Low-frequency Estimates Research Articles

The Divergence of High- and Low-Frequency Estimation: Causes and Consequences

Financial analysts typically estimate volatilities and correlations from monthly or higher-frequency returns when determining the optimal composition of a portfolio. Although it is widely acknowledged that these measures are not necessarily stationary across samples, most analysts assume implicitly that, within sample, volatilities scale with the square root of time and correlations estimated from high-frequency returns are similar to correlations estimated from low-frequency returns. Evidence does not support this view. Instead, evidence shows that relative asset values often evolve through time in ways that are highly inconsistent with their high-frequency volatilities and correlations. As a consequence, portfolios that are optimal based on high-frequency returns often lead to significantly suboptimal results for investors with long horizons. The causes and consequences of this discrepancy are analyzed by the article’s authors, as well as presenting a framework for constructing portfolios that balance short-horizon and long-horizon optimality.

The Divergence of High- and Low-Frequency Estimation: Implications for Performance Measurement

The Divergence of High- and Low-Frequency Estimation: Implications for Performance Measurement

Resolvent estimates on symmetric spaces of noncompact type

In this article we prove resolvent estimates for the Laplace-Beltrami operator or more general elliptic Fourier multipliers on symmetric spaces of noncompact type. Then the Kato theory implies time-global smoothing estimates for corresponding dispersive equations, especially the Schrodinger evolution equation. For low-frequency estimates, a pseudo-dimension appears as an upper bound of the order of elliptic Fourier multipliers. A key of the proof is to show a weighted $L^{2}$-continuity of the modified Radon transform and fractional integral operators.

Variation in low-frequency estimates of sound levels based on different units of analysis.

The measurement and analysis of underwater sound is a complicated process because of the variable durations of contributing sources and constantly changing water column dynamics. Because the ambient sound distribution does not always follow a Gaussian structure and may be nonstationary in time, analysis over an extended period is required to accurately characterize the data. Utilizing recordings from the Indian Ocean, the temporal variation in ambient sound including transient signals was examined using multiple processing window lengths and subsampling intervals. Results illustrate the degree of uncertainty in sound levels based on different units of analysis. The average difference between sound level estimates in the 10-30 Hz band due to subsampling was 2 dB and as high as 4 dB. The difference in the full band (5-110 Hz) was as high as 6 dB. Longer averaging windows (200 vs 60 s) resulted in larger variations over different subsampling intervals. This work demonstrates how sampling protocols within a single dataset can influence results and acknowledges that comparative studies at the same location but with different sampling protocols can be substantial if signal processing parameters are not statistically accounted for to confirm interpretation of results and observed trends.

Transmission eigenvalues for Maxwell’s equations in isotropic absorbing media with frequency-dependent electrical parameters

We study the interior transmission problem for Maxwell’s equations in isotropic absorbing media, taking into account the frequency dependence of the electrical parameters of the media. Using low-frequency estimates together with the Fredholm analytic theory, we prove the discreteness of transmission eigenvalues.

Shifting Boundaries: An Experimental Evaluation of a Dating Violence Prevention Program in Middle Schools

We randomly assigned the Shifting Boundaries interventions to 30 public middle schools in New York City, enrolling 117 sixth and seventh grade classes (over 2,500 students) to receive a classroom, a building, a combined, or neither intervention. The classroom intervention included a six-session curriculum emphasizing the laws and consequences for perpetrators of dating violence and sexual harassment (DV/H), the social construction of gender roles, and healthy relationships. The building-based intervention included the use of building-based restraining orders, higher levels of faculty/security presence in safe/unsafe "hot spots" mapped by students, and posters to increase DV/H awareness and reporting. Student surveys were implemented at baseline, immediately after the intervention, and 6-months post-intervention. As hypothesized, behaviors improved as a result of the interventions. The building-only and the combined interventions were effective in reducing sexual violence victimization involving either peers or dating partners at 6-months post-intervention. This was mirrored by reductions in sexual violence perpetration by peers in the building-only intervention. While the preponderance of results indicates that the interventions were effective, an anomalous result (increase in sexual harassment victimization reports that was contradicted by lower frequency estimates) did emerge. However, after analysis these anomalous results were deemed to be most likely spurious. The success of the building-only intervention alone is important because it can be implemented with very few extra costs to schools.

On the oscillation limits of HBT cross-coupled oscillators

In evaluating the potential of a given integrated-circuit technology, the negative conductance approach is used to estimate a maximum frequency limit for the ability of Heterojunction Bipolar Transistor (HBT) cross-coupled architecture to function as an oscillator at high frequencies. In this paper, the simple low-frequency estimation of the negative conductance, commonly used in the literature, is extended by deriving a new expression that takes into account the HBT parasitics. An expression for the frequency at which the negative conductance of the circuit crosses zero is given, which gives maximum frequency of oscillation for an ideal tank (no tank losses). In addition, the effect of the feedback capacitor, which is commonly added for direct current (DC) decoupling and boosting the negative conductance, is analyzed and new insight on the choice of the value of this capacitance is introduced. The results were proven by simulations using SiGe HBT transistors with an ft of 190 GHz.

A non-linear observer for attitude estimation of a fixed-wing unmanned aerial vehicle without GPS measurements

In this paper we propose a simple non-linear observer for attitude estimation based only on output from a typical inertial measurement unit (IMU) and dynamic pressure sensor embarked on a low-cost unmanned aerial vehicle. In particular, we aim to provide a good quality attitude estimate in the absence of global positioning system (GPS) ground truth and with potential low-frequency bias and high-frequency noise in the IMU sensor measurements. In addition, the case where the IMU only provides gyrometer and accelerometer outputs is considered; that is, there is no magnetometer output or it cannot be used due to local magnetic disturbances such as are common on a vehicle with electric motors. The proposed observer uses a simple centripetal force model (based on gyrometer and dynamic pressure measurements), augmented by a first-order dynamic model for angle of attack, to estimate non-inertial components of the acceleration. This estimate is used to correct the accelerometer output to provide a low-frequency estimate of the gravitational direction. This inertial direction, along with the gyrometer output, is then used to drive a fully non-linear attitude observer posed on the orthogonal group of rotation matrices SO(3). The observer is augmented with an integral state that ensures compensation of gyrometer bias. The resulting observer is simple to implement and fully non-linear. Experimental results are provided on a real-world data set and the performance of the filter is evaluated against the output from a full GPS/inertial navigation system (INS) that was available for the data set.

Nonlinear stability of periodic traveling wave solutions of systems of viscous conservation laws in the generic case

Extending previous results of Oh–Zumbrun and Johnson–Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling wave solutions of viscous systems of conservation laws for systems of generic type, removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions. Key to our analysis is a nonlinear cancellation estimate observed by Johnson and Zumbrun, along with a detailed understanding of the Whitham averaged system. The latter motivates a careful analysis of the Bloch perturbation expansion near zero frequency and suggests factoring out an appropriate translational modulation of the underlying wave, allowing us to derive the sharpened low-frequency estimates needed to close the nonlinear iteration arguments.

A New Visually Evoked Cerebral Blood Flow Response Analysis Using a Low-Frequency Estimation

Transcranial Doppler (TCD) has been widely used to monitor cerebral blood flow velocity (BFV) during the performance of cognitive tasks compared with repose periods. Although one of its main advantages is its high temporal resolution, only some of the previous functional TCD studies have focused on the analysis of the temporal evolution of the BFV signal and none of them has performed a spectral analysis of the signal. In this study, maximum BFV data in both posterior cerebral arteries was monitored during a visual perception task (10 cycles of alternating darkness and illumination) for 23 subjects. A peak was located in the low-frequency band of the spectrum of the maximum BFV of each subject both during visual stimulation and repose periods. The frequency of this peak was in the range between 0.037 and 0.098 Hz, depending on the subject, the vessel and the experimental condition. The component of the signal at this frequency, which is associated with the slow variations caused by the visual stimuli, was estimated. That way, the variations in BFV caused by the experimental stimuli were isolated from the variations caused by other factors. This low-frequency estimation signal was used to obtain parameters about the temporal evolution and the magnitude variations of the BFV in a reliable way, thus, characterizing the neurovascular coupling of the participants. (E-mail: brey@labhuman.i3bh.es)

On Asymptotic Stability of Noncharacteristic Viscous Boundary Layers

We extend our recent work with Kevin Zumbrun on long-time stability of multi-dimensional noncharacteristic viscous boundary layers of a class of symmetrizable hyperbolic-parabolic systems. Our main improvements are (i) to establish the stability for a larger class of systems in dimensions $d\geq2$, yielding the result for certain magnetohydrodynamics (MHD) layers, and (ii) to drop a technical assumption on the so-called glancing set which was used in previous works. We also provide a different proof of low-frequency estimates by employing the method of Kreiss' symmetrizers, giving an alternative to the previous one relying on detailed derivation of pointwise bounds on the resolvent kernel.

HRV and BPV neural network model with wavelet based algorithm calibration

The heart rate and blood pressure power spectrum, especially the power of the low frequency (LF) and high frequency (HF) components, have been widely used in the last decades for quantification of both autonomic function and respiratory activity. Discrete Wavelet Transform (DWT) is an important tool in this field. The paper presents a LF and HF fast estimator that uses artificial neural networks and Daubechies DWT processing techniques. Radial Basis Function and Multilayer Perceptron neural networks were designed and implemented for fast assessment of cardiovascular autonomic nervous system control. The training values to design the networks were obtained after heart rate and blood pressure wavelets processing. The designed neural structures assure a faster evaluation tool of the sympathetic and parasympathetic autonomic nervous system control of the cardiovascular function.

Predicting Pure-Tone Thresholds with Dichotic Multiple Frequency Auditory Steady State Responses

The accuracy of dichotic multiple frequency auditory steady state in predicting pure-tone thresholds at 0.5, 1, 2, and 4.0 kHz compared to an ABR protocol (click and tone burst at 0.5 kHz) were explored in a group of 25 hearing-impaired subjects across the degree and configuration spectrum. Mean steady state thresholds were within 14, 18, 15, and 14 dB of the pure tones at 0.5, 1, 2, and 4 kHz, compared to the tone-burst ABR at 0.5 kHz pure-tone difference of 24 dB, and a click-evoked pure-tone (2-4 kHz) difference of 9 dB. Recording time for the steady state protocol was 28 minutes (+/- 11) compared to 24 minutes (+/- 9) of the ABR protocol. Degree of loss had a significant effect on steady state; configuration of hearing loss had a limited effect. Mf ASSR predicted thresholds with relative accuracy although some configurations showed discrepancies for low-frequency estimates.

Optimized two-frequency phase-measuring-profilometry light-sensor temporal-noise sensitivity.

Temporal frame-to-frame noise in multipattern structured light projection can significantly corrupt depth measurement repeatability. We present a rigorous stochastic analysis of phase-measuring-profilometry temporal noise as a function of the pattern parameters and the reconstruction coefficients. The analysis is used to optimize the two-frequency phase measurement technique. In phase-measuring profilometry, a sequence of phase-shifted sine-wave patterns is projected onto a surface. In two-frequency phase measurement, two sets of pattern sequences are used. The first, low-frequency set establishes a nonambiguous depth estimate, and the second, high-frequency set is unwrapped, based on the low-frequency estimate, to obtain an accurate depth estimate. If the second frequency is too low, then depth error is caused directly by temporal noise in the phase measurement. If the second frequency is too high, temporal noise triggers ambiguous unwrapping, resulting in depth measurement error. We present a solution for finding the second frequency, where intensity noise variance is at its minimum.

Modelling the effect of fluid communication on velocities in anisotropic porous rocks

An inclusion-based anisotropic poroelasticity model (IBAPM) has been developed from the J. D. Eshelby (1957, Proceedings of the Royal Society of London Series A, 241, 376–396) and T. Mura (1987, Micromechanics of Defects in Solids, Martinus Nijhoff, Dordrecht) theories. Eshelby’s interaction energy approach is employed to calculate the effective elastic constants of a solid containing dilute pores, since it offers two approximations : one corresponding to the condition of constant load and the other to the condition of constant displacement. The effect of pore fluid communication on the poroelasticity of a porous rock is modelled via pore connectivity. A totally isolated pore system implies that pore pressure is equilibrated within each individual pore only and may vary from pore to pore, depending on the shape and orientation of each pore. In terms of the local flow mechanism, this gives us a high-frequency estimate of the effective elastic moduli. The low-frequency estimate, on the other hand, is modelled by a communicating pore system. In this case all pores are assumed to be connected and, consequently, pore pressure is equilibrated within the whole pore system. Other related problems discussed in the paper include : (1) extension of the model to the case of pores having arbitrary orientations, (2) extension of the non-interacting model to higher pore concentrations and (3) consistency checks of IBAPM with previous models. In particular the low-frequency version of the model is compared with the anisotropic version of the Gassmann model (R. J. S. Brown and J. Korringa, 1975, Geophysics, 40, 608–616) . Finally the model is applied to the laboratory measurements reported by J. S. Rathore, E. Ejaer, R. M. Holt and L. Renlie (1995, Geophys. Prosp., 43, 711–728) .

Self-consistent retrieval of source parameters using mantle waves

Abstract The large number of high-quality stations from global networks (e.g., IRIS, GEOSCOPE) allows for rapid and robust recovery of source parameters of large earthquakes. We present a self-consistent analysis of surface waves in terms of directivity parameters. The boxcar is often used to recover source parameters but is rarely a faithful representation of an event's time function. We demonstrate that more reliable estimates of directivity parameters can be obtained when we take into account the source time function (STF) of the event. A low-frequency STF is obtained from first (R1) and second (R2) orbit Rayleigh waves in the range 2 to 15 mHz, with a spectral synthesis and inversion method. We measure the differential amplitudes between data and 3D synthetics. We use the R1/R2 ratio of differential amplitudes to invert, in a single narrow-frequency band, for the event's apparent rupture azimuth and velocity. For the Mw 8.1 Chile 1995 event, data are consistent with unilateral southward propagation, with a velocity of about 2.4 km/sec. For the Mw 7.9 Mexico 1995 earthquake, the rupture propagated toward the NW at about 2.0 km/sec. Our low-frequency estimates agree with broadband studies of both events and can be retrieved rapidly on a routine basis after a large earthquake.

Estimating the long-run relationship between interest rates and inflation: A response to McCallum

This note demonstrates that Bennett McCallum's recent critique of low-frequency estimates of macroeconomic relationships is of little empirical significance. It also demonstrates that readily available and frequently used techniques can be used to diagnose the problem McCallum raises. Finally, it shows that the standard critique of expectational distributed lags is not warranted once the role of learning by economic agents is recognized.

On low-frequency estimates of long-run relationships in macroeconomics

A number of recent studies have attempted to test propositions concerning ‘long-run’ economic relationships by means of frequency-domain time-series techniques that concentrate attention on low-frequency comovements of variables. The present paper emphasizes that many of these propositions involve expectational relationships that are not inherently related to specific frequencies or periodicities. Thus the association of low-frequency time-series test statistics with long-run economic propositions is not generally warranted. That such an association can be misleading is demonstrated by analysis of examples taken from notable papers by Geweke, Lucas, and Summers.

Inverse scattering for an exterior Dirichlet problem

In this paper we consider scattering due to a metallic cylinder which is in the field of a wire carrying a periodic current. The aim of the paper is to obtain information such as the location and shape of the cylinder with a knowledge of a far-field measurement in between the wire and the cylinder. The same analysis is applicable in acoustics in the situation that the cylinder is a soft-wall body and the wire is a line source. The associated direct problem in this situation is an exterior Dirichlet problem for the Helmholtz equation in two dimensions. We present an improved low-frequency estimate for the solution of this problem using integral equation methods, and our calculations on inverse scattering are accurate to this estimate. The far-field measurements are related to the solutions of boundary integral equations in the low-frequency situation. These solutions can be expressed in terms of mapping function which maps the exterior of the unknown curve onto the exterior of a unit disk. The coefficients of the Laurent expansion of the conformal transformations can be related to the far-field coefficients. The first far-field coefficient leads to the calculation of the distance between the source and the cylinder. The other coefficients are determined by placing the source in a different location and using the corresponding new far-field measurements.

On the Observational Inequivalence of Classical and Keynesian Models

Previous articleNext article No AccessCommentsOn the Observational Inequivalence of Classical and Keynesian ModelsBennett T. McCallumBennett T. McCallum Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Journal of Political Economy Volume 87, Number 2Apr., 1979 Article DOIhttps://doi.org/10.1086/260765 Views: 8Total views on this site Citations: 34Citations are reported from Crossref Copyright 1979 The University of ChicagoPDF download Crossref reports the following articles citing this article:Gary Koop, M. Hashem Pesaran, Ron P. 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