wavelet analysis

AbstractRainfall characteristics at different temporal resolutions play a significant role in sustainable urban water management. In this study we attempted to identify the temporal characteristics and variability of point rainfall measured in Melbourne, Australia. Statistical moments, lag1 autocorrelation, the Buishand's Q test for homogeneity, the Mann–Kendall (MK) test for trend and wavelet analyses for temporal variability were carried out for rainfall intensities at resolutions of 0.1, 0.5, 1, 3, 6, 12 h and for the monthly rainfall depths and proportion dry ratios. Series of rainfall intensities at different temporal scales and the monthly rainfall depths and proportion dry ratios were accumulated from the high resolution rainfall dataset for the period from 1925 to 2002. Homogeneity of rainfall intensity was found to increase as the temporal scale increases. Both rainfall intensities and monthly rainfall depths were found to be serially correlated. The 2nd, 3rd and 4th statistical moments of rainfall intensities increased as the resolution increased. While no statistically significant trends were found using the MK test, there were indications that trends are more likely as the temporal scale increases. Wavelet power spectra identified a dominant frequency scale (0.25–1 year) in the 3, 6 and 12 h rainfall intensities that were periodically observed in a 5 to 10–year cyclic order. This phenomenon could be influenced by the inter‐annual variability of the El Niño Southern Oscillation (ENSO). Copyright © 2009 Royal Meteorological Society

Velocity distribution in stellar disks: Are higher order moments negligible?

AbstractWe analysed the structure of the velocity space in galactic disks which are subject to a rotating spiral perturbation. A key assumption of the Boltzmann moment equation approach is the zero‐heat flux approximation, i.e. the neglection of third order velocity terms. We tested this assumption by performing test particle simulations for stars in a disk galaxy subject to a rotating spiral perturbation. The third order velocity moments were typically small (normalized values reach 25% of the initial velocity dispersion) and uncorrelated over almost all of the disk with the exception of the 4:1 resonance region (UHR). Even there, the values are smaller than the initial velocity dispersion. Far outside the resonance position a bimodal distribution characterizes the 3rd order moments. A qualitatively similar distribution is found for the 5th order terms. Contrary to these odd moments, the 4th order terms exceed almost everywhere the initial velocity dispersion. Therefore, an extension of the Boltzmann moment equations by only one moment, i.e. up to the third order, is not reasonable without including the fourth order terms. For all moments a large‐scale structure (either two‐armed or four‐armed) is clearly visible inside the UHR. The odd moments show a patchy irregular pattern outside the UHR, whereas the fourth order moments show also a clear large‐scale pattern. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Arbitrary-Moment Internally Mixed Dynamic Equation

Although aerosol models usually endeavor to predict the number or mass distribution of particles, many applications require other constant moments, moments that vary with particle size, or multiple moments. Here we derive the equations governing multi-component condensation/evaporation for a general distribution function that may present an arbitrary moment (either integer or non-integer) or an arbitrary combination of such moments. We used analytical solution of the evolution equation instead of a commonly used operator splitting. A variant of Bott's positive definite advection scheme was employed to simulate advection processes. Several variants of this general distribution function were tested: sum of the mass (3rd moment) and number (0th moment) distributions; an intermediate (1.5th moment) distribution; and the sum of these mass, number and intermediate distributions. These functions were tested using different evolution scenarios (condensation or evaporation) and different size grid resolutions (fin...

Quality control and quality assurance for particle size distribution measurements at an urban monitoring station in Augsburg, Germany

Long-term observations of atmospheric constituents such as aerosol particles are increasingly needed to assess their impact on climate and human health. In contrast to particle mass concentration (MC), there are currently no standardized quality control (QC) and quality assurance (QA) procedures for the measurement of particle size distribution (PSD). This study describes some fundamental QC and QA procedures associated with the collection and evaluation of a 2 year dataset between 2005 and 2006 at an urban background monitoring site in Augsburg, Germany. The considered parametres include ambient PSD between 3 nm and 10 microm (merged from a twin differential mobility and an aerodynamic particle sizer, TDMPS and APS, respectively) as well as total particle number (TNC), length (LC) and MC determined by independent instruments. The hourly 1st and 0th moment of PSD showed good correlations with the independently measured LC (R(2) = 0.86) and TNC (R(2) = 0.79), respectively, the deviation for LC with 4% and for TNC with 22% being rather small. The volume concentration (3rd moment) of hourly measured PSD and the resultant MC (when assuming a realistic apparent density of 1.5 g cm(-3)) correlated well with the independently measured MC of PM(2.5) or PM(10) (R(2) > 0.86) and showed only small deviation from PM(2.5) (1%) or PM(10) (5%), respectively. The study demonstrates that the described QC and QA measures define both a high accuracy of the PSD measurements and their long-term comparability against data obtained in similar measurement programmes.

A note on the Riemann problem for the random transport equation

We present an explicit expression to the solution of the random Riemann problem for the 1D random linear transport equation. We show that the random solution is a similarity solution and the statistical moments have very simple expressions. Furthermore, we verify that the mean, the variance, and the 3rd central moment agree quite well with Monte Carlo simulations. We point out that our approach could be useful in designing numerical methods for more general random transport problems.

Influence of S(+)-ketamine analgesia in renal intraoperative ischemia: histological study in rats

To study in rats the effect of S(+) ketamine on the renal histology after intraoperative hemorrhage. Twenty male Wistar rats, anesthetized with sodium pentobarbital, were randomly divided in 2 groups: G1 - control (n=l0) and G2 - S(+)-ketamine (n=10), both submitted to arterial hemorrhage of 30% of volemia in 3 moments (10% each 10 min) 60 min after anesthesia. G2 received S(+)-ketamine, 15 mg. kg-1, i.m., 5 min after anesthesia and 55 min before the 1st hemorrhage moment (Ml). Medium arterial pressure (MAP), rectal temperature (T) and heart rate were monitored. The animals were sacrificed in M4, 30 min after the 3rd hemorrhage moment (M3) and the kidneys and blood collected from hemorrhage were utilized for histological study and hematocrit (Ht) determination. There were significant reduction of MAP, T, and Ht. The histological study verified G1 = G2 for tubular dilation, congestion, and necrosis. The total score addition were significantly different and G2 > G 1. Hemorrhage and hypotension determined changes in kidney histology. The rise in catecholamine blood concentration probably was the cause of S(+)-ketamine-induced higher score of histological changes.

Reynolds stress models of convection in convective cores

AbstractWe investigate the properties of non-local Reynolds stress models of turbulent convection in a spherical geometry. Regularity at the centre r=0 places constraints on the behaviour of 3rd order moments. Some of the down-gradient and algebraic closure models have inconsistent behaviour at r=0. A combination of down-gradient and algebraic closures gives a consistent prescription that can be used to model convection in stellar cores.

Measurements and analysis of force and moment of caudal fin model in C-start

Abstract The unsteady hydrodynamic forces and moments acting on caudal fin models of fish with different shapes and different swing durations were experimentally measured to simulate the fish C-starts. The motion of models was characterized by rotating the model to a maximum deflection angle in an excursion time Tu and back to the initial position in a return time Td around its root-axis. Studies show that the caudal-fin plays an important role in fish C-starts and the caudal-fins with different shapes and different swing duration generate different forces and moment. In addition, the hydrodynamic forces and moments acting on the models with different shapes can be normalized by the 2nd and 3rd moments of area, respectively. The forces and moments acting on the models with different swing durations, but the same ratio of Tu to Td can also be scaled. *Supported by National Natural Science Foundation of China (Grant No. 10332040) and the Knowledge Innovation Program of the Chinese Academy of Science (Grant ...

On 3rd and 4th moments of finite upper half plane graphs

Terras [A. Terras, Fourier Analysis on Finite Groups and Applications, Cambridge Univ. Press, 1999] gave a conjecture on the distribution of the eigenvalues of finite upper half plane graphs. This is known as a finite analogue of Sato–Tate conjecture. There are several modified versions of them. In this paper, we show that this conjecture is not correct in its original form (i.e., Conjecture 1.1). This is shown for the calculations of the 3rd and 4th moments of the distribution of the eigenvalues. We remark that a weaker version of the conjecture (i.e., Conjecture 1.2) may still hold.