abundance based similarity indices and their estimation when there are unseen species in samples a wide variety of similarity indices for comparing two assemblages based on species incidence i e presence absence data have been proposed in the literature these indices are generally based on three simple incidence counts the number of species shared by two assemblages and the number of species unique to each of them we provide a new probabilistic derivation for any incidence based index that is symmetric i e the index is not affected by the identity ordering of the two assemblages and homogeneous i e the index is unchanged if all counts are multiplied by a constant the probabilistic approach is further extended to formulate abundance based indices thus any symmetric and homogeneous incidence index can be easily modified to an abundance type version applying the laplace approximation formulas we propose estimators that adjust for the effect of unseen shared species on our abundance based indices simulation results show that the adjusted estimators significantly reduce the biases of the corresponding unadjusted ones when a substantial fraction of species is missing from samples data on successional vegetation in six tropical forests are used for illustration advantages and disadvantages of some commonly applied indices are briefly discussed

robust adaptive rate optimal testing for the white noise hypothesis abstract a new test is proposed for the weak white noise null hypothesis the test is based on a new automatic selection of the order for a box pierce 1970 test statistic or the test statistic of hong 1996 the heteroskedasticity and autocorrelation consistent hac critical values from lee 2007 are used allowing for estimation of the error term the data driven order selection is tailored to detect a new class of alternatives with autocorrelation coefficients which can be o n 1 2 provided there are sufficiently many of such coefficients a simulation experiment illustrates the good statistical properties of the test both under the weak white noise null and the alternative

testing for high dimensional white noise using maximum cross correlations we propose a new omnibus test for vector white noise using the maximum absolute autocorrelations and cross correlations of the component series based on an approximation by the l norm of a normal random vector the critical value of the test can be evaluated by bootstrapping from a multivariate normal distribution in contrast to the conventional white noise test the new method is proved to be valid for testing departure from white noise that is not independent and identically distributed we illustrate the accuracy and the power of the proposed test by simulation which also shows that the new test outperforms several commonly used methods including the lagrange multiplier test and the multivariate box pierce portmanteau tests especially when the dimension of the time series is high in relation to the sample size the numerical results also indicate that the performance of the new test can be further enhanced when it is applied to pre transformed data obtained via the time series principal component analysis proposed by j chang b guo and q yao arxiv 1410 2323 the proposed procedures have been implemented in an r package

estimating the species accumulation curve using mixtures as a significant tool in ecological studies the species accumulation curve or the collector s curve is the graph of the expected number of detected species as a function of sampling effort the problem of estimating the species accumulation curve based on an empirical data set arising from quadrat sampling is studied in a nonparametric binomial mixture model it will be shown that estimating the species accumulation curve not only is independent of the unknown number of species but also includes estimating the number of species as a limiting case for the purpose of interpolation moment based estimators associated with asymptotic confidence intervals are developed from several points of view a likelihood based procedure is developed for the purpose of extrapolation associated with bootstrap confidence intervals the proposed methods are illustrated by ecological data sets

modelling multiple time series via common factors we propose a new method for estimating common factors of multiple time series one distinctive feature of the new approach is that it is applicable to some nonstationary time series the unobservable nonstationary factors are identified by expanding the white noise space step by step thereby solving a high dimensional optimization problem by several low dimensional sub problems asymptotic properties of the estimation are investigated the proposed methodology is illustrated with both simulated and real datasets

self weighted lad based inference for heavy tailed threshold autoregressive models abstract the least squares estimator of the threshold autoregressive tar model may not be consistent when its tail is less than or equal to 2 neither theory nor methodology can be applied to model fitting in this case this paper is to develop a systematic procedure of statistical inference for the heavy tailed tar model we first investigate the self weighted least absolute deviation estimation for the model it is shown that the estimated slope parameters are n consistent and asymptotically normal and the estimated thresholds are n consistent each of which converges weakly to the smallest minimizer of a compound poisson process based on this theory the wald test statistic is considered for testing the linear restriction of slope parameters and a procedure is given for inference of threshold parameters we finally construct a sign based portmanteau test for model checking simulations are carried out to assess the performance of our procedure and a real example is given

robust m tests without consistent estimation of the asymptotic covariance matrix we extend the kvb approach of kiefer vogelsang and bunzel 2000 to constructing robust m tests without consistent estimation of the asymptotic covariance matrix we demonstrate that when model parameters have to be estimated the normalizing matrix computed using a full sample estimator is able to eliminate the nuisance parameters when there is no estimation effect but not otherwise to circumvent the problem of estimation effect we propose using recursive estimators to compute the normalizing matrix and show that the resulting m test is asymptotically pivotal this m test is thus robust not only to heteroscedasticity and serial correlations of unknown form but also to the presence of an estimation effect as examples we consider robust tests for serial correlations and robust information matrix tests the former tests extend that of lobato 2001 and are applicable to model residuals for testing higher order moments we find that the latter tests are also robust when a lower order moment is miss

comparing species assemblages via species accumulation curves comparing species assemblages given incidence based data is of importance in ecological studies often done by a visual inspection of estimated species accumulation curves or by an ad hoc use of 95 pointwise confidence bands of these curves it is shown that comparing species assemblages is a challenging problem a chi 2 test is proposed an adjustment using an eigenvalue decomposition is proposed to overcome computational difficulties the bootstrap method is also suggested to approximate the distribution of the proposed test statistic the eigenvalue adjusted eva chi 2 test and the eva bootstrap test are assessed by a simulation study both the eva chi 2 and the eva bootstrap tests are applied to a study that involves two woody seedling species assemblages

a bootstrapped spectral test for adequacy in weak arma models this paper proposes a cramer von mises cm test statistic to check the adequacy of weak arma models without posing a martingale difference assumption on the error terms the asymptotic null distribution of the cm test is obtained moreover this cm test is consistent and has nontrivial power against the local alternative of order n 1 2 due to the unknown dependence of error terms and the estimation effects a new block wise random weighting method is constructed to bootstrap the critical values of the test statistic the new method is easy to implement and its validity is justified the theory is illustrated by a small simulation study and an application to s p 500 stock index

testing that a dependent process is uncorrelated an analysis is presented of a new testing procedure for the null hypothesis that a stochastic process is uncorrelated when the process is possibly dependent unlike with existing procedures the user does not need to choose any arbitrary number to implement the proposed test the asymptotic null distribution of the proposed test statistic is not standard but it is tabulated by means of simulations the test is compared with two alternative test procedures that require selection of user chosen numbers on the basis of asymptotic local power and finite sample behavior although the asymptotic local power of the proposed test is lower than those corresponding to the alternative tests in a monte carlo study i show that in small samples the test typically better controls the type i error and that the loss of power is not substantial

hecke theory of series formed with modular symbols and relations among convolution l functions in g1 g2 the distribution of modular symbols is studied and a new class of functions which satisfy a transformation law involving these objects is introduced the goal of goldfeld s program is to prove szpiro s conjecture which states that for elliptic curves with minimal discriminant d and conductor n there is an absolute constant such that d n to do this an equivalent conjecture involving modular symbols is established in g4 using the now proven conjecture of shimura taniyama and weil it seems that a sufficiently good understanding of the new series proposed by goldfeld should yield a resolution of these conjectures we repeat here their definition in a somewhat more general form to include period polynomials rather than modular symbols only for positive integers m n such that m n let m k be non negative integers such that m k 2 0 and let be a dirichlet character modulo n first for each f sk m holomorphic cusp forms of weight k and level m we denote by rf the map which sends 0 m the hecke congruence group of level m to the polynomial function

asymptotic inference in multiple threshold double autoregressive models abstract this paper investigates a class of multiple threshold models called multiple threshold double ar mtdar models a sufficient condition is obtained for the existence and uniqueness of a strictly stationary and ergodic solution to the first order mtdar model we study the quasi maximum likelihood estimator qmle of the mtdar model the estimated thresholds are shown to be n consistent asymptotically independent and to converge weakly to the smallest minimizer of a two sided compound poisson process the remaining parameters are n consistent and asymptotically multivariate normal in particular these results apply to the multiple threshold arch model with or without ar part and to the multiple threshold ar models with arch errors a score based test is also presented to determine the number of thresholds in mtdar models the limiting distribution is shown to be distribution free and is easy to implement in practice simulation studies are conducted to assess the performance of the qmle and our score based test in finite samples the results are illustrated with an application to the quarterly us real gnp data over the period 1947 2013

inference for autocorrelations under weak assumptions abstract in this article we consider the large sample behavior of estimates of autocorrelations and autoregressive moving average arma coefficients as well as their distributions under weak conditions specifically the usual text book formulas for variances of these estimates are based on strong assumptions and should not be routinely applied without careful consideration such is the case when the time series follows an arma process with uncorrelated innovations that may not be assumed to be independent and identically distributed as a specific case it is well known that if the process is independent and identically distributed then the sample autocorrelation estimates scaled by the square root of the sample size are asymptotically standard normal this result is used extensively as a diagnostic check on the residuals of a fitted model or as an initial test on the observed time series to determine whether further model fitting is warranted in this article we show that this result can be quite

nonidentifiability of population size from capture recapture data with heterogeneous detection probabilities heterogeneity in detection probabilities has long been recognized as problematic in mark recapture studies and numerous models developed to accommodate its effects individual heterogeneity is especially problematic in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes thus even with very large samples the analyst will not be able to distinguish among reasonable models of heterogeneity even though these yield quite distinct inferences about population size the problem is illustrated with models for closed and open populations

an asymptotically pivotal transform of the residuals sample autocorrelations with application to model checking we propose an asymptotically distribution free transform of the sample autocorrelations of residuals in general parametric time series models possibly nonlinear in variables the residuals autocorrelation function is the basic model checking tool in time series analysis but it is not useful when its distribution is incorrectly approximated because the effects of parameter estimation and or higher order serial dependence have not been taken into account the limiting distribution of the residuals sample autocorrelations may be difficult to derive particularly when the underlying innovations are uncorrelated but not independent in contrast our proposal is easily implemented in fairly general contexts and the resulting transformed sample autocorrelations are asymptotically distributed as independent standard normals when innovations are uncorrelated providing an useful and intuitive device for time series model checking in the presence of estimated parameters we also discuss in detail alternatives to

inconsistency of the mle and inference based on weighted ls for larch models this paper considers a class of finite order autoregressive linear arch models the model captures the leverage effect allows the volatility to be arbitrarily close to zero and to reach its minimum for non zero innovations and is appropriate for long memory modeling when infinite orders are allowed however the quasi maximum likelihood estimator is in general inconsistent a self weighted least squares estimator is proposed and is shown to be asymptotically normal a score test for conditional homoscedasticity and diagnostic portmanteau tests are developed their performance is illustrated via simulation experiments it is also investigated whether stock market returns exhibit some of the characteristic features of the linear arch model

white noise testing and model diagnostic checking for functional time series abstract this paper is concerned with white noise testing and model diagnostic checking for stationary functional time series to test for the functional white noise null hypothesis we propose a cramer von mises type test based on the functional periodogram introduced by panaretos and tavakoli 2013a using the hilbert space approach we derive the asymptotic distribution of the test statistic under suitable assumptions a new block bootstrap procedure is introduced to obtain the critical values from the non pivotal limiting distribution compared to existing methods our approach is robust to the dependence within white noise and it does not involve the choices of functional principal components and lag truncation number we employ the proposed method to check the adequacy of functional linear models and functional autoregressive models of order one by testing the uncorrelatedness of the residuals monte carlo simulations are provided to demonstrate the empirical advantages of the proposed method over existing alternatives our method is illustrated via an application to cumulative intradaily returns

diagnostic checking in multivariate arma models with dependent errors using normalized residual autocorrelations in this paper we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise we propose new portmanteau statistics

residual based rank specification tests for ar garch type models this paper derives the asymptotic distribution for a number of rank based and classical residual specification tests in ar garch type models we consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation residual symmetry and no structural breaks we also apply our method to backtesting value at risk for these tests we show that generally no size correction is needed in the asymptotic test distribution when applied to ar garch residuals obtained through gaussian quasi maximum likelihood estimation to be precise we give exact expressions for the limiting null distribution of the test statistics applied to standardized residuals and find that standard critical values often though not always lead to conservative tests for this result we give simple necessary and sufficient conditions simulations show that our asymptotic approximations work well for a large number of ar garch models and parameter values we also show that the rank based tests often though not always have superior power properties over the classical tests even if they are conservative an empirical application illustrates the relevance of these tests to the ar garch models for weekly stock market return indices of some major and emerging countries

autoregressive conditional duration a new model for irregularly spaced transaction data this paper proposes a new statistical model for the analysis of data which arrive at irregular intervals the model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates the conditional intensity is developed and compared with other self exciting processes because the model focuses on the expected duration between events it is called the autoregressive conditional duration acd model asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to arch model results strong evidence is provided for duration clustering for the financial transaction data analyzed both deterministic time of day effects and stochastic effects are important the model is applied to the arrival times of trades and therefore is a model of transaction volume and also to the arrival of other events such as price changes models for the volatility of prices are estimated with price based durations and examined from a market microstructure point of view

properties of eisenstein series formed with modular symbols in this work a new kind of non holomorphic eisenstein series first introduced by goldfeld is studied for an arbitrary fuchsian group of the first kind we fix a holomorphic cusp form and consider eisenstein series constructed with the modular symbol associated with this cusp form we develop the theory analogously with that of the usual eisenstein series starting with its meromorphic continuation to the entire complex plane a functional equation is then obtained relating the values at s to those at 1 s introduction let h z c im z 0 be the upper half plane and let sl2 r be a fixed non co compact fuchsian group of the first kind for example n 0 n acting on h for simplicity assume that has a unique cusp at infinity with stability group 1 m 0 1 m z for each in we shall label its matrix elements a b c d let f z be an element of s2 the space holomorphic cusp forms of weight 2 for following go we define a modified eisenstein series 0 1 e z s f im z s z h where for the modular symbol is given by f 2 i w w f d the definition being independent of w h note that since 1 2 f 1 f 2 f the series is not automorphic the transformation rule is e z s e z s f e z s for all where e z s is the usual eisenstein series for this new type of non holomorphic eisenstein series was introduced by goldfeld in order to study the distribution properties of modular symbols f as ranges over the group the series 0 1 converges for re s 2 and goldfeld hypothesised that it should have an analytic continuation and a functional equation in this paper selberg s method described in iw he is extended to establish the following results typeset by ams tex 1

diagnostic checking in arma models with uncorrelated errors we consider tests for lack of fit in arma models with nonindependent innovations in this framework the standard box pierce and ljung box portmanteau tests can perform poorly specifically the usual text book formulas for asymptotic distributions are based on strong assumptions and should not be applied without careful consideration in this article we derive the asymptotic covariance matrix of a vector of autocorrelations for residuals of arma models under weak assumptions on the noise the asymptotic distribution of the portmanteau statistics follows a consistent estimator of and a modification of the portmanteau tests are proposed this allows us to construct valid asymptotic significance limits for the residual autocorrelations and asymptotically valid goodness of fit tests when the underlying noise process is assumed to be noncorrelated rather than independent or a martingale difference a set of monte carlo experiments and an application to the standard poor 500 returns illustrate the p

quasi maximum likelihood estimation of stochastic volatility models abstract changes in variance or volatility over time can be modelled using stochastic volatility sv models this approach is based on treating the volatility as an unobserved vatiable the logarithm of which is modelled as a linear stochastic process usually an autoregression this article analyses the asymptotic and finite sample properties of a quasi maximum likelihood qml estimator based on the kalman filter the relative efficiency of the qml estimator when compared with estimators based on the generalized method of moments is shown to be quite high for parameter values often found in empirical applications the qml estimator can still be employed when the sv model is generalized to allow for distributions with heavier tails than the normal sv models are finally fitted to daily observations on the yen dollar exchange rate

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

bootstrapping the portmanteau tests in weak auto regressive moving average models this paper uses a random weighting rw method to bootstrap the critical values for the ljung box monti portmanteau tests and weighted ljung box monti portmanteau tests in weak arma models unlike the existing methods no user chosen parameter is needed to implement the rw method as an application these four tests are used to check the model adequacy in power garch models simulation evidence indicates that the weighted portmanteau tests have the power advantage over other existing tests a real example on s p 500 index illustrates the merits of our testing procedure as one extension work the block wise rw method is also studied

an automatic portmanteau test for serial correlation this article introduces a data driven box pierce test for serial correlation the proposed test is very attractive compared to the existing ones in particular implementation of this test is extremely simple for two reasons rst the researcher does not need to specify the order of the autocorrelation tested since the test automatically chooses this number second its asymptotic null distribution is chi square with one degree of freedom so there is no need of using a bootstrap procedure to estimate the critical values in addition the test is consistent and robust to the presence of conditional heteroskedasticity of unknown form finally the proposed test presents higher power in simulations than the existing ones for models commonly employed in empirical nance

estimating missing observations in economic time series abstract two related problems are considered the first concerns the maximum likelihood estimation of the parameters in an arima model when some of the observations are missing or subject to temporal aggregation the second concerns the estimation of the missing observations both problems can be solved by setting up the model in state space form and applying the kalman filter

estimation and forecasting in vector autoregressive moving average models for rich datasets we address the issue of modelling and forecasting macroeconomic variables using rich datasets by adopting the class of vector autoregressive moving average varma models we overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares iols estimator we establish the consistency and asymptotic distribution of the estimator for weak and strong varma p q models monte carlo results show that iols is consistent and feasible for large systems outperforming the mle and other linear regression based efficient estimators under alternative scenarios our empirical application shows that varma models are feasible alternatives when forecasting with many predictors we show that varma models outperform the ar 1 arma 1 1 bayesian var and factor models considering different model dimensions

arithmetic statistics of modular symbols mazur rubin and stein have recently formulated a series of conjectures about statistical properties of modular symbols in order to understand central values of twists of elliptic curve l functions two of these conjectures relate to the asymptotic growth of the first and second moments of the modular symbols we prove these on average by using analytic properties of eisenstein series twisted by modular symbols another of their conjectures predicts the gaussian distribution of normalized modular symbols ordered according to the size of the denominator of the cusps we prove this conjecture in a refined version that also allows restrictions on the location of the cusps

a semi nonparametric estimator of regression discontinuity design with discrete duration outcomes abstract we consider the regression discontinuity rd design with the duration outcome which has discrete support the parameters of policy interest are treatment effects on unconditional duration effect and conditional hazard effect exiting probabilities for each discrete level we propose a novel semi nonparametric estimator which exploits a flexible separability structure of the underlying continuous time duration process simultaneous inference over discrete levels is nonstandard since the asymptotic variance matrix is singular with unknown rank the peculiarity is delivered by the nature of the rd estimand and we provide solutions random censoring and competing risks can also be allowed in our framework

testing second order dynamics for autoregressive processes in presence of time varying variance this article considers the volatility modeling for autoregressive univariate time series a benchmark approach is the stationary autoregressive conditional heteroscedasticity arch model of engle motivated by real data evidence processes with nonconstant unconditional variance and arch effects have been recently introduced we take into account this type of nonstationarity in variance and propose simple testing procedures for arch effects adaptive mcleod and li s portmanteau and arch lm tests for checking the presence of such second order dynamics are provided the standard versions of these tests commonly used by practitioners suppose constant unconditional variance the failure of these standard tests with time varying unconditional variance is highlighted the theoretical results are illustrated by means of simulated and real data supplementary materials for this article are available online

estimating the number of species a review how many kinds are there suppose that a population is partitioned into c classes in many situations interest focuses not on estimation of the relative sizes of the classes but on estimation of c itself for example biologists and ecologists may be interested in estimating the number of species in a population of plants or animals numismatists may be concemed with estimating the number of dies used to produce an ancient coin issue and linguists may be interested in estimating the size of an author s vocabulary in this article we review the problem of statistical estimation of c many approaches have been proposed some purely data analytic and others based in sampling theory in the latter case numerous variations have been considered the population may be finite or infinite if finite samples may be taken with replacement multinomial sampling or without replacement hypergeometric sampling or by bernoulli sampling if infinite sampling may be multinomial or bernoulli or the sample may be th

combining nonparametric and optimal linear time series predictions we introduce a semiparametric procedure for more efficient prediction of a strictly stationary process admitting an arma representation the procedure is based on the estimation of the arma representation followed by a nonparametric regression where the arma residuals are used as explanatory variables compared to standard nonparametric regression methods the number of explanatory variables can be reduced because our approach exploits the linear dependence of the process we establish consistency and asymptotic normality results for our estimator numerical experiments show that significant gains can be achieved with our approach all the supplemental materials used by this article are available online

consistent testing for serial correlation of unknown form this paper proposes three classes of consistent one sided tests for serial correlation of unknown form for the residual from a linear dynamic regression model that includes both lagged dependent variables and exogenous variables the tests are obtained by comparing a kernel based normalized spectral density estimator and the null normalized spectral density using a quadratic norm the hellinger metric and the kullback leibler information criterion respectively under the null hypothesis of no serial correlation the three classes of new test statistics are asymptotically n 0 1 and equivalent the null distributions are obtained without having to specify any alternative model unlike some conventional tests for serial correlation the null distributions of our tests remain invariant when the regressors include lagged dependent variables under a suitable class of local alternatives the three classes of the new tests are asymptotically equally efficient under global alternatives however their relative efficiencies depend on the relative magnitudes of the three divergence measures our approach provides an interpretation for box and pierce s 1970 test which can be viewed as a quadratic norm based test using a truncated periodogram many kernels deliver tests with better power than box and pierce s test or the truncated kernel based test a simulation study shows that the new tests have good power against an ar 1 process and a fractionally integrated process in particular they have better power than the lagrange multiplier tests of breusch 1978 and godfrey 1978 as well as the portmanteau tests of box and pierce 1970 and ljung and box 1978 the cross validation procedure of beltrao and bloomfield 1987 and robinson 1991a works reasonably well in determining the smoothing parameter of the kernel spectral estimator and is recommended for use in practice