Similarity law in spectral estimation of a time series. IV

A continuation of V. Yu. Terebizh, Astrofizika,40, 139, 273, 413 (1997). An explicit representation is found for the Fisher matrix for spectral density, enabling one to calculate the lower limit of the variance of an arbitrary unbiased density estimate. Basic equations describing smoothed density estimates are given for comparison with exact results. By numerical modeling based on the example of an AR-1 process, it is shown that the relative accuracy q of estimation of density is some universal function of the parameter w = (F -1)/N, where F is the number of parameters underlying the estimate and N is the length of the time series. The relationship q = θ(w), a similarity law, explains why a number of density estimates proposed earlier (Schuster’s periodogram, in particular) proved to be statistically inconsistent. It is just these estimates that presume an extremely detailed model of spectral density. The need for the complexity of the model to be consistent with the observational data follows from the limitation of information about the spectrum of the random process included in a sample of readings from a series of fixed volume. Translated from Astrofizika, Vol. 41, No. 1. pp. 113–122, January-March, 1998.     

Similarity law in spectral estimation of a time series. III

A continuation of [V. Yu. Terebizh, Astrofizika, 40, 139 (1997); 40, 273 (1997)]. An exact representation is found for the main quantity characterizing the inverse problem: the Fisher matrix for the covariation coefficients. Application of the (Rao-Cramer) information inequality enabled us to find the lower limit of the dispersion of an arbitrary unbiased estimate of the covariation coefficients. The conclusions are illustrated by an example of a first-order autoregression process. Translated from Astrofizika, Vol. 40, No. 3, pp. 413–423, August, 1997.     

Similarity law in the spectral estimation of a time series. I

The inverse problem of finding a consistent natural estimate of spectral density is studied using the example of a stationary Gaussian process. The initial equations are given and the main results are briefly described in the first part of the paper. Translated from Astrofizika, Vol. 40, No. 1, pp. 139–148, January–March, 1997.     

Similarity law in the spectral estimation of a time series. II

In the second part of this papersee [V. Yu. Terebizh, Astrofizika,40, 139 (1997)] we give results of an auxiliary nature for a first-order autoregression process. A formal statement of the problem of estimating the spectral density of a time series is given as an inverse problem of mathematical physics. The numbering of sections in this and the next three papers in this series is a continuation of the numbering in the first paper, printed in the preceding issue of the journal [Astrofizika,40, 139–148 (1997)]. Translated from Astrofizika, Vol. 40, No. 2, pp. 273–280, April–June, 1 997.     

The analysis of indexed astronomical time series V. Fitting sinusoids to high-speed photometry

The estimation of the frequency, amplitude and phase of a sinusoid from observations contaminated by correlated noise is considered. It is assumed that the observations are regularly spaced, but may suffer missing values or long time stretches with no data. The typical astronomical source of such data is high-speed photoelectric photometry of pulsating stars. The study of the observational noise properties of nearly 200 real data sets is reported: noise can almost always be characterized as a random walk with superposed white noise. A scheme for obtaining weighted non-linear least-squares estimates of the parameters of interest, as well as standard errors of these estimates, is described. Simulation results are presented for both complete and incomplete data. It is shown that, in finite data sets, results are sensitive to the initial phase of the sinusoid.     

Reflection effect in close binaries. V. Effects of reflection on spectral line formation

The effects of reflection on the formation of spectral lines is investigated. We have assumed a purely scattering atmosphere and studied how the equivalent widths change due to irradiation from the secondary. Generally, the flux in the lines is increased at all frequency points, the cores of the lines receiving more flux than the wings. Moreover, the proximity of the secondary component changes the equivalent widths considerably. The further away the secondary is from the primary the higher are the equivalent widths.     

Simultaneous photometric and spectral analysis of a new outburst of V1686 Cyg

We present an analysis of the optical observations of Herbig Ae/Be(HAeBe) star V1686 Cyg,which is associated with a small isolated star-forming region around HAeBe star BD+40?4124. We observed this star as a part of our project investigating young eruptive stars. Observations were conducted on the 2.6-m telescope of Byurakan Observatory from 2015 to 2017. In this period, we obtained direct images of V1686 Cyg and 14 medium-and low-resolution spectra. In the course of observations, we noticed that this star underwent an atypical brightness outburst. After data reduction, we found that the full rise and decline in the brightness of V1686 Cyg had an amplitude of almost 3 magnitudes and lasted about 3 months.We were also able to track changes in the stellar spectrum during the outburst, which are correlated with the photometric variations.     

Astronomical time series analysis in South Africa

This review is essentially a bibliography. In the first part, work done locally on period-finding methods is discussed. Some of the topics referred to are: periodogram significance testing, identification of non-sinusoidal periodicities, and computational shortcuts useful for calculating periodograms of large data sets. A number of aspects of period-finding in ray astronomy are briefly mentioned: these include various test statistics for the presence of a periodicity, the influence of oversampling on significance levels, estimation of the pulse shape, and the specification of a flux limit in the case of a non-detection. The second part of the review deals with the analysis of stochastic astronomical time series. Topics dealt with are ARMA modelling, Kalman filtering, problems associated with O-C analyses, and continuous time ARMA modelling. Two aspects of bivariate astronomical time series are touched on, namely time domain transfer function modelling and the estimation of the lag between two irregularly observed series.     

Sur les petits diviseurs I. (complement). Les series de V. Zeipel [on the small divisors. I. (complement). the V. Zeipel's series]

Résumé On démontre ici la convergence des séries de v. Zeipel excluant les termes à courte période de la fonction perturbatrice.

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The convergence of the v. Zeipel's series excluding the short periodic terms of the perturbation function has been established.

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Cette remarque est due à M.N.N. Vassiliéff, à qui l'auteur expresse ici sa reconnaissance.     

The quiescent spectral energy distribution of V404 Cyg

We present a multiwavelength study of the black hole X-ray binary V404 Cyg in quiescence, focusing upon the spectral energy distribution (SED). Radio, optical, ultraviolet (UV) and X-ray coverage is simultaneous. We supplement the SED with additional non-simultaneous data in the optical through infrared where necessary. The compiled SED is the most complete available for this, the X-ray and radio brightest quiescent black hole system. We find no need for a substantial contribution from accretion light from the near-UV to the near-IR, and in particular the weak UV emission constrains published spectral models for V404 Cyg. We confirm that no plausible companion spectrum and interstellar extinction can fully explain the mid-IR, however, and an infrared (IR) excess from a jet or cool disc appears to be required. The X-ray spectrum is consistent with a  Γ∼ 2  power law as found by all other studies to date. There is no evidence for any variation in the hardness over a range of a factor of 10 in luminosity. The radio flux is consistent with a flat spectrum (in   f _ν  ). The break frequency between a flat and optically thin spectrum most likely occurs in the mid or far-IR, but is not strongly constrained by these data. We find the radio to be substantially variable but with no clear correlation with X-ray variability.     

Two-dimensional spectroscopic time series of solar granulation

In this paper we investigate the dynamics of the solar granulation by analyzing time series of 2D spatially highly resolved spectrograms. These were obtained by spatial scans covering a field of 12 8″ × 20″. The advantage of this method is a high spectral resolution, however, the data are not taken simultaneously and to cover the field described above 50 exposures taken sequentially in time are necessary. Therefore, to obtain one map about 2 minutes are required. Plots of the evolution of different line parameters are given as well as the decay of correlation functions. The correlations between the first map of line parameters and successive maps (which are separated by about 2 minutes) were investigated showing a rapid decay down to a correlation coefficient of 0.4 within 4 minutes, the velocity pattern in the field observed varies on smaller time scales. The temporal variation of correlation between the line parameters for the different lines shows a periodic signal related to 5-min oscillations which could not be totally filtered. The evolution of the correlation functions between line parameters is analyzed which gives an error estimate of all correlation values found in the literature. For the first time it is explicitly shown how evolution in a selected photospheric field influences the evolution of granular/intergranular structures.     

Two-dimensional spectroscopic time series of solar granulation

In this paper we investigate the dynamics of the solar granulation by analyzing time series of 2D spatially highly resolved spectrograms. These were obtained by spatial scans covering a field of 12 8″ × 20″. The advantage of this method is a high spectral resolution, however, the data are not taken simultaneously and to cover the field described above 50 exposures taken sequentially in time are necessary. Therefore, to obtain one map about 2 minutes are required. Plots of the evolution of different line parameters are given as well as the decay of correlation functions. The correlations between the first map of line parameters and successive maps (which are separated by about 2 minutes) were investigated showing a rapid decay down to a correlation coefficient of 0.4 within 4 minutes, the velocity pattern in the field observed varies on smaller time scales. The temporal variation of correlation between the line parameters for the different lines shows a periodic signal related to 5-min oscillations which could not be totally filtered. The evolution of the correlation functions between line parameters is analyzed which gives an error estimate of all correlation values found in the literature. For the first time it is explicitly shown how evolution in a selected photospheric field influences the evolution of granular/intergranular structures.     

The Fourier-Chebychev approximation for time series with a great many terms

A new type of approximation is proposed to evaluate Fourier series with a great many terms. It combines Fourier series and Chebychev polynomials to represent time series over a finite time interval. On one side, the high frequencies are approximate multiples of a basic frequency to represent short periodic terms; on the other side, the slowly variable functions of the time, on a given interval, which contain terms with long periods, are approximated by Chebychev polynomials. Application is made in case of the Lunar Theory ELP which contains about 30 000 trigonometric terms. The computing time necessary to evaluate coordinates is very much reduced when we give to series the intermediary representation inF-T form, as compared to a direct substitution of the time in the arguments.One shows also on a numerical example, that the Fourier-Chebychev approximation smoothly degrades outside its range of representation.Bureau des Longitudes. Equipe de Recherche Associée au CNRS     

Orbit determination from a short arc through the coefficients of power series in time

Summary Attention is called to the method(s) of orbit determination as mentioned in the heading, deriving the values of the coefficients to be applied, by adjustment by least squares, of the power series in either rectangular coordinate, to the values observed, of this, -as initiated in the past by several authors, among others by Silva and De Caro in the 30's and 40's, and critically studied by the present author in the 50ies, with merely a short note published (Lund Ann. 12, C1–C7 (1953)). The avail of modern computers for overcoming the numerical trouble by taking into account the terms of higher order, than those until the fourth necessary for the orbit computation — an account unevitable for a seccessful accomplishment, as shown by the author — may justify a resumed interest in those methods, as the only ones allowing to extract just the information contained in the observations of such a short arc — without any hypothesis in advance.     

Ultraviolet spectral variations of FK Comae and V 1794 Cygni

Ultraviolet spectra of FK Comae and V1794 Cygni observed with the Hubble Space Telescope Cosmic Origins Spectrograph (HST COS) and the International Ultraviolet Explorer (IUE) satellites were analyzed for the period 1981–2011. Temporal variations of line fluxes of the O I 1306 Å, C II 1336 Å, C IV 1550 Å, He II 1640 Å and Mg II k & h 2800 Å, produced in the transition regions and chromospheres of these stars, imply variations in density and temperature changes in the line emitting regions as a result of the rapid rotation and magnetic fields responsible for stellar activity. Results are consistent with the models of Ramsey et al. (1981), Oliveira and Foing (1999), and Korhonen et al. (2000).     

一种新的多变量时间序列数据异常检测方法

介绍了一种通过建立多变量时间序列数据相似度矩阵,对相似度矩阵进行转换以最大化数据之间的相关性,并采用随机游走模型计算数据点之间的连接系数来检测数据点上异常的方法。该方法充分利用了数据之间的相关性,有效减少了数据中不同程度噪声对异常检测的影响,检测过程中的漏报率和误报率明显减少,通过仿真实验验证了该方法的有效性。     

A compact representation of gamma-ray burst time series

Multiscale edge detection (MSED), using wavelet transform extrema, provides a robust method to compress the information in a transient signal. We apply this to gamma-ray burst (GRB) time series. Multiscale edge detection can be used to quantify the variability, identify structures (e.g. FREDs), and suppress noise. We present preliminary results of MSED applied to BATSE 64ms discsc data.     

On the existence of a low-dimensional chaotic attractor in the short-term solar UV time series

A mixture of periodic and chaotic components makes the detection of chaos difficult. The periodic components are sought in the solar UV time series by the Maximum Entropy Method and are removed by a digital notch filter. The filtered output is subjected to investigation for chaotic behavior by three different techniques. (1) Fixed-size method for attractor dimension determination; (2) sensitive initial dependence via prediction error; (3) trajectory direction estimation. All the investigation points to the existence of a chaotic attractor of fractional dimension.