Добірка наукової літератури з теми "Yield Curve Inversion"
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Статті в журналах з теми "Yield Curve Inversion"
1
Ackermann, Hans D., Leroy W. Pankratz, and Danny Dansereau. "Resolution of ambiguities of seismic refraction traveltime curves." GEOPHYSICS 51, no. 2 (February 1986): 223–35. http://dx.doi.org/10.1190/1.1442082.
Повний текст джерелаАнотація:
Ambiguities are inherent in seismic refraction traveltime curves based on first arrivals recorded from a multi‐layered medium. Even for reversed profiles, inflections of traveltime curves caused by the onset of arrivals from successively deeper horizons frequently cannot be delineated from those caused by lateral geologic changes. In addition, the secondary arrivals which may represent essential portions of a traveltime curve are not available. Numerous inversions having different geologic implications are possible. Ambiguities may be resolved by using multiple shotpoints for each spread and combining their individual first‐arrival traveltime curves to yield a consistent set of curves for each refracting horizon. A set of rules applies for combining individual traveltime curves based on reversed, split, and offset profile configurations. The combined curves lend themselves to a unique inversion.
2
Benenson, Olga. "Application of the Yield Curve Inversion Indicator to Determine the Current Phase of the Stock Market." European Journal of Management Issues 30, no. 4 (December 1, 2022): 235–42. http://dx.doi.org/10.15421/192221.
Повний текст джерелаАнотація:
Purpose: To establish the possibility of using the indicator of the inversion of the difference in the yield curve of 10-year and 2-year US Treasury bonds to determine the current phase of the stock market, predict the future direction of market movement and improve the efficiency of managerial investment decisions.
Design/Method/Approach: The following methods were used when writing the paper: empirical – to carry out experimental checks of the revealed regularities; graphic - for a visual presentation of research results; systematization and generalization - for generalization of scientific concepts, developments, and proposals; statistical - to implement a quantitative approach to studying data. The US stock market was chosen as the base for research. The research was carried out by statistical processing of data on the value of the indicator of the inversion of the yield curve difference of 10-year and 2-year US Treasury bonds and the Standard & Poor's stock market index - 500 for the period from 1989 to 2022.
Findings: It has been established that the indicator of the difference of the yield curve of 2-year and 10-year US Treasury bonds is a fairly reliable tool for determining the approaching recession in the economy, but at the same time it is not possible to determine the exact time of the recession. It is shown that this indicator is expedient to use for early warning about a possible fall in international stock markets. At the same time, it was found that not every inversion of the yield curve is followed by a fall in the stock market, but every fall is preceded by an inversion. It was noted that the current dynamics of the yield curve are signaling a possible significant drop in the US stock market in the near future.
Theoretical Implications: Establishing the peculiarities of the indicator of the inversion of the yield curve difference of 10-year and 2-year US Treasury bonds in the conditions of the modern economy.
Practical Implications: The practical application of the research results will allow us to more accurately determine the current phase of the international stock markets and receive early signals about the future decline of the markets, which will contribute to increasing investment efficiency.
Originality/Value: This study expands knowledge about the peculiarities of the use of the indicator of the yield curve difference of 2-year and 10-year US Treasury bonds when determining the likely onset of a recession in the economy and the possibility of a fall in international stock markets, offers an updated model of the use of this indicator when forecasting the direction of movement of international stock markets. The results of the research may be of interest to specialists who work in the field of investing in international financial markets.
Research Limitations/Future Research: The results of the work presented in this article create a basis for conducting similar research on the possibility of using other indicators in order to increase the accuracy of establishing the moment of recession in the economy or the beginning of a fall in international financial markets. From the author's point of view, first of all, such indicators as the movement of gold prices, the dynamics of changes in the Fed's discount rate, and Buffett’s indicator should be studied. This will make it possible to develop an effective application mechanism for making investment decisions and will contribute to increasing investment efficiency.
Paper Type: Empirical
JEL Classification: E44, F21, G15
3
Habermann, M., M. Truffer, and D. Maxwell. "Changing basal conditions during the speed-up of Jakobshavn Isbræ, Greenland." Cryosphere Discussions 7, no. 3 (June 1, 2013): 2153–90. http://dx.doi.org/10.5194/tcd-7-2153-2013.
Повний текст джерелаАнотація:
Abstract. Ice-sheet outlet glaciers can undergo dynamic changes such as the rapid speed-up of Jakobshavn Isbræ following the disintegration of its floating ice tongue. These changes are associated with stress changes on the boundary of the ice mass. We investigate the basal conditions throughout a well-observed period of rapid change and evaluate parameterizations currently used in ice-sheet models. A Tikhonov inverse method with a Shallow Shelf Approximation forward model is used for diagnostic inversions for the years 1985, 2000, 2005, 2006 and 2008. Our ice softness, model norm, and regularization parameter choices are justified using the data-model misfit metric and the L-curve method. The sensitivity of the inversion results to these parameter choices is explored. We find a lowering of basal yield stress in the first 7 km of the 2008 grounding line and no significant changes higher upstream. The temporal evolution in the fast flow area is in broad agreement with a Mohr–Coulomb parameterization of basal shear stress, but with a till friction angle much lower than has been measured for till samples. The lowering of basal yield stress is significant within the uncertainties of the inversion, but it cannot be ruled out that there are other significant contributors to the acceleration of the glacier.
4
Zou, Tianyuan, and Jing Zhang. "A New Fluorescence Quantum Yield Efficiency Retrieval Method to Simulate Chlorophyll Fluorescence under Natural Conditions." Remote Sensing 12, no. 24 (December 11, 2020): 4053. http://dx.doi.org/10.3390/rs12244053.
Повний текст джерелаАнотація:
Chlorophyll fluorescence (ChlF) is a useful indicator of plant photosynthesis and stress conditions. ChlF spectra can be simulated with the Fluspect model, which is a radiative transfer model that simulates leaf reflectance, transmittance, and fluorescence; however, it has never been used or validated under natural conditions. In this paper, a new fluorescence quantum yield efficiency of photosystem (FQE) retrieval method based on the Fluspect model is proposed for use in simulating ChlF in two healthy varieties of soybeans grown under natural conditions. The parameters, Chlorophyll a + b content (Cab), carotenoid (Cca), dry matter content (Cdm), indicator of leaf water content (Cw) and leaf mesophyll structure (N) and the simulated fluorescence from the experiment were compared with the measured values to validate the model under natural conditions. The results show a good correlation (coefficient of determination R2 = 0.7–0.9) with the measured data at wavelengths of 650–880 nm. However, there is a large relative error (RE) that extends up to 150% at the peak of the fluorescence curve. To improve the accuracy of the simulation, an inversion code containing the emission efficiency parameters for photosystems I and II was added, which retrieves FQE I and II from the measured fluorescence spectra. The evaluation results for all wavelengths and two peaks demonstrated a significant reduction in the error at the peak of the curve by the Fluspect model with the FQE inversion code. This new method reduced the overestimation of fluorescence from 150% to 20% for the RE, and the R2 value was higher than 0.9 at the spectra peaks. Additionally, the original plant parameter information remained mostly unchanged upon the addition of the inversion code.
5
Capehart, T. W., and Y.-T. Cheng. "Determining constitutive models from conical indentation: Sensitivity analysis." Journal of Materials Research 18, no. 4 (April 2003): 827–32. http://dx.doi.org/10.1557/jmr.2003.0113.
Повний текст джерелаАнотація:
Several procedures have previously been advanced for extracting constitutive relations from the force–displacement curves obtained from indentation. This work addresses the specific problem of determining the elastic modulus E, yield stress Y, and hardening exponent n, which define the isotropic strain-hardening model from a single force–displacement curve with a sharp conical tip. The sensitivity of the inversion process was tested through a series of finite element calculations using ABAQUS. Different magnitudes of normally distributed noise were superimposed on a calculated force–displacement curve to simulate hypothetical data sets for specific values of E, Y, and n. The sensitivity of the parameter confidence intervals to noise was determined using the χ2-curvature matrix, statistical Monte Carlo simulations, and a conjugate gradient algorithm that explicitly searches the global parameter space. All three approaches demonstrate that 1% noise levels preclude the accurate determination of the strain-hardening parameters based on a single force–displacement curve.
6
Habermann, M., M. Truffer, and D. Maxwell. "Changing basal conditions during the speed-up of Jakobshavn Isbræ, Greenland." Cryosphere 7, no. 6 (November 7, 2013): 1679–92. http://dx.doi.org/10.5194/tc-7-1679-2013.
Повний текст джерелаАнотація:
Abstract. Ice-sheet outlet glaciers can undergo dynamic changes such as the rapid speed-up of Jakobshavn Isbræ following the disintegration of its floating ice tongue. These changes are associated with stress changes on the boundary of the ice mass. We invert for basal conditions from surface velocity data throughout a well-observed period of rapid change and evaluate parameterizations currently used in ice-sheet models. A Tikhonov inverse method with a shallow-shelf approximation forward model is used for diagnostic inversions for the years 1985, 2000, 2005, 2006 and 2008. Our ice-softness, model norm, and regularization parameter choices are justified using the data-model misfit metric and the L curve method. The sensitivity of the inversion results to these parameter choices is explored. We find a lowering of effective basal yield stress in the first 7 km upstream from the 2008 grounding line and no significant changes higher upstream. The temporal evolution in the fast flow area is in broad agreement with a Mohr–Coulomb parameterization of basal shear stress, but with a till friction angle much lower than has been measured for till samples. The lowering of effective basal yield stress is significant within the uncertainties of the inversion, but it cannot be ruled out that there are other significant contributors to the acceleration of the glacier.
7
Korobov, Eugene, Yulia Semernina, Alina Usmanova, and Kristina Odinokova. "Robotizing bond portfolio selection on the Russian debt market on the basis of a modified strategy of riding the yield curve." Business Informatics 15, no. 4 (December 31, 2021): 7–21. http://dx.doi.org/10.17323/2587-814x.2021.4.7.21.
Повний текст джерелаАнотація:
The modern global debt market features historically low average interest rates, convergence of yields on bonds with different maturities, an increase of yield curve inversion emergence frequency and a large-scale trend to automate financial decision making. The researchers’ attention in these fields is mainly focused on designing models that describe the state of the debt market as whole or its individual instruments in particular, as well as on risk management methods. At the same time, the specialized literature offers very few works concerning the topic of computer algorithms for bond portfolio selection based on traditional or advanced investment strategies. The aim of the present research is to create a modification of the existing algorithm of riding the yield curve strategy application, employing, first, average bond yield over the holding period instead of traditional bond yield to maturity; second, a developed algorithm for calculating the market spread on bonds; and, third, alternative risk evaluation indicators (compensation coefficients), which allow us to measure objectively price risk, liquidity risk, transaction costs risk and a general risk. The modification and the development of the algorithm for calculating the market spread were carried out using the direct measurement of the result technique, which entails application of the strategy to the data on bond issues received through the Moscow Exchange API. The selection of financial instruments was conducted in all sectors of the Russian debt market: public bonds, sub-federal and municipal bonds, corporate bonds. The modified algorithm enabled us to get extra yield for each selected bond issue, thereby proving the high effectiveness of the technique compared to the traditional strategy. Software implementation of the algorithm can be integrated into any robotized or semi-robotized stock exchange trading application.
8
Wang, X. Henry, and Bill Z. Yang. "Yield Curve Inversion and the Incidence of Recession: A Dynamic IS-LM Model with Term Structure of Interest Rates." International Advances in Economic Research 18, no. 2 (February 16, 2012): 177–85. http://dx.doi.org/10.1007/s11294-012-9350-7.
Повний текст джерела
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Muinonen, K., J. Torppa, X. B. Wang, A. Cellino, and A. Penttilä. "Asteroid lightcurve inversion with Bayesian inference." Astronomy & Astrophysics 642 (October 2020): A138. http://dx.doi.org/10.1051/0004-6361/202038036.
Повний текст джерелаАнотація:
Context. We assess statistical inversion of asteroid rotation periods, pole orientations, shapes, and phase curve parameters from photometric lightcurve observations, here sparse data from the ESA Gaia space mission (Data Release 2) or dense and sparse data from ground-based observing programs. Aims. Assuming general convex shapes, we develop inverse methods for characterizing the Bayesian a posteriori probability density of the parameters (unknowns). We consider both random and systematic uncertainties (errors) in the observations, and assign weights to the observations with the help of Bayesian a priori probability densities. Methods. For general convex shapes comprising large numbers of parameters, we developed a Markov-chain Monte Carlo sampler (MCMC) with a novel proposal probability density function based on the simulation of virtual observations giving rise to virtual least-squares solutions. We utilized these least-squares solutions to construct a proposal probability density for MCMC sampling. For inverse methods involving triaxial ellipsoids, we update the uncertainty model for the observations. Results. We demonstrate the utilization of the inverse methods for three asteroids with Gaia photometry from Data Release 2: (21) Lutetia, (26) Proserpina, and (585) Bilkis. First, we validated the convex inverse methods using the combined ground-based and Gaia data for Lutetia, arriving at rotation and shape models in agreement with those derived with the help of Rosetta space mission data. Second, we applied the convex inverse methods to Proserpina and Bilkis, illustrating the potential of the Gaia photometry for setting constraints on asteroid light scattering as a function of the phase angle (the Sun-object-observer angle). Third, with the help of triaxial ellipsoid inversion as applied to Gaia photometry only, we provide additional proof that the absolute Gaia photometry alone can yield meaningful photometric slope parameters. Fourth, for (585) Bilkis, we report, with 1-σ uncertainties, a refined rotation period of (8.5750559 ± 0.0000026) h, pole longitude of 320.6° ± 1.2°, pole latitude of − 25.6° ± 1.7°, and the first shape model and its uncertainties from convex inversion. Conclusions. We conclude that the inverse methods provide realistic uncertainty estimators for the lightcurve inversion problem and that the Gaia photometry can provide an asteroid taxonomy based on the phase curves.
10
Leng, Kuangdai, Stephen King, Tim Snow, Sarah Rogers, Anders Markvardsen, Satheesh Maheswaran, and Jeyan Thiyagalingam. "Parameter inversion of a polydisperse system in small-angle scattering." Journal of Applied Crystallography 55, no. 4 (August 1, 2022): 966–77. http://dx.doi.org/10.1107/s1600576722006379.
Повний текст джерелаАнотація:
A general method to invert parameter distributions of a polydisperse system using data acquired from a small-angle scattering (SAS) experiment is presented. The forward problem, i.e. calculating the scattering intensity given the distributions of any causal parameters of a theoretical model, is generalized as a multi-linear map, characterized by a high-dimensional Green tensor that represents the complete scattering physics. The inverse problem, i.e. finding the maximum-likelihood estimation of the parameter distributions (in free form) given the scattering intensity (either a curve or an image) acquired from an experiment, is formulated as a constrained nonlinear programming (NLP) problem. This NLP problem is solved with high accuracy and efficiency via several theoretical and computational enhancements, such as an automatic data scaling for accuracy preservation and GPU acceleration for large-scale multi-parameter systems. Six numerical examples are presented, including both synthetic tests and solutions to real neutron and X-ray data sets, where the method is compared with several existing methods in terms of their generality, accuracy and computational cost. These examples show that SAS inversion is subject to a high degree of non-uniqueness of solution or structural ambiguity. With an ultra-high accuracy, the method can yield a series of near-optimal solutions that fit data to different acceptable levels.
Дисертації з теми "Yield Curve Inversion"
1
GRASSO, ADRIANA. "Essays in macroeconomics and finance." Doctoral thesis, Luiss Guido Carli, 2017. http://hdl.handle.net/11385/201130.
Повний текст джерелаАнотація:
In Chapter 1, which is joint with Filippo Natoli, we propose a consumption-based model
that allows for an inverted term structure of real and nominal risk-free rates. In equilibrium, real
interest rates depend not only on shocks to consumption growth but also on expectations about
future consumption growth volatility. In bad states, a high uncertainty makes agents more
willing to accumulate precautionary savings and to rebalance their bond portfolios towards
longer maturities, pushing the equilibrium short-term yields above long-term ones. Pricing
time-varying volatility risk is essential to obtain the inversion of the real curve and allows to
price the average level and slope of the nominal one.
Chapter 2 is based on a joint work with Tiziano Ropele. In this paper I empirically
investigate the relationship between firms' in
ation expectations and their willingness to invest.
Using survey data on Italian firms I find that higher in
ation expectations do exert a favourable
effect on business investment decisions. While I document a minor role of the firm-level nominal
borrowing cost, other determinants of investment expectations are significant, such as the credit
markets' access conditions and the expected liquidity position of firms. These results bear
important implications for policymakers as they offer support to measures aimed at engineering
higher in
ation expectations in order to stimulate the economy.
2
NATOLI, FILIPPO. "Equilibrium interest rates and the anchoring of inflation expectations." Doctoral thesis, Luiss Guido Carli, 2017. http://hdl.handle.net/11385/201131.
Повний текст джерелаАнотація:
In Chapter 1, based on a paper cohautored by Adriana Grasso (LUISS University), I propose a
consumption-based model that allows for an inverted term structure of real and nominal risk-free rates.
In equilibrium, real interest rates depend not only on shocks to consumption growth but also on expectations
about future consumption growth volatility. In bad states, a high uncertainty makes agents more
willing to accumulate precautionary savings and to rebalance their bond portfolios towards longer maturities,
pushing the equilibrium short-term yields above long-term ones. Pricing time-varying volatility
risk is essential to obtain the inversion of the real curve and allows to price the average level and slope
of the nominal one.
In Chapter 2, based on a paper cohautored by Laura Sigalotti (Bank of Italy), I propose a new indicator
of the anchoring of inflation expectations based on a logistic model. By inspecting the comovement
of daily changes in short and long-term inflation swap rates, it measures the odds that strong variations in
short-term inflation compensation are channelled to large movements of the same sign in long-term one.
The indicator is able to capture the transition from anchored to unanchored expectations, implying a nonlinear
pass-through of shocks to long-term expectations. Since 2014, the asymmetric pass-through from
short- to long-term inflation compensation suggests that the degree of anchoring of euro area inflation
expectations have diverged from the US’s and UK’s one.
3
Chen, HUI-TU, and 陳蕙瑜. "The relations between the yield curves inversion and the economic growth." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/34968934926584151553.
Повний текст джерелаАнотація:
碩士國立高雄第一科技大學
金融營運所
95
The overall economy change is complexities and tedious. Because it is close correlated with the capital market operation, hence the financial circles and the academia all diligently make their efforts on its analysis and discussion. The study is using an autoregressive model AR (4) combined with the dummy variable to predict the economic reverse point when the inverted slope is present. The closing prices of the each month of final transaction date including the two-years, ten-years and thirty-years American government bond from January 1996 to July 2006 total 127 months time series data were used in this study. The economical growth rate was transformed from the real GDP quarter data to the month data by the way of the industrial production index weighting. The results are shown as follows: All models show that the correlation between the yield curve spread and economic growth is significantly negative in time lag of five periods when the slope is negative. But the independent variable R2 appears significantly positive correlation in time lag of one period. In other words, the GDP growth rate is positively correlated with the yield curve spread in the next month after negative slope to present. This result is not accord with our expectation. It is possible because the flat yield curve lose predictive susceptibility. Therefore, the economic growth rate does not oppose to the yield curve spread in the presence of regression coefficient during the slope is negative. In summary, using the parameters of the interest rate of long-term and short term bonds to judge the economic growth rate is best.
Частини книг з теми "Yield Curve Inversion"
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Puspa Rahman, Maya. "Has the Yield Curve Accurately Predicted the Malaysian Economy in the Previous Two Decades?" In Banking and Finance. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92214.
Повний текст джерелаАнотація:
Previous researchers have argued that yield curve contains information for future growth, and to a certain extent, was accurate in predicting recessions through the signal of yield curve inversion. This paper provides new evidence on the long- and short-run relationship between economic growth and yield spread in Malaysia, based on a 20-year span of data ranging from January 1996 to December 2016. By using the autoregressive distributed lag (ARDL) framework, the sample data are divided into three samples after taking into consideration the two major crises occurred in Malaysia over the last two decades. We find strong evidence of cointegration between the yield spread and growth, concurring on the long-run and short-run dynamics between them. Though significant, the instability of the yield spread to affect the movement of growth does not support the priori expectation on the predictive ability of the yield curve in Malaysia.
2
Björk, Tomas. "Martingale Models for the Short Rate." In Arbitrage Theory in Continuous Time, 280–95. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198851615.003.0021.
Повний текст джерелаАнотація:
This chapter is devoted to an overview and analysis of the most common short rate models, such as the Vasiček, Dothan, Hull–White, and CIR models. These models are analyzed and classified from the point of view of positive short rates, normal distribution, mean reversion, and computability. In particular we present the theory of affine term structures, and discuss the inversion of the yield curve. Analytical results for bond prices and bond options are presented for all the affine models.
Тези доповідей конференцій з теми "Yield Curve Inversion"
1
Fullerton, Anne M., Thomas C. Fu, David A. Drazen, and Don C. Walker. "Analysis Methods for Vessel Generated Spray." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-31313.
Повний текст джерелаАнотація:
The droplet sizes and velocities contained in vessel generated spray are difficult to quantify. This paper describes three different methods to quantify velocity and size distributions from high speed video of spray from a planing boat. These methods include feature tracking, displacement tracking and video inversion. For the feature tracking method, the images were preprocessed using contrast limited adaptive histogram equalization, and then converted to binary images with a specific intensity cutoff level. Image statistics were then generated from this image, including droplet area and effective diameter. These images were processed using commercial PIV software to obtain velocities. For the displacement tracking method, the images were also converted to binary images with a specific intensity cutoff level. Image statistics were again compiled from this binary image. A droplet filter was then applied using a binary erosion image processing technique, where large droplets were removed because the entire droplet may not be in frame, and small droplets were removed because they might not overlap between frames. Droplets were then tracked by comparing the bounding boxes of two droplets between time frames. The video inversion method consisted of the manipulating the original high speed videos from spatial x-y frames in time space to time-y frames in x-space, where the x-axis is longitudinally along the ship and the y axis is vertical to the ship. From this orientation, the speed of the general spray mass could be determined by summing the pixels in time columns for each × frame. Comparisons of droplet size distribution between the feature and displacement tracking method yield qualitatively similar results, with some disagreement likely due to the different threshold levels. The trend of the distribution curve suggests that both methods are unable to resolve the smallest droplet sizes, due to the processing filters applied as well as the field of view of the camera. The three analysis methods compare well in their spray velocity computation, and are also similar to spray speed predictions found in the literature for a given geometry and vessel speed.
2
Wardaya, P. "Imaging of Subsurface Velocity Structure on Volcanic Area of South East Java: An Application of Passive Seismic Ambient Noise Tomography for Sub-Volcanic Hydrocarbon Exploration." In Indonesian Petroleum Association 44th Annual Convention and Exhibition. Indonesian Petroleum Association, 2021. http://dx.doi.org/10.29118/ipa21-g-294.
Повний текст джерелаАнотація:
Petroleum exploration in sub-volcanic area always poses an inevitable challenge. Active seismic exploration method fails to obtain reliable imaging of the sediment beneath volcanic formation due to massive attenuation. This issue has been a long-standing problem in onshore seismic activity in Indonesia, especially in areas where volcanic formations present above the sedimentary formation of interest. To address this issue, we propose an alternative method utilizing a passive seismic approach to obtain reliable subsurface information. This paper discusses our experience in employing ambient noise tomography to evaluate the sedimentary structure beneath the volcanic area in Southern Malang, East Java. The passive seismic network deploying 70 seismometers were installed in a relatively regular grid. With the maximum offset between two furthest stations was 44.5km, we can capture the maximum wavelength of 15 km which is associated with the minimum frequency as low as 0.08 Hz to be used in the inversion. In principle, the seismometers record the coherent seismic noise coming from the atmospheric activity, sea wave, or industrial activity in the surface. Cross correlation between signal received in each station and their continuous stacking yields useful signals to reveal the dispersion curve which can produce the subsurface velocity profile through an inversion technique. From the inversion result we obtain the subsurface s-wave velocity structure down to a depth of 6 km. Higher s-wave velocity structure on the shallow depth in the northern area of the survey confirms the presence of the thick volcanic sediment situated near volcanic mountain. Towards the southern area we observe a slower s-wave velocity profile that indicates the thinning of volcanic formation. Although the method has successfully delivered a reliable s-wave structure over an entire survey area, its resolution is limited due to large spacing between stations. We suggest deploying denser stations to improve the velocity resolution.