empirical likelihood for regression discontinuity design this paper proposes empirical likelihood based inference methods for causal effects identified from regression discontinuity designs we consider both the sharp and fuzzy regression discontinuity designs and treat the regression functions as nonparametric the proposed inference procedures do not require asymptotic variance estimation and the confidence sets have natural shapes unlike the conventional wald type method these features are illustrated by simulations and an empirical example which evaluates the effect of class size on pupils scholastic achievements furthermore for the sharp regression discontinuity design we show that the empirical likelihood statistic admits a higher order refinement so called the bartlett correction bandwidth selection methods are also discussed

can one make any crash prediction in finance using the local hurst exponent idea abstract we apply the hurst exponent idea for investigation of djia index time series data the behavior of the local hurst exponent prior to drastic changes in financial series signal is analyzed the optimal length of the time window over which this exponent can be calculated in order to make some meaningful predictions is discussed our prediction hypothesis is verified with examples of 1929 and 1987 crashes as well as with more recent phenomena in stock market from the period 1995 to 2003 some interesting agreements are found

reducing variance in univariate smoothing a variance reduction technique in nonparametric smoothing is proposed at each point of estimation form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged the nearby points are chosen to maximize the variance reduction we study in detail the case of univariate local linear regression while the new estimator retains many advantages of the local linear estimator it has appealing asymptotic relative efficiencies bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation a simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes this technique is very general and has a wide range of applications

a reexamination of diffusion estimators with applications to financial model validation time homogeneous diffusion models have been widely used for describing the stochastic dynamics of the underlying economic variables recently stanton proposed drift and diffusion estimators based on a higher order approximation scheme and kernel regression method he claimed that higher order approximations must outperform lower order approximations and concluded nonlinearity in the instantaneous return function of short term interest rates to examine the impact of higher order approximations we develop general and explicit formulas for the asymptotic behavior of both drift and diffusion estimators we show that these estimators will reduce the numerical approximation errors in asymptotic biases but their asymptotic variances escalate nearly exponentially with the order of approximation simulation studies also confirm our asymptotic results this variance inflation problem arises not only from nonparametric fitting but also from parametric fitting stanton s work also postulates the interesting qu

data driven confidence intervals for diffusion process using double smoothing empirical likelihood abstract in this paper we propose an innovative estimation method for the volatility function in diffusion process and construct the empirical likelihood confidence interval for it compared with double smoothing local constant estimator double smoothing local linear estimator proposed in this paper is an inventive estimation method moreover we find that the empirical likelihood confidence interval constructed with the approximate estimating equation is much better than the one based on the estimating equation since the latter undermines the predictability of the estimator accordingly new algorithm for simulation is proposed through monte carlo simulation and empirical analysis both these approaches are superior to traditional asymptotic normality confidence interval in terms of coverage rate etc

empirical likelihood ratio confidence intervals for a single functional summary the empirical distribution function based on a sample is well known to be the maximum likelihood estimate of the distribution from which the sample was taken in this paper the likelihood function for distributions is used to define a likelihood ratio function for distributions it is shown that this empirical likelihood ratio function can be used to construct confidence intervals for the sample mean for a class of m estimates that includes quantiles and for differentiable statistical functionals the results are nonparametric extensions of wilks s 1938 theorem for parametric likelihood ratios the intervals are illustrated on some real data and compared in a simulation to some bootstrap confidence intervals and to intervals based on student s t statistic a hybrid method that uses the bootstrap to determine critical values of the likelihood ratio is introduced

option pricing formulas based on a non gaussian stock price model options are financial instruments that depend on the underlying stock we explain their non gaussian fluctuations using the nonextensive thermodynamics parameter q a generalized form of the black scholes bs partial differential equation and some closed form solutions are obtained the standard bs equation q 1 which is used by economists to calculate option prices requires multiple values of the stock volatility known as the volatility smile using q 1 5 which well models the empirical distribution of returns we get a good description of option prices using a single volatility

empirical likelihood confidence intervals for nonparametric density estimation summary we suggest using empirical likelihood in conjunction with the kernel method to construct confidence intervals for the value of a probability density f at a point x this suggestion arises from a simulation study which shows that confidence intervals produced by the kernel based percentle t bootstrap do not have the coverage claimed by the theory this coverage discrepancy is due to a conflict between the prescribed undersmoothing and the explicit variance estimate needed by the percentile t method empirical likelihood avoids this conflict by studentising internally we show that the empirical likelihood produces confidence intervals having theoretical coverage accuracy of the same order of magnitude as the bootstrap and which are also empirically more accurate

simultaneous confidence bands for linear regression and smoothing suppose we observe y i f x i varepsilon i i 1 ldots n we wish to find approximate 1 alpha simultaneous confidence regions for f x x in mathscr x our regions will be centered around linear estimates hat f x of nonparametric or nonparametric f x there is a large amount of previous work on this subject substantial restrictions have been usually placed on some or all of the dimensionality of x the class of functions f that can be considered the class of linear estimates hat f and the region mathscr x the method we present is an approximation to the tube formula dn can be used for multidimensional x and a wide class of linear estimates by considering the effect of bias we are able to relax assumptions on the class of functions f which are considered simultaneous and numerical computations are used to illustrate the performance

confidence bands for regression functions abstract a method for obtaining conservative confidence bands for regression functions in low dimensions is given of particular importance is the applicability of the method to nonparametric regression computations examples and comparisons indicate the effectiveness of the method

on the power of bounded concurrency i finite automata we investigate the descriptive succinctness of three fundamental notions for modeling concurrency nondeterminism and pure parallelism the two facets of alternation and bounded cooperative concurrency whereby a system configuration consists of a bounded number of cooperating states our results are couched in the general framework of finite state automata but hold for appropriate versions of most concurrent models of computation such as petri nets statecharts or finite state versions of concurrent programming languages we exhibit exhaustive sets of upper and lower bounds on the relative succinctness of these features over s and s establishing that 1 each of the three features represents an exponential saving in succinctness of the representation in a manner that is independent of the other two and additive with respect to them 2 of the three bounded concurrency is the strongest representing a similar exponential saving even when substituted for each of the others for example we prove exponential upper and lower bounds on the simulation of deterministic concurrent automata by afas and triple exponential bounds on the simulation of alternating concurrent automata by dfas

simultaneous confidence bounds in multiple regression using predictor variable constraints abstract this article presents a method for approximating the coverage probability of simultaneous confidence bounds for multiple regression functions when the vector of predictor variables is constrained to lie in a polyhedral convex set the method is useful because it allows one to construct simultaneous confidence intervals with prescribed coverage probability for the regression function evaluated at various settings of the predictor variables which are narrower than bounds obtained without using the predictor variable constraints for a family of two sided simultaneous confidence bounds that includes scheffe type and constant width bounds the probability of coverage is related to the distribution of the maximum euclidean norm of the projection onto a polyhedral cone for a pair of random vectors with known joint distribution an analogous relation holds for one sided bounds if an algorithm for computing the projection onto the cone is available then these results enable one to use the monte carlo

generalized exponential function and discrete growth models abstract here we show that a particular one parameter generalization of the exponential function is suitable to unify most of the popular one species discrete population dynamic models into a simple formula a physical interpretation is given to this new introduced parameter in the context of the continuous richards model which remains valid for the discrete case from the discretization of the continuous richards model generalization of the gompertz and verhulst models one obtains a generalized logistic map and we briefly study its properties notice however that the physical interpretation for the introduced parameter persists valid for the discrete case next we generalize the scramble competition ricker discrete model and analytically calculate the fixed points as well as their stabilities in contrast to previous generalizations from the generalized ricker model one is able to retrieve either scramble or contest models

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

tsallis statistics and gradually truncated levy flight distribution of an economical index abstract tsallis postulated a generalized form for entropy and give rise to a new statistics now known as tsallis statistics in the present work we compare the tsallis statistics with the gradually truncated levy flight and discuss the distribution of an economical index the standard and poor s 500 using the values of standard deviation as calculated by our model we find that both statistics give almost the same distribution thus we feel that gradual truncation of levy distribution after certain critical step size for describing complex systems is a requirement of generalized thermodynamics or similar the gradually truncated levy flight is based on physical considerations and bring a better physical picture of the dynamics of the whole system tsallis statistics gives a theoretical support both statistics together can be utilized for the development of a more exact portfolio theory or to understand better the complexities in human and financial behaviors a comparison of both statistics is made

on the fractal dimension of self affine profiles one dimensional profiles f x can be characterized by a minkowski bouligand dimension d and by a scale dependent generalized roughness w f epsilon this roughness can be defined as the dispersion around a chosen fit to f x in an epsilon scale it is shown that d limepsilon to 0 2 in w f epsilon in epsilon holds for profiles nowhere differentiable this establishes a close connection between the roughness and the fractal dimension and proves that d 2 h for self affine profiles h is the roughness or hurst exponent two numerical algorithms based on the roughness one around the local average f x epsilon usual roughness and the other around the local rms straight line a generalized roughness are discussed the estimates of d for standard self affine profiles are reliable and robust especially for the last method

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

hurst exponent footprints from activities on a large structural system abstract this paper presents hurst exponent footprints from pseudo dynamic measurements of significantly varied activities on a damaged bridge structure during rehabilitation through continuous monitoring the system is interesting due to associated uncertainty in large scale structures and significant presence of human intervention arising from fundamentally different processes investigations into the variation of computed hurst exponents on time series of limited lengths are carried out in this regard the hurst exponents are compared with respect to specific events during the rehabilitation as well as with the data collection locations the variations of local hurst exponents about the values computed for each activity are presented the scaling of hurst exponents for different activities is also investigated these are representative of the extent of multifractality for each event the extent of multifractality is assessed along with its source and time dependency

is the expression h 1 3 q valid for real financial data non extensive thermodynamics is one of the most intriguing physics new frontiers a large number of researchers have been successfully finding connections between the new concepts introduced by this new field and other complex systems already presented in particular borland phys rev e 57 1998 6634 6642 has introduced a very interesting relation between the entropic index q that arises in the non extensive entropy and the well known hurst exponent h used to measure long range dependence in complex systems in this paper we provide statistical support to borland results and test the validity of these results in real financial data

a rice style theorem for parallel automata we present a general result similar to rice s theorem concerning the complexity of detecting properties on finite automata enriched by bounded cooperative concurrency such as statecharts and abstract parallel automata which we denote by cfas concurrent finite automata on one extreme the complexity of detecting non trivial properties that preserve equivalence of machines i e properties of the accepted language on finite automata can be as little as o 1 on the other extreme rice s theorem states that all such properties on turing machines are undecidable we state that all the non trivial properties of the regular or w regular languages are pspace hard on cfas with e moves and on cfas without e moves accepting infinite words we also extend this result to cfas without e moves accepting finite words that satisfy a condition that holds for many properties

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

a note on the relevance of the q exponential function in the context of intertemporal choices abstract this paper shows that the q exponential function well known in the deformed algebra inspired in the tsallis s nonextensive thermodynamics may be used to model discount functions in intertemporal choices which present the phenomenon known as increasing patience moreover we show that this insight may also be used to provide a measure of the degree of dynamic inconsistency presented in such decisions

a test for model specification of diffusion processes we propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process the empirical likelihood is used to formulate a statistic for each kernel smoothing bandwidth which is effectively a studentized l2 distance between the kernel transitional density estimator and the parametric transitional density implied by the parametric process to reduce the sensitivity of the test on smoothing bandwidth choice the final test statistic is constructed by combining the empirical likelihood statistics over a set of smoothing bandwidths to better capture the finite sample distribution of the test statistic and data dependence the critical value of the test is obtained by a parametric bootstrap procedure properties of the test are evaluated asymptotically and numerically by simulation and by a real data example

fully nonparametric estimation of scalar diffusion models we propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process we show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter the asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens we prove almost sure consistency and weak convergence to mixtures of normal laws where the mixing variates depend on the chronological local time of the underlying diffusion process that is the random time spent by the process in the vicinity of a generic spatial point the estimation method and asymptotic results apply to both stationary and nonstationary recurrent processes

scaling behaviors in differently developed markets scaling properties of four di erent stock market indices are studied in terms of a generalized hurst exponent approach we nd that the deviations from pure brownian motion behavior are associated with the degrees of development of the markets and we observe strong di erentiations in the scaling properties of markets at di erent development stage c

bootstrap simultaneous error bars for nonparametric regression simultaneous error bars are constructed for nonparametric kernel estimates of regression functions the method is based on the bootstrap where resampling is done from a suitably estimated residual distribution the error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints applications to an economic problem are given and comparison to both pointwise and bonferroni type bars is presented through a simulation study

exact confidence bands for linear regression over intervals abstract exact simultaneous confidence intervals and bands for the regression line on a set cx in simple linear regression have been known only when cx is a finite set with one or two points or when cx is a finite or infinite interval otherwise conservative bands have been used in this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points also tables are provided for cases of finite cx with three points and of cx an interval

alternation and bounded concurrency are reverse equivalent numerous models of concurrency have been considered in the framework of automata among the more interesting concurrency models are classical nondeterminism and pure concurrency the two facets of alternation and the bounded concurrency model bounded concurrency was previously considered to be similar to nondeterminism and pure concurrency in the sense of the succinctness of automata augmented with these features in this paper we show that when viewed more broadly the power of succinctness of bounded concurrency is in fact most similar to the power of alternation our contribution is that just like nondeterminism and pure concurrency are complement equivalent bounded concurrency and alternation are reverse equivalent over finite automata the reverse equivalence is expressed by the existence of polynomial transformations in both directions between bounded concurrency and alternation for the reverse of the language accepted by the other it follows that bounded concurrency is double exponentially more succinct than dfas with respect to reverse while alternation only saves one exponent this is as opposed to the direct case where alternation saves two exponents and bounded concurrency saves only one an immediate corollary is that for languages over a one letter alphabet bounded concurrency and alternation are equivalent we complete the picture of succinctness results for these languages by considering the different combinations of the concurrency models using additional lower bounds

on the functional estimation of jump diffusion models abstract we provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous time models with discontinuous sample paths of the jump diffusion type minimal requirements are placed on the dynamic properties of the underlying jump diffusion process i e stationarity is not required our theoretical framework justifies consistent in a statistical sense nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest i e the potentially nonaffine and level dependent intensity of the jump arrival being an example from the estimated infinitesimal conditional moments as suggested in johannes 2003 the statistical and economic role of jumps in continuous time interest rate models journal of finance forthcoming

empirical likelihood based inference for nonparametric recurrent diffusions this paper provides a new approach to constructing confidence intervals for nonparametric drift and diffusion functions in the continuous time diffusion model via empirical likelihood el the log el ratios are constructed through the estimating equations satisfied by the local linear estimators limit theories are developed by means of increasing time span and shrinking observational intervals the results apply to both stationary and nonstationary recurrent diffusion processes simulations show that for both drift and diffusion functions the new procedure performs remarkably well in finite samples and clearly dominates the conventional method in constructing confidence intervals based on asymptotic normality an empirical example is provided to illustrate the usefulness of the proposed method

empirical likelihood confidence intervals for local linear smoothers summary empirical likelihood is considered in conjunction with the local linear smoother to construct confidence intervals for a nonparametric regression function with bounded support the coverage error of the empirical likelihood confidence intervals is evaluated and is shown to be of the same order throughout the support of the regression function this is a significant improvement over confidence intervals based directly on the asymptotic normal distribution of the local linear estimator which have a larger order of coverage error near the boundary this improvement is attributable to the natural variance estimator that empirical likelihood implicitly chooses for the local linear smoother