a nonparametric test for equality of distributions with mixed categorical and continuous data in this paper we consider the problem of testing for equality of two density or two conditional density functions defined over mixed discrete and continuous variables we smooth both the discrete and continuous variables with the smoothing parameters chosen via least squares cross validation the test statistics are shown to have asymptotic normal null distributions however we advocate the use of bootstrap methods in order to better approximate their null distribution in finite sample settings and we provide asymptotic validity of the proposed bootstrap method simulations show that the proposed tests have better power than both conventional frequency based tests and smoothing tests based on ad hoc smoothing parameter selection while a demonstrative empirical application to the joint distribution of earnings and educational attainment underscores the utility of the proposed approach in mixed data settings

a single blind controlled competition among tests for nonlinearity and chaos interest has been growing in testing for nonlinearity or chaos in economic data but much controversy has arisen about the available results this paper explores the reasons for these empirical difficulties we designed and ran a single blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series the data generating mechanisms include linear processes chaotic recursions and nonchaotic stochastic processes and both large and small samples were included in the experiment the data series were produced in a single blind manner by the competition manager and sent by e mail without identifying information to the experiment participants each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test the results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos

testing time reversibility without moment restrictions in this paper we propose a class of new tests for time reversibility it is shown that this test has an asymptotic normal distribution under the null hypothesis and non trivial power under local alternatives a novel feature of this test is that it does not have any moment restriction in contrast with other time reversibility and linearity tests our simulations also confirm that the proposed test is very robust when data do not possess proper moments an empirical study of stock market indices is also included to illustrate the usefulness of the new test

comparison of maximum entropy and higher order entropy estimators abstract we show that generalized maximum entropy gme is the only estimation method that is consistent with a set of five axioms the gme estimator can be nested using a single parameter into two more general classes of estimators gme estimators each of these gme estimators violates one of the five basic axioms however small sample simulations demonstrate that certain members of these gme classes of estimators may outperform the gme estimation rule

riddled basins of the optimal states in learning dynamical systems abstract a new phenomenon called riddled basin has been drawing attention of nonlinear scientists riddled basin is an extremely complicated domain of attraction usually accompanying invariant sets for dynamical systems driven by chaotic signal e g chaotic synchronizing systems in this paper the optimal state of a back propagation learning of chaotic time series is shown to have a locally riddled basin by a numerical experiment it is also rigorously proved that the optimal state of learning of the tent map by a gradient descent method can be an attractor with a riddled basin

on time reversibility and the uniqueness of moving average representations for non gaussian stationary time series a recent result by findley 1986 on the uniqueness of moving average representations for non gaussian time series is shown to establish a conjecture by weiss 1975 on the time reversibility of general linear processes 1988 biometrika trust

dynamical singularities in adaptive delayed feedback control we demonstrate the dynamical characteristics of adaptive delayed feedback control systems exploiting a discrete time adaptive control method derived for carrying out detailed analysis in particular the systems exhibit singularities such as power law decay of the distribution of transient times and almost zero finite time lyapunov exponents we can explain these results by characterizing such systems as having 1 a jacobian matrix with unity eigenvalue in the whole phase space and 2 parameters approaching a stability boundary proven to be identical with that of nonadaptive delayed feedback control

asymptotic distribution theory for nonparametric entropy measures of serial dependence entropy is a classical statistical concept with appealing properties establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging in this paper we develop an asymptotic theory for a class of kernel based smoothed nonparametric entropy measures of serial dependence in a time series context we use this theory to derive the limiting distribution of granger and lin s 1994 normalized entropy measure of serial dependence which was previously not available in the literature we also apply our theory to construct a new entropy based test for serial dependence providing an alternative to robinson s 1991 approach to obtain accurate inferences we propose and justify a consistent smoothed bootstrap procedure the naive bootstrap is not consistent for our test our test is useful in for example testing the random walk hypothesis evaluating density forecasts and identifying important lags of a time series it is asymptotically locally more powerful than robinson s 1991 test as is confirmed in our simulation an application to the daily s p 500 stock price index illustrates our approach

information and entropy econometrics editor s view amos golan department of economics american university roper 200 4400 massachusetts ave nw washington dc 20016 usa

entropy and predictability of stock market returns abstract we examine the predictability of stock market returns by employing a new metric entropy measure of dependence with several desirable properties we compare our results with a number of traditional measures the metric entropy is capable of detecting nonlinear dependence within the returns series and is also capable of detecting nonlinear affinity between the returns and their predictions obtained from various models thereby serving as a measure of out of sample goodness of fit or model adequacy several models are investigated including the linear and neural network models as well as nonparametric and recursive unconditional mean models we find significant evidence of small nonlinear unconditional serial dependence within the returns series but fragile evidence of superior conditional predictability profit opportunity when using market switching versus buy and hold strategies

generalized redundancies for time series analysis abstract extensions to various information theoretic quantities such as entropy redundancy and mutual information are discussed in the context of their role in nonlinear time series analysis we also discuss linearized versions of these quantities and their use as benchmarks in tests for nonlinearity many of these quantities can be expressed in terms of the generalized correlation integral and this expression permits us to more clearly exhibit the relationships of these quantities to each other and to other commonly used nonlinear statistics such as the bds and green savit statistics further numerical estimation of these quantities is found to be more accurate and more efficient when the the correlation integral is employed in the computation finally we consider several local versions of these quantities including a local kolmogorov sinai entropy which gives an estimate of variability of the short term predictability

on the approximation property of excellent rings where d is a smooth finite type a algebra a theorem which would imply the existence of an embedding of the above type yields the positive solution of the bass quillen conjecture so far this theorem is only known in special cases there is the following result by artin 3 4

a consistent test for conditional symmetry in time series models the assumption of conditional symmetry is often invoked to validate adaptive estimation and consistent estimation of arch garch models by quasi maximum likelihood imposing conditional symmetry can increase the efficiency of bootstraps if the symmetry assumption is valid this paper proposes a procedure for testing conditional symmetry the proposed test does not require the data to be stationary or i i d and the dimension of the conditional variables can be infinite the proposed test is consistent and is asymptotically distribution free in addition the test is shown to have nontrivial power against root t local alternatives the size and power of the test are satisfactory even for small samples applying the test to various time series we reject conditional symmetry in inflation exchange rate and stock returns among the nonfinancial time series considered we find that investment the consumption of durables and manufacturing employment also reject conditional symmetry

kernel based nonlinear canonical analysis and time reversibility we consider a kernel based approach to nonlinear canonical correlation analysis and its implementation for time series we deduce a test procedure of the reversibility hypothesis the method is applied to the analysis of stochastic differential equation from high frequency data on stock returns

scaling laws for noise induced temporal riddling in chaotic systems recent work has considered the situation of riddling where when a chaotic attractor lying in an invariant subspace is transversely stable the basin of the attractor can be riddled with holes that belong to the basin of another attractor the existence of invariant subspace often relies on certain symmetry of the system which is however a nongeneric property as system defects and small random noise can destroy the symmetry this paper addresses the influence of noise on riddling we show that riddling can actually be induced by arbitrarily small noise even in parameter regimes where one expects no riddling in the absence of noise specifically we argue that when there are attractors located off the invariant subspace the basins of these attractors can be temporally riddled even when the chaotic attractor in the invariant subspace is transversely unstable w e investigate universal scaling laws for noise induced temporal riddling our results imply that the phenomenon of riddling is robust and it can be more prevalent than expected before as noise is practically inevitable in physical systems s1063 651x 97 01410 4

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

the transition to chaotic attractors with riddled basins abstract recently it has been shown that there are chaotic attractors whose basins are such that any point in the basin has pieces of another attractor basin arbitrarily nearby the basin is riddled with holes here we consider the dynamics near the transition to this situation as a parameter is varied using a simple analyzable model we obtain the characteristic behaviors near this transition numerical tests on a more typical system are consistent with the conjecture that these results are universal for the class of systems considered

a versatile and robust metric entropy test of time reversibility and other hypotheses abstract we examine the performance of a metric entropy statistic as a robust test for time reversibility tr symmetry and serial dependence it also serves as a measure of goodness of fit the statistic provides a consistent and unified basis in model search and is a powerful diagnostic measure with surprising ability to pinpoint areas of model failure we provide empirical evidence comparing the performance of the proposed procedure with some of the modern competitors in nonlinear time series analysis such as robust implementations of the bds and characteristic function based tests of tr along with correlation based competitors such as the ljung box q statistic unlike our procedure each of its competitors is motivated for a different specific context and hypothesis our evidence is based on monte carlo simulations along with an application to several stock indices for the us equity market

basins of attraction in piecewise smooth hamiltonian systems piecewise smooth hamiltonian systems arise in physical and engineering applications for such a system typically an infinite number of quasiperiodic attractors coexist here we use the term attractors to indicate invariant sets to which typically initial conditions approach as a result of the piecewise smoothness of the underlying system these attractors are therefore characteristically different from the attractors in dissipative dynamical systems we find that the basins of attraction of different attractors exhibit a riddledlike feature in that they mix with each other on arbitrarily fine scales this practically prevents prediction of attractors from specific initial conditions and parameters the mechanism leading to the complicated basin structure is found to be characteristically different from those reported previously for similar basin structure in smooth dynamical systems we demonstrate the phenomenon using a class of electronic relaxation oscillators with voltage protection and provide a theoretical explanation

on the concept of attractor this note proposes a definition for the concept of attractor based on the probable asymptotic behavior of orbits the definition is sufficiently broad so that every smooth compact dynamical system has at least one attractor

the stationary bootstrap abstract this article introduces a resampling procedure called the stationary bootstrap as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on weakly dependent stationary observations previously a technique based on resampling blocks of consecutive observations was introduced to construct confidence intervals for a parameter of the m dimensional joint distribution of m consecutive observations where m is fixed this procedure has been generalized by constructing a blocks of blocks resampling scheme that yields asymptotically valid procedures even for a multivariate parameter of the whole i e infinite dimensional joint distribution of the stationary sequence of observations these methods share the construction of resampling blocks of observations to form a pseudo time series so that the statistic of interest may be recalculated based on the resampled data set but in the context of applying this method to stationary data it is natural