estimating dynamic equilibrium models using mixed frequency macro and financial data abstract we provide a framework for inference in dynamic equilibrium models including financial market data at daily frequency along with macro series at standard lower frequency our formulation of the macro finance model in continuous time conveniently accounts for the difference in observation frequency we suggest the use of martingale estimating functions mef to infer the structural parameters of the model directly through a nonlinear scheme this method is compared to regression based methods and the generalized method of moments gmm we illustrate our approaches by estimating various versions of the ak vasicek model with mean reverting interest rates we provide asymptotic theory and monte carlo evidence on the small sample behavior of the estimators and report empirical estimates using 30 years of us macro and financial data

the inverse optimal problem a dynamic programming approach infinity when the production function has a finite slope at the origin we show that a solution to the aforementioned problem exists for a twice continuously differentiable strictly increasing consumption function provided the savings function starting from the origin is steep initially and flat eventually three well known consumption functions linear in the capital labor ratio keynesian and cantabrigian are also studied within the stochastic framework a well known result in discrete time models that a logarithmic utility function and a cobb douglas production function imply a keynesian consumption function does not carry through to the continuous time case

a nonembeddable noetherian ring abstract we provide an example of a left and right noetherian c algebra which cannot be embedded into any artinian ring

flat endofinite modules prime ideals and duality abstract bijective correspondences are established between endofinite injective left modules endofinite flat right modules finite collections of minimal noetherian prime ideals normalized rank functions on left ideals and characters endofinite flat modules are identified as flat covers of modules associated to a minimal noetherian prime ideal while endofinite flat injectives are characterized by localizations with a semiprimary qf 3 quotient ring

quotient rings and localization for noetherian rings abstract criteria are obtained for the localizability of a noetherian ring at a semiprime ideal s particularly when s is the nil radical of r the results are applied to the existence of quotient rings a decomposition theorem is obtained for certain noetherian rings which admit artinian quotient rings

convergence properties of the likelihood of computed dynamic models this paper studies the econometrics of computed dynamic models since these models generally lack a closed form solution their policy functions are approximated by numerical methods hence the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function what are the consequences for inference of the use of approximated likelihoods first we find conditions under which as the approximated policy function converges to the exact policy the approximated likelihood also converges to the exact likelihood second we show that second order approximation errors in the policy function which almost always are ignored by researchers have first order effects on the likelihood function third we discuss convergence of bayesian and classical estimates finally we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods

structural estimation of jump diffusion processes in macroeconomics this paper shows how to solve and estimate a continuous time dynamic stochastic general equilibrium dsge model with jumps it also shows that a continuous time formulation can make it simpler relative to its discrete time version to compute and estimate the deep parameters using the likelihood function when non linearities and or non normalities are considered we illustrate our approach by solving and estimating the stochastic ak and the neoclassical growth models our monte carlo experiments demonstrate that non normalities can be detected for this class of models moreover we provide strong empirical evidence for jumps in aggregate us data

direct sum cancellation of noetherian modules abstract leta b andcbe modules over a unital ringrsuch thatcis noetherian anda c b c even thoughaandbneed not be isomorphic we show that they have isomorphic submodule series and equivalently thataandbare indistinguishable by functions on the category ofr modules that respect short exact sequences

error correction and long run equilibrium in continuous time this paper deals with error correction models ecm s and cointegrated systems that are formulated in continuous time long run equilibrium coefficients in the continuous system are always identified in the discrete time reduced form so that there is no aliasing problem for these parameters the long run relationships are also preserved under quite general data filtering frequency domain procedures are outlined for estimation and inference these methods are asymptotically optimal under gaussian assumptions and they have the advantages of simplicity of computation and generality of specification thereby avoiding some methodological problems of dynamic specification in addition they facilitate the treatment of data irregularities such as mixed stock and flow data and temporally aggregated partial equilibrium formulations models with restricted cointegrating matrices are also considered

some observations on the questions is ventricular fibrillation chaos abstract ventricular fibrillation has been modeled as cardiac chaos occuring after a series of subharmonic bifurcations however previous experimental studies have suggested that fibrillatory oscillations have a relatively narrow band frequency spectrum inconsistent with a turbulent process similarly during the first minute of canine fibrillation we observed only a few localized frequency peaks from the epicardial and body surface electrocardiogram rather than a broadband type of spectrum as would be predicted for chaotic dynamics further narrowing of the frequency spectrum occured during the second minute of fibrillation the frequency spectrum of ventricular fibrillation contrasts with scaled broadband spectra observed in normal cardiac function we suggest that ventricular fibrillation may serve as a general model for transitions from broadband stability to certain types of pathological periodicities in other physiological perturbations

nonparametric pricing of interest rate derivative securities we propose a nonparametric estimation procedure for continuous time stochastic models because prices of derivative securities depend crucially on the form of the instantaneous volatility of the underlying process we leave the volatility function unrestricted and estimate it nonparametrically only discrete data are used but the estimation procedure still does not rely on replacing the continuous time model by some discrete approximation instead the drift and volatility functions are forced to match the densities of the process we estimate the stochastic differential equation followed by the short term interest rate and compute nonparametric prices for bonds and bond options

links between prime ideals in differential operator rings in recent years much work has been done on a localization theory for noetherian rings links between prime ideals play a central role in this development when a ring r is not commutative it is rarely possible to localize r at a prime ideal p having a link between p and another prime ideal is an obstruction to localization in this paper we will investigate the links between prime ideals in differential operator rings showing that it is possible to localize these rings in a certain sense recall that a multiplicatively closed subset s of a ring r is a right ore set if for all r in r and all s in s we have rs n sr qr the set s is an ore set if it is both a right and a left ore set it is always possible to construct a ring rf where the elements of s become units however if we insist on writing the elements of rf as right fractions rs with r in r and s in s then the set s must be a right ore set 9 sect 12 11 let p be a prime ideal of r and let 7 p r e r 1 r p is regular in r p we say that p is a localizable prime ideal if the set u p is an ore set we will shortly give an example of a prime ideal which is not localizable but first we introduce the differential operator ring let r be a ring and let 6 be an additive map from r to itself we call 6 a derivation if it satisfies the product rule 6 ab a b ad b the differential operatqr ring over r denoted r 0 s is a free left r module with basis 1 8 13 thus every element of r 0 s is a polynomial in 0 with coefficients from r the addition in r l s is defined as usual for polynomials but multiplication is extended from r by the rule br rti 6 r the differential operator ring is an associative ring and is determined up to isomorphism by an obvious universal property 9 sect 12 21

dynamic analysis of heartbeat rate signals of epileptics using multidimensional phase space reconstruction approach abstract the heartbeat rate signal provides an invaluable means of assessing the sympathetic parasympathetic balance of the human autonomic nervous system and thus represents an ideal diagnostic mechanism for detecting a variety of disorders such as epilepsy cardiac disease and so forth the current study analyses the dynamics of the heartbeat rate signal of known epilepsy sufferers in order to obtain a detailed understanding of the heart rate pattern during a seizure event in the proposed approach the ecg signals are converted into heartbeat rate signals and the embedology theorem is then used to construct the corresponding multidimensional phase space the dynamics of the heartbeat rate signal are then analyzed before during and after an epileptic seizure by examining the maximum lyapunov exponent and the correlation dimension of the attractors in the reconstructed phase space in general the results reveal that the heartbeat rate signal transits from an aperiodic highly complex behaviour before an epileptic seizure to a low dimensional chaotic motion during the seizure event following the seizure the signal trajectories return to a highly complex state and the complex signal patterns associated with normal physiological conditions reappear

nonlinear dynamics chaos and complex cardiac arrhythmias periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one dimensional finite difference equations as stimulation parameters are varied a large number of different phase locked and chaotic rhythms is observed similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites simplified models are analysed which show some correspondence to clinical observations the normal adult human heart at rest usually beats at a rate of between 50 and 100 times per minute in many circumstances some of which are lifethreatening but most of which are not the normal rhythmicity is altered resulting in abnormal rhythms called cardiac arrhythmias the point of this paper is to show that a branch of mathematics called nonlinear dynamics may be useful in the analysis of physiological processes believed to underlie normal heart rate regulation and some cardiac arrhythmias the idea that mathematical analysis can play a role in understanding cardiac arrhythmias is not novel indeed in the 1920s it was demonstrated that as parameters in mathematical models for the heart were varied several different rhythms that resembled clinically observed arrhythmias could be generated mobitz 1924 van de pol van der mark 1928 in nonlinear mathematics these changes in the qualitative features of the rhythms that are observed as parameters vary are called bifurcations thus the problem of understanding cardiac arrhythmias in the human heart is identified with understanding the bifurcations and complex dynamics in mathematical models of the human heart one type of dynamic behaviour that is the object of intensive analysis in mathematics is chaos loosely chaos is defined as aperiodic dynamics in deterministic systems in which there is sensitive dependence to the initial conditions this means that although in principle one could determine precisely the future evolution of the system starting from some initial condition for chaotic dynamics any difference in the initial condition no matter how small will eventually lead to marked differences in the future evolution of the system although the existence of chaos was known to poincare and others since the end of the last century in the

additive rank functions in noetherian rings let r be a ring with unit element a function 1 that assigns to each finitely generated r module m a nonnegative integer 1 m such that j m a n 1 l for each short exact sequence 0 n f m l f 0 of finitely right r modules is called an additive rank function such a function is constant on isomorphism classes of finitely generated right r modules so that 1 m cr m 0 whenever ci a4 m is an injective endomorphism of m when r is semisimple artinian then an additive rank function arises very naturally by defining a m length m the number of simple direct summands in a decomposition of m in 1964 goldie 2 adapted this idea to finitely generated modules over a right noetherian ring the resulting additive rank function is presently called the reduced rank the concept lay dormant for over 10 years until goldie started using it in 1976 providing new and strikingly elegant proofs of several important results of ring theory some of these appear in 3 others are included in 11 since then the reduced rank has become a widely used tool particularly in the theory of noncommutative noetherian rings we recall the definition of the reduced rank p m of a finitely generated right r module m over a right noetherian ring r if n denotes the nilpotent radical of r then r n has a classical semisimple artinian quotient ring q r n for a finitely generated right r n module m set prin m length m q r n since r nq r n is flat prin is an additive rank function for finitely generated right r n modules for a finitely generated right r module m set

embedding noetherian rings in artinian rings abstract a criterion is presented which is easy to check in specific examples and provides information as to when a given noetherian ring is not embeddable in an artinian one on the other hand we provide sufficient conditions for artinian embeddability of several types of noetherian rings that have no nontrivial right ideals of reduced rank zero

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

characterization of strange attractors a new measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable the relation of this new measure to fractal dimension and information theoretic entropy is discussed

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow