generalized browder s theorem for tensor product and elementary operators abstract the transfer property for the generalized browder s theorem both of the tensor product and of the left right multiplication operator will be characterized in terms of the b weyl spectrum inclusion in addition the isolated points of these two classes of operators will be fully characterized

generalized browder s and weyl s theorems for left and right multiplication operators abstract the main objective of this work is to study generalized browder s and weyl s theorems for the multiplication operators l a and r b and for the elementary operator a b l a r b

adaptive noise smoothing filter for images with signal dependent noise in this paper we consider the restoration of images with signal dependent noise the filter is noise smoothing and adapts to local changes in image statistics based on a nonstationary mean nonstationary variance nmnv image model for images degraded by a class of uncorrelated signal dependent noise without blur the adaptive noise smoothing filter becomes a point processor and is similar to lee s local statistics algorithm 16 the filter is able to adapt itself to the nonstationary local image statistics in the presence of different types of signal dependent noise for multiplicative noise the adaptive noise smoothing filter is a systematic derivation of lee s algorithm with some extensions that allow different estimators for the local image variance the advantage of the derivation is its easy extension to deal with various types of signal dependent noise film grain and poisson signal dependent restoration problems are also considered as examples all the nonstationary image statistical parameters needed for the filter can be estimated from the noisy image and no a priori information about the original image is required

on the determination of general scientific models with application to asset pricing we consider a consumption based asset pricing model that uses habit persistence to overcome the known statistical inadequacies of the classical consumption based asset pricing model we find that the habit model fits reasonably well and agrees with results reported in the literature if conditional heteroskedasticity is suppressed but that it does not fit nor do results agree if conditional heteroskedasticity well known to be present in financial market data is allowed to manifest itself we also find that it is the preference parameters of the model that are most affected by the presence or absence of conditional heteroskedasticity especially the risk aversion parameter the habit model exhibits four characteristics that are often present in models developed from scientific considerations 1 a likelihood is not available 2 prior information is available 3 a portion of the prior information is expressed in terms of functionals of the model that cannot be converted into an analytic prior on model

detection of intensity bursts using hawkes processes an application to high frequency financial data given a stationary point process an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate it might signal a local nonstationarity or the presence of an external perturbation to the system in this paper we propose a procedure for the detection of intensity bursts within the hawkes process framework by using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown moreover the initial time of the burst can be determined with a precision given by the typical interevent time we apply our methodology to the midprice change in foreign exchange fx markets showing that these bursts are frequent and that only a relatively small fraction is associated with news arrival we show lead lag relations in intensity burst occurrence across different fx rates and we discuss their relation with price jumps

threshold bipower variation and the impact of jumps on volatility forecasting this study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility this result becomes apparent once volatility is separated into its continuous and discontinuous components using estimators which are not only consistent but also scarcely plagued by small sample bias with the aim of achieving this we introduce the concept of threshold bipower variation which is based on the joint use of bipower variation and threshold estimation we show that its generalization threshold multipower variation admits a feasible central limit theorem in the presence of jumps and provides less biased estimates with respect to the standard multipower variation of the continuous quadratic variation in finite samples we further provide a new test for jump detection which has substantially more power than tests based on multipower variation empirical analysis on the s p500 index individual stocks and us bond yields shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump

nonlinear restoration of noisy images the restoration of images degraded by an additive white noise is performed by nonlinearly filtering a noisy image the standard wiener approach to this problem is modified to take into account the edge information of the image various filters of increasing complexity are derived experimental results are shown and compared to the standard wiener filter results and other earlier attempts involving nonstationary filters

b weyl spectrum and poles of the resolvent abstract let t be a bounded linear operator acting on a banach space and let bw t c such that t i is not a b fredholm operator of index 0 be the b weyl spectrum of t define also e t to be the set of all isolated eigenvalues in the spectrum t of t and t to be the set of the poles of the resolvent of t in this paper two new generalized versions of the classical weyl s theorem are considered more precisely we seek for conditions under which an operator t satisfies the generalized weyl s theorem bw t t e t or the version ii of the generalized weyl s theorem bw t t t

quantitative image quality analysis of a nonlinear spatio temporal filter digital temporal and spatial filtering of fluoroscopic image sequences can be used to improve the quality of images acquired at low x ray exposure in this study we characterized a nonlinear edge preserving spatio temporal noise reduction filter the bidirectional multistage bms median filter of arce 1991 to assess image quality signal detection and discrimination experiments were performed on stationary targets using a four alternative forced choice paradigm a measure of detectability d was obtained for filtered and unfiltered noisy image sequences at different signal amplitudes filtering gave statistically significant average d improvements of 20 detection and 31 discrimination a nonprewhitening detection model modified to include the human spatio temporal visual system contrast sensitivity underestimated enhancement predicting an improvement of 6 pixel noise standard deviation a commonly applied image quality measure greatly overestimated effectiveness giving 67 improvement in d we conclude that human testing is required to evaluate the filter effectiveness and that human perception models must be improved to account for the spatio temporal filtering of image sequences

x ray fluoroscopy spatio temporal filtering with object detection one potential way to reduce patient and staff x ray fluoroscopy dose is to reduce the quantum exposure to the detector and compensate the additional noise with digital filtering a new filtering method spatio temporal filtering with object detection is described that reduces noise while minimizing motion and spatial blur as compared to some conventional motion detection filtering schemes this object detection method incorporates additional a priori knowledge of image content i e much of the motion occurs in isolated long thin objects catheters guide wires etc we create object likelihood images and use these to control spatial and recursive temporal filtering such as to reduce blurring the objects of interest we use automatically computed receiver operating characteristic roc curves to optimize the object likelihood enhancement method and determine that oriented matched filter kernels with 4 orientations are appropriate the matched filter kernels are simple projected cylinders we demonstrate the method on several representative x ray fluoroscopy sequences to which noise is added to simulate very low dose acquisitions with processing we find that noise variance is significantly reduced with slightly less noise reduction near moving objects we estimate an effective exposure reduction greater than 80

image sequence filtering in quantum limited noise with applications to low dose fluoroscopy clinical angiography requires hundreds of x ray images putting the patients and particularly the medical staff at risk dosage reduction involves an inevitable sacrifice in image quality in this work the latter problem is addressed by first modeling the signal dependent poisson distributed noise that arises as a result of this dosage reduction the commonly utilized noise model for single images is shown to be obtainable from the new model stochastic temporal filtering techniques are proposed to enhance clinical fluoroscopy sequences corrupted by quantum mottle the temporal versions of these filters as developed here are more suitable for filtering image sequences as correlations along the time axis can be utilized for these dynamic sequences the problem of displacement field estimation is treated in conjunction with the filtering stage to ensure that the temporal correlations are taken along the direction of motion to prevent object blur

a reduced form framework for modeling volatility of speculative prices based on realized variation measures abstract building on realized variance and bipower variation measures constructed from high frequency financial prices we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility we decompose the total daily return variability into the continuous sample path variance the variation arising from discontinuous jumps that occur during the trading day as well as the overnight return variance our empirical results based on long samples of high frequency equity and bond futures returns suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long memory har garch model while the overnight returns may be modeled by an augmented garch type structure the dynamic dependencies in the non parametrically identified significant jumps appear to be well described by the combination of an ach model for the time varying jump intensities coupled with a relatively simple log linear structure for the jump sizes finally we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out of sample forecasts for the total return volatility

estimating stochastic volatility diffusion using conditional moments of integrated volatility we exploit the distributional information contained in high frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions the estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility the realization of which is effectively approximated by the sum of the squared high frequency increments of the process our simulation evidence indicates that the resulting gmm estimator is highly reliable and accurate our empirical implementation based on high frequency five minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps

weyl s theorem tensor products and multiplication operators abstract the transmission of weyl s theorem from operators on banach spaces to their tensor products and also to their associated multiplication operators is deconstructed

consistent ranking of volatility models abstract we show that the empirical ranking of volatility models can be inconsistent for the true ranking if the evaluation is based on a proxy for the population measure of volatility for example the substitution of a squared return for the conditional variance in the evaluation of arch type models can result in an inferior model being chosen as best with a probability that converges to one as the sample size increases we document the practical relevance of this problem in an empirical application and by simulation experiments our results provide an additional argument for using the realized variance in out of sample evaluations rather than the squared return we derive the theoretical results in a general framework that is not specific to the comparison of volatility models similar problems can arise in comparisons of forecasting models whenever the predicted variable is a latent variable

iterative maximum likelihood displacement field estimation in quantum limited image sequences we develop an algorithm for obtaining the maximum likelihood ml estimate of the displacement vector field dvp from two consecutive image frames of an image sequence acquired under quantum limited conditions the estimation of the dvf has applications in temporal filtering object tracking stereo matching and frame registration in low light level image sequences as well as low dose clinical x ray image sequences in the latter case a controlled x ray dosage reduction may be utilized to lower the radiation exposure to the patient and the medical staff the quantum limited effect is modeled as an undesirable poisson distributed signal dependent noise artifact a fisher bayesian formulation is used to estimate the dvf and a block component search algorithm is employed in obtaining the solution several experiments involving a phantom sequence and a teleconferencing image sequence with realistic motion demonstrate the effectiveness of this estimator in obtaining the dvf under severe quantum noise conditions 20 25 events pixel

the effect of temporal image filters on observer dependent contrast metrics interframe correlation resulting from filtering diminishes eye integration signal to noise ratio snr improvement this reduces the snr improvement used to predict improved minimum resolvable contrast or temperature difference to approximately half of that achieved at the monitor results are included for mean and recursive filters versus filter delay and blurring parameters

generalized browder s and weyl s theorems for banach space operators abstract we find necessary and sufficient conditions for a banach space operator t to satisfy the generalized browder s theorem we also prove that the spectral mapping theorem holds for the drazin spectrum and for analytic functions on an open neighborhood of t as applications we show that if t is algebraically m hyponormal or if t is algebraically paranormal then the generalized weyl s theorem holds for f t where f h t the space of functions analytic on an open neighborhood of t we also show that if t is reduced by each of its eigenspaces then the generalized browder s theorem holds for f t for each f h t

linear quadratic noise smoothing filters for quantum limited images we consider the use of nonlinear estimators for the noise smoothing of images obtained under quantum limited imaging conditions a volterra expansion is investigated from which a set of linear quadratic filters is derived using higher order statistics the filters are applicable for single frame and multiple frames of a single scene imaged under low light levels

realised quantile based estimation of the integrated variance in this paper we propose a new jump robust quantile based realised variance measure of ex post return variation that can be computed using potentially noisy data the estimator is consistent for the integrated variance and we present feasible central limit theorems which show that it converges at the best attainable rate and has excellent efficiency asymptotically the quantile based realised variance is immune to finite activity jumps and outliers in the price series while in modified form the estimator is applicable with market microstructure noise and therefore operational on high frequency data simulations show that it has superior robustness properties in finite sample while an empirical application illustrates its use on equity data

the distribution of realized exchange rate volatility using high frequency data on deutschemark and yen returns against the dollar we construct model free estimates of daily exchange rate volatility and correlation that cover an entire decade our estimates termed realized volatilities and correlations are not only model free but also approximately free of measurement error under general conditions which we discuss in detail hence for practical purposes we may treat the exchange rate volatilities and correlations as observed rather than latent we do so and we characterize their joint distribution both unconditionally and conditionally noteworthy results include a simple normality inducing volatility transformation high contemporaneous correlation across volatilities high correlation between correlation and volatilities pronounced and persistent dynamics in volatilities and correlations evidence of long memory dynamics in volatilities and correlations and remarkably precise scaling laws under temporal aggregation

designing realised kernels to measure the ex post variation of equity prices in the presence of noise this paper shows how to use realised kernels to carry out efficient feasible inference on the expost variation of underlying equity prices in the presence of simple models of market frictions the issue is subtle with only estimators which have symmetric weights delivering consistent estimators with mixed gaussian limit theorems the weights can be chosen to achieve the best possible rate of convergence and to have an asymptotic variance which is close to that of the maximum likelihood estimator in the parametric version of this problem realised kernels can also be selected to i be analysed using endogenously spaced data such as that in databases on transactions ii allow for market frictions which are endogenous iii allow for temporally dependent noise the finite sample performance of our estimators is studied using simulation while empirical work illustrates their use in practice

do high frequency measures of volatility improve forecasts of return distributions many finance questions require the predictive distribution of returns we propose a bivariate model of returns and realized volatility rv and explore which features of that time series model contribute to superior density forecasts over horizons of 1 to 60 days out of sample this term structure of density forecasts is used to investigate the importance of the intraday information embodied in the daily rv estimates the functional form for log rv dynamics the timing of information availability and the assumed distributions of both return and log rv innovations we find that a joint model of returns and volatility that features two components for log rv provides a good fit to s p 500 and ibm data and is a significant improvement over an egarch model estimated from daily returns

probabilistic forecasts of volatility and its risk premia abstract the object of this paper is to produce distributional forecasts of asset price volatility and its associated risk premia using a non linear state space approach option and spot market information on the latent variance process is captured by using dual model free variance measures to define a bivariate observation equation in the state space model the premium for variance diffusive risk is defined as linear in the latent variance in the usual fashion whilst the premium for variance jump risk is specified as a conditionally deterministic dynamic process driven by a function of past measurements the inferential approach adopted is bayesian implemented via a markov chain monte carlo algorithm that caters for the multiple sources of non linearity in the model and for the bivariate measure the method is applied to spot and option price data on the s p500 index from 1999 to 2008 with conclusions drawn about investors required compensation for variance risk during the recent financial turmoil the accuracy of the probabilistic forecasts of the observable variance measures is demonstrated and compared with that of forecasts yielded by alternative methods to illustrate the benefits of the approach it is used to produce forecasts of prices of derivatives on volatility itself in addition the posterior distribution is augmented by information on daily returns to produce value at risk predictions linking the variance risk premia to the risk aversion parameter in a representative agent model probabilistic forecasts of approximate relative risk aversion are also produced

likelihood based scoring rules for comparing density forecasts in tails abstract we propose new scoring rules based on conditional and censored likelihood for assessing the predictive accuracy of competing density forecasts over a specific region of interest such as the left tail in financial risk management these scoring rules can be interpreted in terms of kullback leibler divergence between weighted versions of the density forecast and the true density existing scoring rules based on weighted likelihood favor density forecasts with more probability mass in the given region rendering predictive accuracy tests biased toward such densities using our novel likelihood based scoring rules avoids this problem

kalman filtering in two dimensions further results the two dimensional reduced update kalman filter was recently introduced the corresponding scalar filtering equations were derived for the case of estimating a gaussian signal in white gaussian noise and were shown to constitute a general nonsymmetric half plane recursive filter this paper extends the method to the deconvolution problem of image restoration this paper also provides a more thorough treatment of the uniquely two dimensional boundary condition problems numerical and subjective examples are presented

econometric analysis of realized volatility and its use in estimating stochastic volatility models summary the availability of intraday data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets called realized volatility to study the stochastic properties of returns here under the assumption of a rather general stochastic volatility model we derive the moments and the asymptotic distribution of the realized volatility error the difference between realized volatility and the discretized integrated volatility which we call actual volatility these properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation intensive methods

alternative models for stock price dynamics abstract this paper evaluates the role of various volatility specifications such as multiple stochastic volatility sv factors and jump components in appropriate modeling of equity return distributions we use estimation technology that facilitates nonnested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns we consider two broad families of models 1 the multifactor loglinear family and 2 the affine jump family both classes of models have attracted much attention in the derivatives and econometrics literatures there are various tradeoffs in considering such diverse specifications if pure diffusion sv models are chosen over jump diffusions it has important implications for hedging strategies if logarithmic models are chosen over affine ones it may seriously complicate option pricing comparing many different specifications of pure diffusion multifactor models and jump diffusion models we find that 1 log linear models have to be extended to two factors with feedback in the mean reverting factor 2 affine models have to have a jump in returns stochastic volatility or probably both models 1 and 2 are observationally equivalent on the data set in hand in either 1 or 2 the key is that the volatility can move violently as we obtain models with comparable empirical fit one must make a choice based on arguments other than statistical goodness of fit criteria the considerations include facility to price options to hedge and parsimony the affine specification with jumps in volatility might therefore be preferred because of the closed form derivatives prices

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

perception of temporally filtered x ray fluoroscopy images for noisy x ray fluoroscopy image sequences the authors quantitatively evaluated image quality after digital temporal filtering to reduce noise using an experimental paradigm called a reference test adaptive forced choice method the authors compared detectability of stationary low contrast disks in filtered and un filtered computer generated image sequences in the first experiment a low pass first order recursive filter used in x ray fluoroscopy was found to be much less effective at enhancing detectability than predicted from the reduction of display noise variance a common measurement of filter effectiveness detectability was reasonably predicted by a nonprewhitening human observer model npw hvs that included an independently determined human temporal contrast sensitivity function in another experiment designed to test models over a range of temporal frequencies the authors used paired high pass and low pass temporal filters that both reduced noise variance by 25 the high pass filter was artificially applied to the noise only and greatly improved detectability while the low pass filter had little effect the human observer model quantitatively described the measurements but classical prewhitening and nonprewhitening signal detectors did not as compared to the nonprewhitening spatio temporal matched filter human observer efficiency was low and variable at 2 1 2 9 and 0 06 for 60 frames of un filtered low pass and high pass noise respectively as compared to this detector humans were not very effective at combining information across frames on the other hand signal to noise ratios snrs from the human observer model were comparable to human performance and efficiencies were reasonably constant at 40 52 and 32 respectively the authors conclude that it is imperative to include human observer models and experiments in the analysis of noise reduction filtering of noisy image sequences such as x ray fluoroscopy

a discrete time model for daily s p500 returns and realized variations jumps and leverage effects abstract we develop an empirically highly accurate discrete time daily stochastic volatility model that explicitly distinguishes between the jump and continuous time components of price movements using nonparametric realized variation and bipower variation measures constructed from high frequency intraday data the model setup allows us to directly assess the structural inter dependencies among the shocks to returns and the two different volatility components the model estimates suggest that the leverage effect or asymmetry between returns and volatility works primarily through the continuous volatility component the excellent fit of the model makes it an ideal candidate for an easy to implement auxiliary model in the context of indirect estimation of empirically more realistic continuous time jump diffusion and levy driven stochastic volatility models effectively incorporating the interdaily dependencies inherent in the high frequency intraday data

chasing volatility a persistent multiplicative error model with jumps abstract persistence and unpredictable large increments characterize the volatility of financial returns we propose the multiplicative error model with volatility jumps mem j to describe and predict the probability and the size of these extreme events under the mem j the conditional density of the realized measure is a countably infinite mixture of gamma and kappa distributions with closed form conditional moments we derive stationarity conditions and the asymptotic theory for the maximum likelihood estimation estimates of the volatility jump component confirm that the probability of jumps dramatically increases during the financial crises the mem j improves over other models with fat tails

browder weyl theorems tensor products and multiplications article history received 1 september 2008 available online 10 june 2009 submitted by r curto a banach space operator t b x satisfies browder s theorem if the complement of the weyl spectrum w t of t in t equals the set of riesz points of t t is polaroid if the isolated points of t are poles no restriction on rank of the resolvent of t l et t denote the set of fredholm points of t browder s theorem transfers from a b b x to s l a r b resp s a b i f and only if a and b resp a and b h ave svep at points a and b for which w s i f a and b are finitely polaroid then the polaroid property transfers from a b x and b b y to l a r b again restricting ourselves to the completion of x y in the projective topology if a and b are finitely polaroid then the polaroid property transfers from a b x and b b y to a b

drazin spectra of banach space operators and banach algebra elements abstract given a banach algebra a and a a several relations among the drazin spectrum of a and the drazin spectra of the multiplication operators l a and r a will be stated the banach space operator case will be also examined furthermore a characterization of the drazin spectrum will be considered