Autoregressive Spectral Estimates under Ignored Changes in the Mean

An analytic determination of the frequency resolution for maximum entropy and conventional Blackman‐Tukey spectral estimates is made for the case of known autocorrelation. As the signal‐to‐noise ratio decreases, the maximum entropy resolution is no better than that achievable by the Blackman‐Tukey spectral estimate. The mean resolution of an ensemble of spectra constructed from sampled data sequences agrees with the analytic result.

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On the estimation of spectra from randomly sampled signals: a method of reducing variability

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1980.0078 ◽

1980 ◽

Vol 371 (1745) ◽

pp. 235-258 ◽

Cited By ~ 20

Keyword(s):

Numerical Experiments ◽

Simulated Data ◽

Spectral Energy ◽

Mean Square ◽

Sampled Data ◽

Spectral Estimates ◽

The Mean ◽

The Stability ◽

Analytical Expressions

Spectral estimates obtained from randomly sampled data arrays incur excess variability over and above that arising from the stochastic character of the signal. In previous papers estimators have been derived for both the direct transform and the correlation plane methods. Expressions for the excess variability showed its dependence on the magnitude of the mean square of the data. Here we show how improved estimates can be obtained by filtering out parts of the spectral energy so that the actual analysis for other parts of the spectrum can be performed on data of smaller mean square. The variability associated with this filtering operation limits the improvement in the stability of estimates that can be achieved. Analytical expressions for the bias and variability of these new estimates are compared with numerical experiments on simulated data arrays.

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Transient Characteristics of Simple Systems to Modulated Random Noise

Journal of Applied Mechanics ◽

10.1115/1.3422975 ◽

1973 ◽

Vol 40 (1) ◽

pp. 73-77 ◽

Cited By ~ 12

Author(s):

R. L. Barnoski ◽

J. R. Maurer

Keyword(s):

Random Noise ◽

Structural Systems ◽

Time Varying ◽

Shaping Filter ◽

Spectral Estimates ◽

Nonstationary Response ◽

Mean Square Response ◽

Nonstationary Data ◽

The Mean ◽

Simple Systems

Discussed are the mean-square response exceedance characteristics of a single-tuned system to amplitude modulated noise. The results bear on the accuracy of spectral estimates of nonstationary data, and subsequently, relate directly to the design, analysis, and testing of structural systems in environments as gusts, earthquakes, and ignition transients. For noise correlated as an exponentially damped cosine, the nonstationary response may exceed its stationary value by a factor in excess of two. A time-varying shaping filter explanation is offered for this behavior. For white noise, such exceedances do not occur.

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APPARENT LONG MEMORY IN TIME SERIES AS AN ARTIFACT OF A TIME-VARYING MEAN: CONSIDERING ALTERNATIVES TO THE FRACTIONALLY INTEGRATED MODEL

Macroeconomic Dynamics ◽

10.1017/s1365100509991052 ◽

2010 ◽

Vol 14 (S1) ◽

pp. 59-87 ◽

Cited By ~ 11

Author(s):

Richard A. Ashley ◽

Douglas M. Patterson

Keyword(s):

Time Series ◽

Time Variation ◽

Long Memory ◽

Structural Breaks ◽

Integrated Model ◽

Time Varying ◽

Penalized Spline ◽

Spectral Estimates ◽

The Mean ◽

Modeling Strategy

Structural breaks and switching processes are known to induce apparent long memory in a time series. Here we show that any significant time variation in the mean renders the sample correlogram (and related spectral estimates) inconsistent. In particular, smooth time variation in the mean—i.e., even a weak trend, either stochastic or deterministic—induces apparent long memory. This apparent long memory can be eliminated by either high-pass filtering or by detrending. Here we demonstrate the effectiveness in this regard of nonlinear detrending via penalized-spline nonparametric regression. A time-varying mean can be of economic interest in its own right. This suggests that isolating out and separately examining both a local mean (i.e., a nonlinear trend or the realization of a stochastic trend) and deviations from it is preferable as a modeling strategy to simply estimating a fractionally integrated model. We illustrate the superiority of this strategy using stock return volatility data.

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Photo-electric Hβ and uvby photometry

Symposium - International Astronomical Union ◽

10.1017/s0074180900053407 ◽

1966 ◽

Vol 24 ◽

pp. 170-180

Author(s):

D. L. Crawford

Keyword(s):

Narrow Band ◽

Line Strength ◽

Interference Filter ◽

B Stars ◽

Relative Line ◽

The Mean ◽

F Stars ◽

Two Parameters ◽

Filter Photometry ◽

The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

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A one-dimensional self-gravitating stellar gas

Symposium - International Astronomical Union ◽

10.1017/s0074180900105261 ◽

1966 ◽

Vol 25 ◽

pp. 46-48 ◽

Cited By ~ 2

Author(s):

M. Lecar

Keyword(s):

Gravitational Field ◽

Phase Space ◽

Motion Picture ◽

Space Distribution ◽

Two Dimensional ◽

One Dimensional ◽

Phase Space Distribution ◽

Dimensional Phase Space ◽

The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

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The motion of a lunar orbiter

Symposium - International Astronomical Union ◽

10.1017/s0074180900105686 ◽

1966 ◽

Vol 25 ◽

pp. 373

Author(s):

Y. Kozai

Keyword(s):

Degrees Of Freedom ◽

Dimensional Space ◽

Artificial Satellite ◽

Equations Of Motion ◽

Triaxial Ellipsoid ◽

The Moon ◽

Secular Motion ◽

The Earth ◽

Close Satellite ◽

The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

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On nearly-commensurable periods in the restricted problem of three bodies, with calculations of the long-period variations in the interior 2:1 case

Symposium - International Astronomical Union ◽

10.1017/s0074180900105480 ◽

1966 ◽

Vol 25 ◽

pp. 197-222 ◽

Cited By ~ 4

Author(s):

P. J. Message

Keyword(s):

Periodic Solution ◽

Periodic Solutions ◽

Large Amplitude ◽

Restricted Problem ◽

Small Amplitude ◽

Minor Planets ◽

Long Period ◽

Numerical Integrations ◽

Period Variations ◽

The Mean

An analytical discussion of that case of motion in the restricted problem, in which the mean motions of the infinitesimal, and smaller-massed, bodies about the larger one are nearly in the ratio of two small integers displays the existence of a series of periodic solutions which, for commensurabilities of the typep+ 1:p, includes solutions of Poincaré'sdeuxième sortewhen the commensurability is very close, and of thepremière sortewhen it is less close. A linear treatment of the long-period variations of the elements, valid for motions in which the elements remain close to a particular periodic solution of this type, shows the continuity of near-commensurable motion with other motion, and some of the properties of long-period librations of small amplitude.To extend the investigation to other types of motion near commensurability, numerical integrations of the equations for the long-period variations of the elements were carried out for the 2:1 interior case (of which the planet 108 “Hecuba” is an example) to survey those motions in which the eccentricity takes values less than 0·1. An investigation of the effect of the large amplitude perturbations near commensurability on a distribution of minor planets, which is originally uniform over mean motion, shows a “draining off” effect from the vicinity of exact commensurability of a magnitude large enough to account for the observed gap in the distribution at the 2:1 commensurability.

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the effects of resonance with Jupiter in the system of short-period comets

International Astronomical Union Colloquium ◽

10.1017/s0252921100033959 ◽

1974 ◽

Vol 22 ◽

pp. 193-203

Author(s):

L̆ubor Kresák

Keyword(s):

Structural Effects ◽

Order Resonance ◽

Mean Motion ◽

Short Period ◽

The Mean ◽

Compound Effect ◽

Low Order

AbstractStructural effects of the resonance with the mean motion of Jupiter on the system of short-period comets are discussed. The distribution of mean motions, determined from sets of consecutive perihelion passages of all known periodic comets, reveals a number of gaps associated with low-order resonance; most pronounced are those corresponding to the simplest commensurabilities of 5/2, 2/1, 5/3, 3/2, 1/1 and 1/2. The formation of the gaps is explained by a compound effect of five possible types of behaviour of the comets set into an approximate resonance, ranging from quick passages through the gap to temporary librations avoiding closer approaches to Jupiter. In addition to the comets of almost asteroidal appearance, librating with small amplitudes around the lower resonance ratios (Marsden, 1970b), there is an interesting group of faint diffuse comets librating in characteristic periods of about 200 years, with large amplitudes of about±8% in μ and almost±180° in σ, around the 2/1 resonance gap. This transient type of motion appears to be nearly as frequent as a circulating motion with period of revolution of less than one half that of Jupiter. The temporary members of this group are characteristic not only by their appearance but also by rather peculiar discovery conditions.

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Contrast of Filament Bright Rims

International Astronomical Union Colloquium ◽

10.1017/s0252921100025628 ◽

1994 ◽

Vol 144 ◽

pp. 365-367

Author(s):

E. V. Kononovich ◽

O. B. Smirnova ◽

P. Heinzel ◽

P. Kotrč

Keyword(s):

High Altitude ◽

Line Profile ◽

Line Center ◽

Magnetic Structures ◽

The Mean

AbstractThe Hα filtergrams obtained at Tjan-Shan High Altitude Observatory near Alma-Ata (Moscow University Station) were measured in order to specify the bright rims contrast at different points along the line profile (0.0; ± 0.25; ± 0.5; ± 0.75 and ± 1.0 Å). The mean contrast value in the line center is about 25 percent. The bright rims interpretation as the bases of magnetic structures supporting the filaments is suggested.

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