cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

rank based tests for randomness against first order serial dependence abstract optimal rank based procedures were derived in hallin ingenbleek and puri 1985 1987 and hallin and puri 1988 for some fundamental testing problems arising in time series analysis the optimality properties of these procedures are of an asymptotic nature however whereas much of the attractiveness of rank based methods lies in their small sample applicability and robustness features accordingly the objective of this article is twofold a a study of the finite sample behavior of the asymptotically optimal tests for randomness against first order autoregressive moving average dependence proposed in hallin et al 1985 both under the null hypothesis tables of critical values and under alternatives of serial dependence evaluation of the power function and b an heuristic investigation of the robustness properties of the proposed procedures with emphasis on the identification problem in the presence of outliers we begin sec 2 with a brief description of the rank based measu

gromov witten classes quantum cohomology and enumerative geometry the paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry in particular it contains an axiomatic treatment of gromov witten classes and a discussion of their properties for fano varieties cohomological field theories are defined and it is proved that tree level theories are determined by their correlation functions application to counting rational curves on del pezzo surfaces and projective spaces are given

testing serial correlations in high dimensional time series via extreme value theory abstract this paper proposes a simple test for detecting serial correlations in high dimensional time series the proposed test makes use of the robust properties of spearman s rank correlation and the theory of extreme values asymptotic properties of the test statistics are derived under some minor conditions as both the sample size and dimension go to infinity the test is not sensitive to the underlying distribution of the time series so long as the data are continuously distributed in particular the existence of finite order moments of the underlying distribution is not required and asymptotic critical values of the test statistics are available in closed form in finite samples we correct biases of the sample autocorrelations and conduct simulations to study the performance of the proposed test statistics simulation results show that the proposed test statistics enjoy good properties of size and power in finite samples we apply the proposed test to a 92 dimensional series of asset returns finally a simple r code is available to obtain finite sample critical values of the test statistics if needed

alternative variance and efficiency calculations for the case cohort design summary we define a bootstrap sampling plan for the case cohort design and present bootstrap variance estimates and confidence intervals for the log relative hazard the coverages of these confidence intervals are found to be near nominal levels in simulations a simple null variance calculation based on a superpopulation model is shown to provide good estimates of the power and efficiency of the case cohort design

geometric invariant theory and the generalized eigenvalue problem let g be a connected reductive subgroup of a complex connected reductive group hat g fix maximal tori and borel subgroups of g and hat g consider the cone mathcal lr g hat g generated by the pairs nu hat nu of dominant characters such that v nu is a submodule of v hat nu with usual notation here we give a minimal set of inequalities describing mathcal lr g hat g as a part of the dominant chamber in other words we describe the facets of mathcal lr g hat g which intersect the interior of the dominant chamber we also describe smaller faces finally we are interested in some classical redundant inequalities

t test in a structural equation properties of t ratios associated with the liml tsls and ols estimators in a structural form estimation are studied the existence of moments of these t ratios including the liml form is proved first second monte carlo simulations are performed to find out real sizes of the t test and the likelihood ratio test third asymptotic expansions of the distributions of t ratios are derived under the null hypothesis to find out deviations of real sizes from nominal sizes theoretically the asymptotic power functions are also derived

distribution free bounds for serial correlation coefficients in heteroskedastic symmetric time series abstract we consider the problem of testing whether the observations x 1 x n of a time series are independent with unspecified possibly nonidentical distributions symmetric about a common known median various bounds on the distributions of serial correlation coefficients are proposed exponential bounds eaton type bounds chebyshev bounds and berry esseen zolotarev bounds the bounds are exact in finite samples distribution free and easy to compute the performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment the procedures proposed are applied to u s data on interest rates commercial paper rate

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

infinite grassmannians and moduli spaces of g bundles let c be a smooth projective irreducible algebraic curve over c of any genus and g a connected simply connected simple affine algebraic group over c in this paper we elucidate the relationship between 1 the space of vacua conformal blocks defined in conformal field theory using an integrable highest weight representation of the affine kac moody algebra associated to g and 2 the space of regular sections generalised theta functions of a line bundle on the moduli space ta of semistable principal g bundles on c fix a point p in c and let p resp kp be the completion of the local ring p of c at p resp the quotient field of c p let g kp the kp rational points of the algebraic group g be the loop group of g and let g p be the standard maximal parahoric subgroup of then the generalised flag variety x n is an inductive limit of projective varieties in fact of generalised schubert varieties one has a natural r line bundle s on x cf sect 2 2 and the picard group pic x is isomorphic to z which is generated by s proposition 2 3 where f is the universal central extension of by the multiplicative group c cf sect 2 2 by an analogue of the borel weil theorem proved in the kac moody setting by kumar and also by mathieu the space h 162 s of the regular sections of the line bundle y dxo y xo for any d 0 is canonically isomorphic with the full vector space dual v dxo of the integrable highest weight irreducible module v dxo of the affine kacmoody group or of the associated affine kac moody algebra which is a certain one dimensional central extension of the loop algebra lie g with highest weight dxo cf sect 6 1

power calculation for case cohort studies with nonrare events summary case cohort design has been advocated in many epidemiologic studies when studying rare diseases or events in this design with a rare event all the events are selected for risk factor assessment when the event is not rare it is desirable to consider a generalized case cohort design where only a fraction of events are sampled we provide a valid test statistic to compare hazards functions between two samples for this generalized design and give a method for calculating power our result generalizes the result in cai and zeng 2004 biometrics60 1015 1024 and it shows numerically that efficiency loss due to sampling only part of the events is very low under nonrare events situation

more efficient estimators for case cohort studies the case cohort study design used to reduce costs in large cohort studies is a random sample of the entire cohort named the subcohort augmented with subjects having the disease of interest but not in the subcohort sample when several diseases are of interest several case cohort studies may be conducted using the same subcohort with each disease analyzed separately ignoring the additional exposure measurements collected on subjects with the other diseases this is not an efficient use of the data and in this paper we propose more efficient estimators we consider both joint and separate analyses for the multiple diseases we propose an estimating equation approach with a new weight function and we establish the consistency and asymptotic normality of the resulting estimator simulation studies show that the proposed methods using all available information gain efficiency we apply our proposed method to the data from the busselton health study

the use of subseries values for estimating the variance of a general statistic from a stationary sequence let z i infty i infty be a strictly stationary infty mixing sequence without specifying the dependence model giving rise to z i and without specifying the marginal distribution of z i we address the question of variance estimation for a general statistic t n t n z 1 z n for estimating var t n from just the available data z 1 z n we propose computing subseries values t m z i 1 z i 2 z i m 0 leq i i m leq n these subseries values are used as replicates to model the sampling variability of t n in particular we use adjacent nonoverlapping subseries of length m m n with m rightarrow infty and m n n rigtharrow 0 our variance estimator is just the usual sample variance computed amongst these subseries values after appropriate standardization this estimator is shown to be consistent under mild integrability conditions we present optimal i e minimum m s e choices of m n for the special case where t n overset z n and z i is a normal ar 1 sequence a simulation study is conducted showing that those same choices of m n are effective when t n is a robust estimator of location and z i is subject to contamination

optimal rank based procedures for time series analysis testing an arma model against other arma models the problem of testing a given arma model in which the density of the generating white noise is unspecified against other arma models is considered a distribution free asymptotically most powerful test based on a generalized linear serial rank statistic is provided against contiguous arma alternatives with specified coefficients in the case when the arma model in the alternative has unspecified coefficients the asymptotic sufficiency in the sense of le cam of a finite dimensional vector of rank statistics is established this asymptotic sufficiency is used to derive an asymptotically maximin most powerful test based on a generalized quadratic serial rank statistic the asymptotically maximin optimal test statistic can be interpreted as a rank based weighted version of the classical box pierce portmanteau statistic to which it reduces in some particular problems asymptotically and under gaussian assumptions

a laplace approximation to the moments of a ratio of quadratic forms summary the laplace method for approximating integrals is applied to give a general approximation for the kth moment of a ratio of quadratic forms in random variables the technique utilises the existence of a dominating peak at the boundary point on the range of integration as closed form and tractable formulae do not exist in general this simple approximation which only entails basic algebraic operations has evident practical appeal we exploit the approximation to provide an approximate mean bias function for the least squares estimator of the coefficient of the lag dependent variable in a first order stochastic difference equation

moments of the ratio of quadratic forms in non normal variables with econometric examples abstract in this paper we have provided a general result on the higher order approximate moments of the ratio of quadratic forms in the non normal vector the results for the normal case are then presented as a special case of this result it is also indicated that the results for a large class of econometric estimators and test statistics can be obtained by using our general result

properties of predictors for autoregressive time series abstract the prediction of the n s th observation of the pth order autoregressive process is investigated the mean square of the predictor error through terms of order n 1 conditional on yn y n 1 y n p 1 is obtained for the stationary normal process the mean squared error expression is similar to the usual regression formula for the variance of the predictor error the usual regression formula for the estimated variance of a predictor error and its generalization to s period prediction is shown to provide a consistent estimator of the mean squared error of the least squares predictor for both stationary and non stationary processes

empirical likelihood based inference in conditional moment restriction models this paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions our estimator generalizes the maximum empirical likelihood estimator mele of qin and lawless 1994 using a kernel smoothing method we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood based procedure this yields a one step estimator which avoids estimating optimal instruments our likelihood ratio type statistic for parametric restrictions does not require the estimation of variance and achieves asymptotic pivotalness implicitly the estimation and testing procedures we propose are normalization invariant simulation results suggest that our new estimator works remarkably well in finite samples

the exact moments of ols in dynamic regression models with non normal errors abstract this paper studies the finite sample sensitivity of ols estimators of the autoregressive coefficient in a first order stochastic difference equation with i i d errors drawn from an edgeworth gram charlier population analytic formula for the first and second moments of the estimator are derived using the results of davis 1976 and sawa 1972 also numerical evaluation of these general formulae is undertaken and the results are presented under selected alternative parameter scenarios the results suggest that the exact bias is relatively insensitive to skewness and kurtosis in the underlying error distribution but that the exact mse is relatively sensitive to both skewness and kurtosis and this sensitivity increases as the signal to noise ratio increases

properties of optimal forecasts under asymmetric loss and nonlinearity abstract evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss under this loss function optimal forecasts should be unbiased and forecast errors serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows using analytical results we show that standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast we establish instead that a suitable transformation of the forecast error known as the generalized forecast error possesses an equivalent set of properties the paper also provides empirical examples to illustrate the significance in practice of asymmetric loss and nonlinearities and discusses the effect of parameter estimation error on optimal forecasts

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

the second order bias and mean squared error of estimators in time series models we develop analytical results on the second order bias and mean squared error of estimators in time series models these results provide a unified approach to developing the properties of a large class of estimators in linear and nonlinear time series models and they are valid for both normal and nonnormal samples of observations and where the regressors are stochastic the estimators included are the generalized method of moments maximum likelihood least squares and other extremum estimators our general results are applied to four time series models we investigate the effects of nonnormality on the second order bias results for two of these models while for all four models the second order bias and mean squared error results are given under normality numerical results for some of these models are also presented

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

the student s t approximation in a stationary first order autoregressive model the basic model is a gaussian ar 1 model with an intercept but no additional exogenous variables the paper studies the distribution of the t statistic for testing the value of the autoregressive parameter when the model is estimated by least squares the monte carlo estimates of the quantiles of the t statistic show that student s t is not a satisfactory approximation for sample sizes typical in economic applications the main problem is not the shape of the distribution of the t statistic but its location adjusting the t statistic so that it has the same mean and standard deviation as student s t the distribution of this adjusted t statistic is accurately approximated by student s t techniques are presented for accurately approximating the mean and standard deviation of the t statistic such that the adjusted t statistic can be readily calculated in practice the analysis is extended in two directions the first is to examine the effect of introducing an exogenous variable into the basic model in the expanded model student s t also accurately approximates the distribution of the t statistic for testing the autoregressive parameter and for testing the coefficient of the exogenous variable after these t statistics are adjusted for mean and standard deviation the problem of obtaining a feasible adjustment procedure is that the moments of these t statistics now depend on nuisance parameters the second is to examine the robustness of the results in the basic model to several nonnormal error distributions for each nonnormal distribution the t statistic is adjusted using the mean and standard deviation appropriate for the case of normal errors and then the distribution of the modified t statistic is compared with that of student s t

bias reduction in nonlinear and dynamic panels in the presence of cross section dependence abstract fixed effects estimation of nonlinear dynamic panel models is subject to the incidental parameter issue leading to a biased asymptotic distribution while this problem has been studied extensively in the literature a general analysis allowing for both serial and cross sectional dependence is missing in this paper we investigate the large n t theory of the profile and integrated likelihood estimators allowing for dependence across both dimensions we show that under stronger dependence types the asymptotic bias disappears but a o p 1 t small sample bias remains we provide bias correction and inference methods and also obtain primitive conditions for asymptotic normality under various dependence settings

robust score and portmanteau tests of volatility spillover abstract this paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or garch type feedback the tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent we negligibly trim test equations or components of the equations and construct heavy tail robust score and portmanteau statistics trimming is either simple based on an indicator function or smoothed in particular we develop the tail trimmed sample correlation coefficient for robust inference and prove that its gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness further if spillover occurs within a specified horizon our test statistics obtain power of one asymptotically we discuss the choice of trimming portion including a smoothed p value over a window of extreme observations a monte carlo study shows our tests provide significant improvements over extant garch based tests of spillover and we apply the tests to financial returns data finally based on ideas in patton 2011 we construct a heavy tail robust forecast improvement statistic which allows us to demonstrate that our spillover test can be used as a model specification pre test to improve volatility forecasting

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

smoothed quantile regression for panel data abstract this paper studies fixed effects estimation of quantile regression models for panel data under an asymptotic framework where both the numbers of individuals and time periods grow at the same rate we show that the fixed effects estimator for the smoothed objective function has a limiting normal distribution with a bias in the mean and provide the analytic form of the asymptotic bias we propose a one step bias correction estimator based on the analytic bias formula obtained from the asymptotic analysis importantly our results cover the case that observations are dependent over time we illustrate the effects of the bias correction through simulations

a theorem of validity for edgeworth expansisons on considere des equations autoregressives a variables exogenes et un terme de bruit blanc normal ce qui generalise les modeles dynamiques etudies precedemment

the exact multi period mean square forecast error for the first order autoregressive model the finite sample behaviour of the multi period least squares forecast is considered in the simple normal autoregressive model yt yt 1 ut where 1 necessary and sufficient conditions are established for the existence of the forecast bias and the mean square forecast error msfe and an exact expression for the msfe is given exact numerical results are obtained for both the stationary and the fixed start up case our main conclusions are that for small values of the msfe is a decreasing function of the number of forecast periods and that the behaviour of the msfe in the stationary and the fixed start up case is very similar except for values of close to 1

the rank version of von neumann s ratio test for randomness abstract although rank tests for randomness were proposed in the literature as early as 1943 no such test has gained wide acceptance comparable to say spearman s rho test this may be due to the lack of small sample theory and of tables of critical values to enable such a test to be carried out on small samples in this article we consider the rank version of the von neumann ratio statistic and we obtain the critical values of this statistic under the randomization hypothesis in a monte carlo experiment we then show that the resulting nonparametric test for randomness has far greater power than the test based on the number of runs up and down moreover under normality its power vis a vis the normal theory von neumann ratio test is also very good it is therefore suggested that with the tables presented in this article the rank von neumann ratio test for randomness provides an easy and powerful alternative to nonparametric tests now in common use

some robust exact results on sample autocorrelations and tests of randomness abstract several exact results on the second moments of sample autocorrelations for both gaussian and non gaussian series are presented general formulae for the means variances and covariances of sample autocorrelations are given for the case where the variables in a sequence are exchangeable bounds for the variances and covariances of sample autocorrelations from an arbitrary random sequence are derived exact and explicit formulae for the variances and covariances of sample autocorrelations from a gaussian white noise are given it is observed that the latter results hold for all spherically symmetric distributions a simulation experiment with gaussian series indicates that normalizing each sample autocorrelation with its exact mean and variance instead of the usual approximate moments can improve considerably the accuracy of the asymptotic n 0 1 distribution to obtain critical values for tests of randomness the exact second moments of rank autocorrelations are also studied

the exact multi period mean square forecast error for the first order autoregressive model with an intercept abstract we study the exact finite sample behaviour of the mean square forecast error msfe of multi period least squares forecasts in the normal autoregressive model y t y t 1 u t we obtain necessary and sufficient conditions for the existence of the msfe and give an exact expression which we use to obtain numerical results for both the stationary and the fixed start up model we conclude inter alia that the behaviour of the msfe in the model with intercept can be very different from that in the model without intercept especially when is close to unity

efficient information theoretic inference for conditional moment restrictions abstract the generalised method of moments estimator may be substantially biased in finite samples especially so when there are large numbers of unconditional moment conditions this paper develops a class of first order equivalent semi parametric efficient estimators and tests for conditional moment restrictions models based on a local or kernel weighted version of the cressie read power divergence family of discrepancies this approach is similar in spirit to the empirical likelihood methods of kitamura et al 2004 empirical likelihood based inference in conditional moment restrictions models econometrica 72 1667 1714 and tripathi and kitamura 2003 testing conditional moment restrictions annals of statistics 31 2059 2095 these efficient local methods avoid the necessity of explicit estimation of the conditional jacobian and variance matrices of the conditional moment restrictions and provide empirical conditional probabilities for the observations

the multiplicative eigenvalue problem and deformed quantum cohomology abstract we construct deformations of the small quantum cohomology rings of homogeneous spaces g p and obtain an irredundant set of inequalities determining the multiplicative eigen polytope for the compact form k of g

an equivariant version of grauert s oka principle for example a theorem of oka asserts that every holomorphic line bundle over a domain of holomorphy in 12 is holomorphicaily trivial if and only if it is topologically trivial in g3 grauer t proves that the category of bundles over a stein space x with a complex lie group as a structure group is the same up to isomorphism if considered in the topological or complex analytic category we would like to underl ine that grauert s method of proof also has far reaching consequences see e g fr1 fr2 in this article we prove the equivariant version of grauert s oka principle for a compact lie group of holomorphic t ransformations on x the precise statements can be found in w w and w for example as a consequence of the main results we obtain

exact permutation tests for non nested non linear regression models abstract this paper proposes exact distribution free permutation tests for the specification of a non linear regression model against one or more possibly non nested alternatives the new tests may be validly applied to a wide class of models including models with endogenous regressors and lag structures these tests build on the well known j test developed by davidson and mackinnon 1981 several tests for model specification in the presence of alternative hypotheses econometrica 49 781 793 and their exactness holds under broader assumptions than those underlying the conventional j test the j type test statistics are used with a randomization or monte carlo resampling technique which yields an exact and computationally inexpensive inference procedure a simulation experiment confirms the theoretical results and also shows the performance of the new procedure under violations of the maintained assumptions the test procedure developed is illustrated by an application to inflation dynamics

the exact moments of the least squares estimator for the autoregressive model corrections and extensions abstract for a first order autoregressive model with unknown intercept and normal errors the mean and variance of the finite sample distribution of the least squares estimator of the autoregressive parameter are numerically computed using formulae for evaluating the first and second moments of a ratio of two quadratic forms in normally distributed variables previous results in the literature are corrected and results for the case where the value of the autoregressive parameter is near unity in absolute value are presented

properties of predictors in misspecified autoregressive time series models abstract this article investigates major effects of misspecification in stationary linear time series models when we fit a pth order autoregressive model the true model can be an autoregressive moving average model we derive the formulas of bias and mean squared error mse of the least squares estimator and the hth period ahead prediction mse in the time domain contrary to previous studies the process in estimation is not necessarily independent of the process in prediction and the distribution of process is not necessarily gaussian we examine the effects of this dependence and nonnormality on prediction in misspecified models

jackknife and analytical bias reduction for nonlinear panel models fixed effects estimators of panel models can be severely biased because of the well known incidental parameters problem we show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large t we give bias corrections for averages over the fixed effects as well as model parameters we find large bias reductions from using these approaches in examples we consider asymptotics where t grows with n as an approximation to the properties of the estimators in econometric applications we show that if t grows at the same rate as n the fixed effects estimator is asymptotically biased so that asymptotic confidence intervals are incorrect but that they are correct for the panel jackknife we show t growing faster than n 1 3 suffices for correctness of the analytic correction a property we also conjecture for the jackknife

bias in dynamic panel estimation with fixed effects incidental trends and cross section dependence abstract explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size n the results extend earlier work by nickell 1981 biases in dynamic models with fixed effects econometrica 49 1417 1426 and later authors in several directions that are relevant for practical work including models with unit roots deterministic trends predetermined and exogenous regressors and errors that may be cross sectionally dependent the asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient another finding of interest is that when there is cross section error dependence the probability limit of the dynamic panel regression estimator is a random variable rather than a constant which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where n is very large some proposals for bias correction are suggested and finite sample performance is analyzed in simulations

multi step estimation and forecasting in dynamic models abstract we consider the situation in which a researcher uses a misspecified model for forecasting if the interest is in multi step forecasting and the accuracy of the forecasts is measured through the sum of squared multi step forecast errors then in large samples it is preferable to minimize corresponding sum of squared in sample multi step forecast errors we derive the asymptotic properties of the resulting estimator to asses the behavior of the estimator in small samples we perform a monte carlo experiment in most of the cases considered ols outperforms the estimator we conjecture that this occurs because the estimator is still defined on the basis of squared errors

multiplicative models and cohort analysis abstract three methods of cohort analysis are presented for a statistical model wherein the explanatory or exposure variables act multiplicatively on age calendar year specific death rates the first method which assumes that the baseline rates are known from national vital statistics is a multiple regression analysis of the standardized mortality ratio the second method is a variant of cox s proportional hazards analysis in which the baseline rates are treated as unknown nuisance parameters the third method consists of case control sampling from the risk sets formed in the course of applying cox s model it requires substantially less computation than do the other two in illustrative analysis of respiratory cancer deaths among a cohort of smelter workers all three approaches yield roughly equivalent estimates of the relative risk associated with arsenic exposure the discussion centers on the tradeoff between efficiency and bias in the selection of a particular method of analysis and on practica

bootstrap inference for linear dynamic panel data models with individual fixed effects abstract this paper s main contribution is to propose and theoretically justify the application of bootstrap methods for inference in autoregressive panel data models with fixed effects whereas the focus of the existing literature has been on bias correcting the standard fixed effects ols estimator due to the well known incidental parameter bias our focus here is on improving the quality of inference by relying on the bootstrap instead of the standard normal distribution when computing critical values for test statistics in particular we show by simulation that confidence intervals based on the normal distribution can be very distorted in finite samples instead a bootstrap that resamples the residuals and generates the bootstrap observations recursively using the estimated autoregressive panel data model greatly reduces these distortions we show that this recursive design residual based bootstrap fixed effects ols estimator contains a built in bias correction term that mimics the incidental parameter bias thus this method can be used to approximate the bias as well as the entire distribution of the biased fixed effects ols estimator this is in contrast with two other methods we consider a fixed design residual based bootstrap and a pairs bootstrap whose distributions are incorrectly centered at zero as it turns out both the recursive design and the pairs bootstrap are asymptotically valid when applied to the bias corrected estimator but the fixed design bootstrap is not in the simulations the recursive design bootstrap is the method that does best overall

a simple r estimation method for semiparametric duration models modeling nonnegative financial variables e g durations between trades traded volumes or asset volatilities is central to a number of studies across financial econometrics and despite the efforts still poses several statistical challenges among them the efficiency aspects of semiparametric estimation in this paper we concentrate on estimation problems in autoregressive conditional duration acd models with unspecified innovation densities exponential quasi likelihood estimators qmle are the usual practice in that context the efficiency of those qmles the only fisher consistent qmles unfortunately rapidly deteriorates away from the reference exponential density a phenomenon that has been emphasized earlier by drost and werker 2003 who propose various semiparametrically efficient procedures to palliate that phenomenon those procedures rely on a general semiparametric approach which typically requires kernel estimation of the underlying innovation density we propose rank based estimators r estimators as a substitute just as the qmle r estimators remain root n consistent irrespective of the underlying density and rely on the choice of a reference density under which they achieve semiparametric efficiency that density however needs not be the exponential one contrary to the semiparametric estimators proposed by drost and werker 2003 r estimators neither require tangent space calculations nor kernel based density estimation numerical results moreover indicate that r estimators based on exponential reference densities uniformly outperform the exponential qmle under such families of innovations as the weibull or burr densities a real data example about modeling the price range of the swiss stock market index concludes the paper

permutational extreme values of autocorrelation coefficients and a pitman test against serial dependence somewhat more difficult this problem which is shown to reduce to a particular case of the well known travelling salesman problem is explicitly solved here for the autocorrelation coefficient of order one allowing for a simple computation of permutational critical values for pitman tests against serial dependence the case of higher order autocorrelations is however of a different nature and requires another approach

quantum generalization of the horn conjecture recall that the lie algebra of the special unitary group su n is isomorphic to the real vector space of traceless hermitian matrices as representations of su n and hence the terminology additive eigenvalue problem for su n in 1962 horn 17 gave a conjectural solution to a problem equivalent to the above additive eigenvalue problem for su n by a recursively determined system of inequalities in 19 klyachko gave a solution to the additive eigenvalue problem for su n in terms of a certain system of inequalities to write down this system we need to know which structure constants in the cohomology of gr r n written in the schubert basis 0 2 be a positive integer characterize the possible eigenvalues a1 a2 as of matrices a a 2 a e su n which satisfy a a a 1

modified models and simulations for estimating dynamic functional connectivity in resting state functional magnetic resonance imaging as understanding the nature of brain networks through dynamic functional connectivity dfc estimation is of paramount significant the introduction and revision of blood oxygen level dependent bold signal simulation methods in brain regions and dfc estimation methods have gained significant ground in recent years based on the observation of bold signals with multivariate nonnormal distribution in functional magnetic resonance imaging fmri images we first propose a copula based method for the production of these signals in which nonnormal data are generated with a selected time varying covariance matrix therefore we can compare the performance of models in the cases where brain signals have a multivariate nonnormal distribution then two kendallized exponentially weighted moving average kewma and kendallized dynamic conditional correlation kdcc multivariate volatility models are introduced which are based on two well known and commonly used exponentially weighted moving average emwa and dynamic conditional correlation dcc models the results show that kdcc model can estimate conditional correlation significantly far better than the former ones ie dcc standardized dynamic conditional correlation ewma and standardized exponentially weighted moving average on both types of data ie multivariate normal and nonnormal in the next step the bivariate normal distribution in iranian resting state fmri data is confirmed by using statistical tests and it is shown that the dynamic nature of fc is not optimally detected using prevalent methods two alternative portmanteau and rank based tests are proposed for the examination of conditional heteroscedasticity in data finally dfc in these data is estimated by employing the kdcc model

how to implement the bootstrap in static or stable dynamic regression models test statistic versus confidence region approach by combining two alternative formulations of a test statistic with two alternative resampling schemes we obtain four different bootstrap tests in the context of static linear regression models two of these are shown to have serious size and power problems whereas the remaining two are adequate and in fact equivalent the equivalence between the two valid implementations is shown to break down in dynamic regression models then the procedure based on the test statistic approach performs best at least in the ar 1 model similar finite sample phenomena are illustrated in the arma 1 1 model through a small scale monte carlo study and an empirical example

optimal bandwidth selection in heteroskedasticity autocorrelation robust testing the paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors the studentization is based on robust standard errors with truncation lag m bt for some constant b 2 0 1 and sample size t it is shown that the nonstandard xed b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the nite sample distributions than the standard small b limit distribution we further show that for typical economic time series the optimal bandwidth that minimizes a weighted average of type i and type ii errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long run variance estimator a plug in procedure for implementing this optimal bandwidth is suggested and simulations not reported here con rm that the new plug in procedure works well in nite samples

marginal hazards model for case cohort studies with multiple disease outcomes case cohort study designs are widely used to reduce the cost of large cohort studies while achieving the same goals especially when the disease rate is low a key advantage of the case cohort study design is its capacity to use the same subcohort for several diseases or for several subtypes of disease in order to compare the effect of a risk factor on different types of diseases times to different events need to be modelled simultaneously valid statistical methods that take the correlations among the outcomes from the same subject into account need to be developed to this end we consider marginal proportional hazards regression models for case cohort studies with multiple disease outcomes we also consider generalized case cohort designs that do not require sampling all the cases which is more realistic for multiple disease outcomes we propose an estimating equation approach for parameter estimation with two different types of weights consistency and asymptotic normality of the proposed estimators are established large sample approximation works well in small samples in simulation studies the proposed methods are applied to the busselton health study

a note on autoregressive error components models abstract the purpose of this paper is to shed some light on the asymptotic behavior of a wide class of estimators for a dynamic error components model when only the number of individuals tends to infinity the number of time periods being kept fixed in particular it is shown that this asymptotic behavior is highly dependent on the assumption about the initial observations and that it offers very good approximations to the small sample behavior of the various estimators under consideration

inference for unit roots in dynamic panels where the time dimension is fixed this paper derives similar asymptotic unit root tests for first order autoregressive panel data models assuming that the time dimension of the panel is fixed it is shown that the limiting distributions of the test statistics are normal the assumption that the time dimension is fixed allows us to derive analytical expressions for the moments of the distributions similarity with respect to the initial conditions of the data generating process is achieved by including fixed effect dummy variables in the regression model while similarity with respect to fixed effects in the data generating process is achieved by including a linear deterministic trend for each individual unit of the panel when fixed effects or individual trends are included as regressors the least squares estimator of the autoregressive parameter is inconsistent and thus the test statistics must be appropriately adjusted monte carlo evidence suggests that the proposed tests have empirical size that is very close to the nominal five percent level and substantially more power than the corresponding unit root tests for the single time series case

jackknife bootstrap and other resampling methods in regression analysis motivated by a representation for the least squares estimator we propose a class of weighted jackknife variance estimators for the least squares estimator by deleting any fixed number of observations at a time they are unbiased for homoscedastic errors and a special case the delete one jackknife is almost unbiased for heteroscedastic errors the method is extended to cover nonlinear parameters regression m estimators nonlinear regression and generalized linear models interval estimators can be constructed from the jackknife histogram three bootstrap methods are considered two are shown to give biased variance estimators and one does not have the bias robustness property enjoyed by the weighted delete one jackknife a general method for resampling residuals is proposed it gives variance estimators that are bias robust several bias reducing estimators are proposed some simulation results are reported

the strange duality conjecture for generic curves let sux r be the moduli space of semi stable vector bundles of rank r with trivial determinant over a connected smooth projective algebraic curve x of genus g 1 over c recall that a vector bundle e on x is called semi stable if for any subbundle v deg v rk v deg e rk e points of sux r correspond to isomorphism classes of semi stable rank r vector bundles with trivial determinant up to an equivalence relation for any line bundle l of degree g 1 onx define l e sux r h e l 1 this turns out be a non zero cartier divisor whose associated line bundle l o l does not depend upon l it is known that l generates the picard group of sux r for this and the precise definition of l in terms of determinant of cohomology see dn let u x k be the moduli space of semi stable rank k and degree k g 1 bundles on x recall that on u x k there is a canonical non zero theta cartier divisor k whose underlying set is f u x k h x f 0 put m o k consider the natural map k r sux r u x k u x kr given by tensor product from the theorem of the square it follows that k rm is isomorphic to l m the canonical element kr h0 u x kr m and the kunneth theorem give a map well defined up to scalars

common correlated effects estimation of heterogeneous dynamic panel data models with weakly exogenous regressors abstract this paper extends the common correlated effects cce approach developed by pesaran 2006 to heterogeneous panel data models with lagged dependent variables and or weakly exogenous regressors we show that the cce mean group estimator continues to be valid but the following two conditions must be satisfied to deal with the dynamics a sufficient number of lags of cross section averages must be included in individual equations of the panel and the number of cross section averages must be at least as large as the number of unobserved common factors we establish consistency rates derive the asymptotic distribution suggest using covariates to deal with the effects of multiple unobserved common factors and consider jackknife and recursive de meaning bias correction procedures to mitigate the small sample time series bias theoretical findings are accompanied by extensive monte carlo experiments which show that the proposed estimators perform well so long as the time series dimension of the panel is sufficiently large

the moments of ols and 2sls when the disturbances are non normal abstract this paper examines the exact moments of ols and 2sls structural estimators under the assumption that the reduced form disturbances follow a non normal distribution of the edgeworth type with specified skewness 3 and kurtosis 4 the exact results are given as functions of hypergeometric functions and 3 and 4 the technique used is that developed by davis 1976 and it is shown that when 3 4 0 the results correspond to sawa s 1972

geometric proof of a conjecture of fulton we give a geometric proof of a conjecture of fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for gl r

the bias of autoregressive coefficient estimators abstract this article presents simple expressions for the bias of estimators of the coefficients of an autoregressive model of arbitrary but known finite order the results include models both with and without a constant term the effects of overspecification of the model order on the bias are described the emphasis is on least squares and yule walker estimators but the methods extend to other estimators of similar design although only the order t 1 component of the bias is captured where t is the series length this asymptotic approximation is shown to be very accurate for least squares estimators through some numerical simulations the simulations examine fourth order autoregressions chosen to resemble some data series from the literature the order t 1 bias approximations for yule walker estimators need not be accurate especially if the zeros of the associated polynomial have moduli near 1 examples are given where the approximation is accurate and where it is useless the bias expressions are

selecting an efficient design for assessing exposure disease relationships in an assembled cohort summary we develop approximate methods to compare the efficiencies and to compute the power of alternative potential designs for sampling from a cohort before beginning to collect exposure data our methods require only that the cohort be assembled meaning that the numbers of individuals nkj at risk at pairs of event times tk and ti tk are available to compute nkj one needs to know the entry follow up censoring and event history but not the exposure for each individual our methods apply to any unbiased control sampling design in which cases are compared to a random sample of noncases at risk at the time of an event we apply our methods to approximate the efficiencies of the nested case control design the case cohort design and an augmented case cohort design compared to the full cohort design in an assembled cohort of 17 633 members of an insurance cooperative who were followed for mortality from prostatic cancer the assumptions underlying the approximation are that exposure is unrelated both to the hazard of an event and to the hazard for censoring the approximations performed well in simulations when both assumptions held and when the exposure was moderately related to censoring

edgeworth approximations in first order stochastic difference equations with exogenous variables abstract this article obtains the edgeworth approximate distribution of the ols estimator of the autoregressive parameter of a first order stochastic difference equation with exogenous variables the approximate distribution is compared with the exact distribution computed using the imhof algorithm phillips results on the pure autoregressive process are also revised

on blocking rules for the bootstrap with dependent data summary we address the issue of optimal block choice in applications of the block bootstrap to dependent data it is shown that optimal block size depends significantly on context being equal to n 3 n 4 and nll5 in the cases of variance or bias estimation estimation of a onesided distribution function and estimation of a two sided distribution function respectively a clear intuitive explanation of this phenomenon is given together with outlines of theoretical arguments in specific cases it is shown that these orders of magnitude of block sizes can be used to produce a simple practical rule for selecting block size empirically that technique is explored numerically

an asymptotic expansion associated with the maximum likelihood estimators in arma models summary a technique is given for the edgeworth type asymptotic expansion for the joint as well as marginal and conditional distributions of the maximum likelihood estimators in autoregressive moving average arma models our methodology is illustrated and results on the expansions for some simple arma models are presented the present paper suggests a technique for obtaining the edgeworth type asymptotic expansion associated with the maximum likelihood estimator mle in arma models the expansion relates to joint as well as marginal and conditional distributions the approach developed here is simple and divided into two steps the first is to obtain the taylor expansion for the mle itself from the implicit function determining the mle on the basis of the explicit expression for the mle an asymptotic expansion for the distribution of the mle is derived at the second step these procedures are described in section 2 in section 3 our methodology is illustrated using a simple model and results on the expansions for some simple arma models are shown this paper ends with some discussion in section 4

a robust goodness of fit test for generalized autoregressive conditional heteroscedastic models summary the estimation of time series models with heavy tailed innovations has been widely discussed but corresponding goodness of fit tests have attracted less attention primarily because the autocorrelation function commonly used in constructing goodness of fit tests necessarily imposes certain moment conditions on the innovations as a bounded random variable has finite moments of all orders we address the problem by first transforming the residuals with a bounded function more specifically we consider the sample autocorrelation function of the transformed absolute residuals of a fitted generalized autoregressive conditional heteroscedastic model with the corresponding residual empirical distribution function naturally employed as the transformation a robust goodness of fit test is then constructed the asymptotic distributions of the test statistic under the null hypothesis and local alternatives are derived and monte carlo experiments are conducted to examine finite sample properties the proposed test is shown to be more powerful than existing tests when the innovations are heavy tailed

jackknife estimation of stationary autoregressive models abstract this paper explores the properties of jackknife methods of estimation in stationary autoregressive models some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non overlapping sub samples are derived for the case of a stationary autoregression of order p when the number of sub samples is either fixed or increases with the sample size at an appropriate rate the results of a detailed investigation into the finite sample properties of various jackknife and alternative estimators are reported and it is found that the jackknife can deliver substantial reductions in bias in autoregressive models this finding is robust to departures from normality arch effects and misspecification the median unbiasedness and mean squared error properties are also investigated and compared with alternative methods as are the coverage rates of jackknife based confidence intervals

tests for autocorrelation and randomness in multiple time series abstract there exist several tests for autocorrelation and randomness in multiple time series unfortunately the exact distributions of these statistics are unknown and the asymptotic distributions that are known do not provide adequate approximation to the exact ones in small samples in this article the test statistics are modified asymptotically these modified statistics are equivalent to their original counterparts however it is found that the asymptotic distributions of these statistics provide adequate approximation to the exact ones in relatively small samples and possibly when the time series are nonnormal the adequacy of the approximations is examined by simulation experiments the original test statistics are based on sample lag cross covariances autocovariances cross correlations and autocorrelations standardized by their asymptotic means and covariances the modified statistics are obtained when the asymptotic means and covariances in the standardization are replaced by the exact mea

rank based extensions of the brock dechert and scheinkman test this article proposes new tests of randomness for innovations in a large class of time series models these tests are based on functionals of empirical processes constructed from either the model residuals or their associated ranks the asymptotic behavior of these processes is determined under the null hypothesis of randomness the limiting distributions are seen to be independent of estimation errors under appropriate regularity conditions several test statistics are derived from these processes the classical brock dechert and scheinkman statistic and a rank based analog are included as special cases because the limiting distributions of the rank based test statistics are margin free their finite sample p values can be easily calculated by simulation monte carlo experiments show that these statistics are quite powerful against several classes of alternatives

on the distribution of the sample autocorrelation coefficients abstract sample autocorrelation coefficients are widely used to test the randomness of a time series despite its unsatisfactory performance the asymptotic normal distribution is often used to approximate the distribution of the sample autocorrelation coefficients this is mainly due to the lack of an efficient approach in obtaining the exact distribution of sample autocorrelation coefficients in this paper we provide an efficient algorithm for evaluating the exact distribution of the sample autocorrelation coefficients under the multivariate elliptical distribution assumption the exact distribution as well as exact moments and joint moments of sample autocorrelation coefficients are presented in addition the exact mean and variance of various autocorrelation based tests are provided actual size properties of the box pierce and ljung box tests are investigated and they are shown to be poor when the number of lags is moderately large relative to the sample size using the exact mean and variance of the box pierce test statistic we propose an adjusted box pierce test that has a far superior size property than the traditional box pierce and ljung box tests

the sampling distributions of the predictor for an autoregressive model under misspecifications abstract approximations to the sampling distributions of the predictor are given misspecifying the autoregressive moving average model as an autoregressive model we deal with both conditional and unconditional distributions for the dependent and independent cases according to whether the sample data used in estimation and in prediction are dependent or not the bias and mean squared error are easily obtained from these approximations

on bias inconsistency and efficiency of various estimators in dynamic panel data models abstract when a model for panel data includes lagged dependent explanatory variables then the habitual estimation procedures are asymptotically valid only when the number of observations in the time dimension t gets large usually however such datasets have substantial sample size in the cross section dimension n whereas t is often a single digit number results on the asymptotic bias n in this situation have been published a decade ago but hence far analytic small sample assessments of the actual bias have not been presented here we derive a formula for the bias of the least squares dummy variable lsdv estimator which has a o n 1 t 3 2 approximation error in a simulation study this is found to be remarkably accurate due to the small variance of the lsdv estimator which is usually much smaller than the variance of consistent generalized method of moments estimators a very efficient procedure results when we remove the bias from the lsdv estimator the simulations contain results for a particular operational corrected lsdv estimation procedure which in many situations proves to be much more efficient than various instrumental variable type estimators