testing and modeling multivariate threshold models abstract threshold autoregressive models in which the process is piecewise linear in the threshold space have received much attention in recent years in this article i use predictive residuals to construct a test statistic for detecting threshold nonlinearity in a vector time series and propose a procedure for building a multivariate threshold model the thresholds and the model are selected jointly based on the akaike information criterion the finite sample performance of the proposed test is studied by simulation the modeling procedure is then used to study arbitrage in security markets and results in a threshold cointegration between logarithms of future contracts and spot prices of a security after adjusting for the cost of carrying the contracts in this particular application thresholds are determined in part by the transaction costs i also apply the proposed procedure to u s monthly interest rates and two river flow series of iceland

a unified approach to validating univariate and multivariate conditional distribution models in time series abstract modeling conditional distributions in time series has attracted increasing attention in economics and finance we develop a new class of generalized cramer von mises gcm specification tests for time series conditional distribution models using a novel approach which embeds the empirical distribution function in a spectral framework our tests check a large number of lags and are therefore expected to be powerful against neglected dynamics at higher order lags which is particularly useful for non markovian processes despite using a large number of lags our tests do not suffer much from loss of a large number of degrees of freedom because our approach naturally downweights higher order lags which is consistent with the stylized fact that economic or financial markets are more affected by recent past events than by remote past events unlike the existing methods in the literature the proposed gcm tests cover both univariate and multivariate conditional distribution models in a unified framework they exploit the information in the joint conditional distribution of underlying economic processes moreover a class of easy to interpret diagnostic procedures are supplemented to gauge possible sources of model misspecifications distinct from conventional cm and kolmogorov smirnov ks tests which are also based on the empirical distribution function our gcm test statistics follow a convenient asymptotic n 0 1 distribution and enjoy the appealing nuisance parameter free property that parameter estimation uncertainty has no impact on the asymptotic distribution of the test statistics simulation studies show that the tests provide reliable inference for sample sizes often encountered in economics and finance

detection of intensity bursts using hawkes processes an application to high frequency financial data given a stationary point process an intensity burst is defined as a short time period during which the number of counts is larger than the typical count rate it might signal a local nonstationarity or the presence of an external perturbation to the system in this paper we propose a procedure for the detection of intensity bursts within the hawkes process framework by using a model selection scheme we show that our procedure can be used to detect intensity bursts when both their occurrence time and their total number is unknown moreover the initial time of the burst can be determined with a precision given by the typical interevent time we apply our methodology to the midprice change in foreign exchange fx markets showing that these bursts are frequent and that only a relatively small fraction is associated with news arrival we show lead lag relations in intensity burst occurrence across different fx rates and we discuss their relation with price jumps

testing dependence among serially correlated multicategory variables the contingency table literature on tests for dependence among discrete multicategory variables is extensive standard tests assume however that draws are independent and only limited results exist on the effect of serial dependency a problem that is important in areas such as economics finance medical trials and meteorology this article proposes new tests of independence based on canonical correlations from dynamically augmented reduced rank regressions the tests allow for an arbitrary number of categories as well as multiway tables of arbitrary dimension and are robust in the presence of serial dependencies that take the form of finite order markov processes for three way or higher order tables we propose new tests of joint and marginal independence monte carlo experiments show that the proposed tests have good finite sample properties an empirical application to microeconomic survey data on firms forecasts of changes to their production and prices demonstrates the importance of correcting fo

testing a linear dynamic panel data model against nonlinear alternatives abstract the most popular econometric models in the panel data literature are the class of linear panel data models with unobserved individual and or time specific effects the consistency of parameter estimators and the validity of their economic interpretations as marginal effects depend crucially on the correct functional form specification of the linear panel data model in this paper a new class of residual based tests is proposed for checking the validity of dynamic panel data models with both large cross sectional units and time series dimensions the individual and time effects can be fixed or random and panel data can be balanced or unbalanced the tests can detect a wide range of model misspecifications in the conditional mean of a dynamic panel data model including functional form and lag misspecification they check a large number of lags so that they can capture misspecification at any lag order asymptotically no common alternative is assumed thus allowing for heterogeneity in the degrees and directions of functional form misspecification across individuals thanks to the use of panel data with large n and t the proposed nonparametric tests have an asymptotic normal distribution under the null hypothesis without requiring the smoothing parameters to grow with the sample sizes this suggests better nonparametric asymptotic approximation for the panel data than for time series or cross sectional data this is confirmed in a simulation study we apply the new tests to test linear specification of cross country growth equations and found significant nonlinearities in mean for oecd countries growth equation for annual and quintannual panel data

estimation and inference with weak semi strong and strong identification this paper analyzes the properties of standard estimators tests and confidence sets cs s for parameters that are unidentified or weakly identified in some parts of the parameter space the paper also introduces methods to make the tests and cs s robust to such identification problems the results apply to a class of extremum estimators and corresponding tests and cs s that are based on criterion functions that satisfy certain asymptotic stochastic quadratic expansions and that depend on the parameter that determines the strength of identification this covers a class of models estimated using maximum likelihood ml least squares ls quantile generalized method of moments generalized empirical likelihood minimum distance and semi parametric estimators the consistency lack of consistency and asymptotic distributions of the estimators are established under a full range of drifting sequences of true distributions the asymptotic sizes in a uniform sense of standard and identification robust tests and cs s are established the results are applied to the arma 1 1 time series model estimated by ml and to the nonlinear regression model estimated by ls in companion papers the results are applied to a number of other models

a unified framework for the comparison of treatments with ordinal responses different latent variable models have been used to analyze ordinal categorical data which can be conceptualized as manifestations of an unobserved continuous variable in this paper we propose a unified framework based on a general latent variable model for the comparison of treatments with ordinal responses the latent variable model is built upon the location scale family and is rich enough to include many important existing models for analyzing ordinal categorical variables including the proportional odds model the ordered probit type model and the proportional hazards model a flexible estimation procedure is proposed for the identification and estimation of the general latent variable model which allows for the location and scale parameters to be freely estimated the framework advances the existing methods by enabling many other popular models for analyzing continuous variables to be used to analyze ordinal categorical data thus allowing for important statistical inferences such as location and or dispersion comparisons among treatments to be conveniently drawn analysis on real data sets is used to illustrate the proposed methods

consistent tests for stochastic dominance methods are proposed for testing stochastic dominance of any pre specified order with primary interest in the distributions of income we consider consistent tests that are similar to kolmogorov smirnov tests of the complete set of restrictions that relate to the various forms of stochastic dominance for such tests in the case of tests for stochastic dominance beyond first order we propose and justify a variety of approaches to inference based on simulation and the bootstrap we compare these approaches to one another and to alternative approaches based on multiple comparisons in the context of a monte carlo experiment and an empirical example

testing linearity against smooth transition autoregressive models summary we study a general univariate smooth transition autoregressive star model it contains as a special case the self exciting threshold autoregressive setar model we present three tests for testing linearity against star models and discuss their properties the power of the tests in small samples is investigated by simulation when the alternative is the logistic star model one of the tests is identical to tsay s 1986 test statistic and is recommended only in a special case of the two remaining tests with wider applicability one seems superior to the other in small samples it is also more powerful than the cusum test recently proposed for testing linearity against setar models

misspecified structural change threshold and markov switching models sudden perturbations of a large amplitude occur frequently in macroeconomic and financial time series a usual practice is to test linearity against a permanent structural change however changes can also be captured by nonlinear stationary models such that threshold and markov switching models in this paper we show that tests designed for a threshold alternative have also power against parameter instability originating from structural change or markov switching models on the other hand it is shown that tests for structural change have no power if the data are generated by a markov switching or threshold model therefore it appears that testing the null of parameter stability against a threshold alternative is a robust way to detect parameter instability in economic and financial time series a monte carlo analysis based on several models studied in the literature illustrates how the tests perform in practice

a nonlinear long memory model with an application to us unemployment two important empirical features of us unemployment are that shocks to the series seem rather persistent and that it seems to rise faster during recessions than that it falls during expansions to jointly capture these features of long memory and nonlinearity we put forward a new time series model and evaluate its empirical performance we find that the model describes the data rather well and that it outperforms related competitive models on various measures of fit

testing for unobserved heterogeneity in exponential and weibull duration models abstract we examine the use of the likelihood ratio lr statistic to test for unobserved heterogeneity in duration models based on mixtures of exponential or weibull distributions we consider both the uncensored and censored duration cases the asymptotic null distribution of the lr test statistic is not the standard chi square as the standard regularity conditions do not hold instead there is a nuisance parameter identified only under the alternative and a null parameter value on the boundary of the parameter space as in cho and white 2007a we accommodate these and provide methods delivering consistent asymptotic critical values we conduct a number of monte carlo simulations comparing the level and power of the lr test statistic to an information matrix im test due to chesher 1984 and lagrange multiplier lm tests of kiefer 1985 and sharma 1987 our simulations show that the lr test statistic generally outperforms the im and lm tests we also revisit the work of van den berg and ridder 1998 on unemployment durations and of ghysels et al 2004 on interarrival times between stock trades and as it turns out affirm their original informal inferences

robust inference in nonlinear models with mixed identification strength abstract the paper studies inference in regression models composed of nonlinear functions with unknown transformation parameters and loading coefficients that measure the importance of each component in these models non identification and weak identification present in multiple parts of the parameter space resulting in mixed identification strength for different unknown parameters this paper proposes robust tests and confidence intervals for sub vectors and linear functions of the unknown parameters in particular the results cover applications where some nuisance parameters are non identified under the null davies 1977 1987 and some nuisance parameters are subject to a full range of identification strength to construct this robust inference procedure we develop a local limit theory that models mixed identification strength the asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence a sequential argument is used to peel the criterion function based on identification strength of the parameters

testing for serial correlation against an arma 1 1 process abstract this article is concerned with tests for serial correlation in time series and in the errors of regression models in particular the nonstandard problem of testing for white noise against autoregressive moving average model arma 1 1 alternatives is considered the likelihood ratio lr sup lagrange multiplier lm and exponential average lm and lr tests are shown to be asymptotically admissible for arma 1 1 alternatives in addition they are shown to be consistent against all weakly stationary strong mixing non white noise alternatives simulation results compare the tests to several tests in the literature these results show that the lr and exp lr tests have very good all around power properties for nonseasonal alternatives

testing constancy of the error covariance matrix in vector models in this paper a lagrange multiplier test of the hypothesis that the covariance matrix of a multivariate time series model is constant over time is considered it is assumed that under the alternative the error variances are time varying whereas the correlations remain constant over time under the parameterized alternative hypothesis the variances may change continuously as a function of time or some observable stochastic variables small sample properties of the test statistic are investigated by simulation the assumption of constant correlations does not appear overly restrictive

testing for co integration in vector autoregressions with non stationary volatility abstract many key macroeconomic and financial variables are characterized by permanent changes in unconditional volatility in this paper we analyse vector autoregressions with non stationary unconditional volatility of a very general form which includes single and multiple volatility breaks as special cases we show that the conventional rank statistics computed as in johansen 1988 johansen 1991 are potentially unreliable in particular their large sample distributions depend on the integrated covariation of the underlying multivariate volatility process which impacts on both the size and power of the associated co integration tests as we demonstrate numerically a solution to the identified inference problem is provided by considering wild bootstrap based implementations of the rank tests these do not require the practitioner to specify a parametric model for volatility or to assume that the pattern of volatility is common to or independent across the vector of series under analysis the bootstrap is shown to perform very well in practice

testing for threshold effects in regression models in this article we develop a general method for testing threshold effects in regression models using sup likelihood ratio lr type statistics although the sup lr type test statistic has been considered in the literature our method for establishing the asymptotic null distribution is new and nonstandard the standard approach in the literature for obtaining the asymptotic null distribution requires that there exist a certain quadratic approximation to the objective function the article provides an alternative novel method that can be used to establish the asymptotic null distribution even when the usual quadratic approximation is intractable we illustrate the usefulness of our approach in the examples of the maximum score estimation maximum likelihood estimation quantile regression and maximum rank correlation estimation we establish consistency and local power properties of the test we provide some simulation results and also an empirical application to tipping in racial segregation this ar

s estimation of nonlinear regression models with dependent and heterogeneous observations in time series regression where a single outlier can appear in the regressor vector multiple times due to the presence of lagged variables resistance of an estimator to outliers is of serious concern we show that the high resistance of s estimators in cross section regression carries over to time series we investigate the large sample properties of s estimators in nonlinear regression with dependent heterogeneous data and conduct monte carlo simulations to examine the performance of s estimators and assess the accuracy of our asymptotic approximations finally we offer a simple empirical example applying s estimators to a financial time series

testing for garch effects a one sided approach arch models often lie at the boundary of the parameter space under conditional homoskedasticity which invalidates the usual s2 distribution of lr and wald tests although lm tests are not a ected the one sided nature of the alternative hypothesis should result in more powerful tests we propose a simple one sided version of the lm test which is closely related to the kuhn tucker multiplier test we also present critical values for lr wald and one sided lm tests the results of a monte carlo comparison suggest that one sided tests are indeed more powerful than their two sided counterparts 1998 elsevier science s a all rights reserved jel classification c22

least squares estimation of large dimensional threshold factor models abstract this paper studies large dimensional factor models with threshold type regime shifts in the loadings we estimate the threshold by concentrated least squares and factors and loadings by principal components the estimator for the threshold is superconsistent with convergence rate that depends on the time and cross sectional dimensions of the panel and it does not affect the estimator for factors and loadings this has the same convergence rate as in linear factor models we propose model selection criteria and a linearity test empirical application of the model shows that connectedness in financial variables increases during periods of high economic policy uncertainty

some heteroskedasticity consistent covariance matrix estimators with improved finite sample properties abstract we examine several modified versions of the heteroskedasticity consistent covariance matrix estimator of hinkley 1977 and white 1980 on the basis of sampling experiments which compare the performance of quasi t statistics we find that one estimator based on the jackknife performs better in small samples than the rest we also examine the finite sample properties of using modified critical values based on edgeworth approximations as proposed by rothenberg 1984 in addition we compare the power of several tests for heteroskedasticity and find that it may be wise to employ the jackknife heteroskedasticity consistent covariance matrix even in the absence of detected heteroskedasticity

threshold autoregressive models for interval valued time series data abstract modeling and forecasting symbolic data especially interval valued time series its data has received considerable attention in statistics and related fields the core of available methods on its analysis is based on various applications of conventional linear modeling however few works have considered possible nonlinearities in its data in this paper we propose a new class of threshold autoregressive interval tari models for its data by matching the interval model with interval observations we develop a minimum distance estimation method for tari models and establish the asymptotic theory for the proposed estimators we show that the threshold parameter estimator is t consistent and follows an asymptotic compound poisson process as the sample size t and the estimators for other tari model parameters are root t consistent and asymptotically normal simulation studies show that the proposed tari model provides more accurate out of sample forecasts than the existing center radius self exciting threshold cr setar model for its data in the literature empirical applications to the s p 500 price index document significant asymmetric reactions of the stock markets in japan u k and france to shocks from the u s stock market and that incorporating this asymmetric effect yield better out of sample forecasts than a variety of popular models available in the literature

gauss extensions and total graded subrings for crossed product algebras abstract let v be a total subring of a skew field k and let g p be a right ordered group with p the cone of non negative elements so that a crossed product k g of g over k has a right quotient skew field q k g we want to determine total subrings r of q k g with r k v that is extensions of v in q k g we describe the class of all those extensions r called gauss extensions of v for which a r k g is a graded subring of k g with x a 1 a if x a a for x g and a k this can be applied to give explicit constructions of such subrings a and their corresponding extensions r obtained through localization information about the prime ideals of r and the graded prime ideals of a is obtained and it is shown that the skew fields r r j r are quotient skew fields of the crossed products v e for certain subgroups e of g with v the residue skew field v j v of v this result is one of the motivations to consider crossed products k g rather than just the skew group ring of g over k

valid tests of whether technical inefficiency depends on firm characteristics abstract we wish to test whether technical inefficiency depends on observable characteristics of the firm we consider a two step procedure in which the second step is a regression of estimated inefficiency on firm characteristics a valid test of the hypothesis of no effect requires an adjustment to the variance matrix of the estimates unfortunately the adjustment is not distribution free we show that this test is the lm test in the exponential case we also consider tests based on nonlinear least squares which do not require a distributional assumption the size and power of these tests are examined in simulations

inference on co integration parameters in heteroskedastic vector autoregressions we consider estimation and hypothesis testing on the coefficients of the co integrating relations and the adjustment coefficients in vector autoregressions driven by shocks which display both conditional and unconditional heteroskedasticity of a quite general and unknown form we show that the conventional results in johansen 1996 for the maximum likelihood estimators and associated likelihood ratio tests derived under homoskedasticity do not in general hold under heteroskedasticity as a result standard confidence intervals and hypothesis tests on these coefficients are potentially unreliable solutions based on wald tests using a sandwich estimator of the variance matrix and on the use of the wild bootstrap are discussed these do not require the practitioner to specify a parametric model for volatility we establish the conditions under which these methods are asymptotically valid a monte carlo simulation study demonstrates that significant improvements in finite sample size can be obtained by the bootstrap over the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments an application to the term structure of interest rates in the us illustrates the difference between standard and bootstrap inferences regarding hypotheses on the co integrating vectors and adjustment coefficients

inference when a nuisance parameter is not identified under the null hypothesis many econometric testing problems involve nuisance parameters which are not identified under the null hypotheses this paper studies the asymptotic distribution theory for such tests the asymptotic distributions of standard test statistics are described as functionals of chi square processes in general the distributions depend upon a large number of unknown parameters we show that a transformation based upon a conditional probability measure yields an asymptotic distribution free of nuisance parameters and we show that this transformation can be easily approximated via simulation the theory is applied to threshold models with special attention given to the so called self exciting threshold autoregressive model monte carlo methods are used to assess the finite sample distributions the tests are applied to u s gnp growth rates and we find that potter s 1995 threshold effect in this series can be possibly explained by sampling variation

bayes factors and nonlinearity evidence from economic time series this paper argues in favor of a bayesian approach to evaluating evidence of nonlinearity in economic time series over the classical approach that has been dominant in the applied literature an application is presented concerning nonlinearity in us gnp

threshold effects in non dynamic panels estimation testing and inference abstract threshold regression methods are developed for non dynamic panels with individual specific fixed effects least squares estimation of the threshold and regression slopes is proposed using fixed effects transformations a non standard asymptotic theory of inference is developed which allows construction of confidence intervals and testing of hypotheses the methods are applied to a 15 year sample of 565 us firms to test whether financial constraints affect investment decisions

the dynamic invariant multinomial probit model identification pretesting and estimation we present a new specification for the multinomial multiperiod probit model with autocorrelated errors in sharp contrast with commonly used specifications ours is invariant with respect to the choice of a baseline alternative for utility differencing it also nests these standard models as special cases allowing for data based selection of the baseline alternatives for the latter likelihood evaluation is achieved under an efficient importance sampling eis version of the standard ghk algorithm several simulation experiments highlight identification estimation and pretesting within the new class of multinomial multiperiod probit models

testing a linear time series model against its threshold extension this paper derives the asymptotic null distribution of a quasilikelihood ratio test statistic for an autoregressive moving average model against its threshold extension the null hypothesis is that of no threshold and the error term could be dependent the asymptotic distribution is rather complicated and all existing methods for approximating a distribution in the related literature fail to work hence a novel bootstrap approximation based on stochastic permutation is proposed in this paper besides being robust to the assumptions on the error term our method enjoys more flexibility and needs less computation when compared with methods currently used in the literature monte carlo experiments give further support to the new approach and an illustration is reported

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

a score type test for heterogeneity in zero inflated models in a stratified population we propose a score type statistic to evaluate heterogeneity in zero inflated models for count data in a stratified population where heterogeneity is defined as instances in which the zero counts are generated from two sources evaluating heterogeneity in this class of models has attracted considerable attention in the literature but existing testing procedures have primarily relied on the constancy assumption under the alternative hypothesis in this paper we extend the literature by describing a score type test to evaluate homogeneity against general alternatives that do not neglect the stratification information under the alternative hypothesis the limiting null distribution of the proposed test statistic is a mixture of chi squared distributions which can be well approximated by a simple parametric bootstrap procedure our numerical simulation studies show that the proposed test can greatly improve efficiency over tests of heterogeneity that ignore the stratification information an empirical application to dental caries data in early childhood further shows the importance and practical utility of the methodology in using the stratification profile to detect heterogeneity in the population

comment on threshold autoregressions with a unit root in this paper we revisit the results in caner and hansen 2001 where the authors obtained novel limiting distributions of wald type test statistics for testing for the presence of threshold nonlinearities in autoregressive models containing unit roots using the same framework we obtain a new formulation of the limiting distribution of the wald statistic for testing for threshold effects correcting an expression that appeared in the main theorem presented by caner and hansen subsequently we show that under a particular scenario that excludes stationary regressors such as lagged dependent variables and despite the presence of a unit root this same limiting random variable takes a familiar form that is free of nuisance parameters and already tabulated in the literature thus removing the need to use bootstrap based inferences this is a novel and unusual occurrence in this literature on testing for the presence of nonlinear dynamics

a hypothesis testing procedure for random changepoint mixed models in biomedical research random changepoint mixed models are used to take into account an individual breakpoint in a biomarker trajectory this may be observed in the cognitive decline measured by psychometric tests in the prediagnosis phase of alzheimer s disease the existence intensity and duration of this accelerated decline can depend on individual characteristics the main objective of our work is to propose inferential methods to assess the existence of this phase of accelerated decline ie the existence of a random changepoint to do so we use a mixed model with two linear phases and test the nullity of the parameter measuring the difference of slopes between the two phases because we face the issue of nuisance parameters being unidentifiable under the null hypothesis the supremum of the classic score test statistic on these parameters is used the asymptotic distribution of the supremum under the null is approached with a perturbation method based on the multiplier bootstrap the performance of our testing procedure is assessed via simulations and the test is applied to the french cohort paquid of elderly subjects to study the shape of the prediagnosis decline according to educational level the test is significant for both educational levels and the estimated trajectories confirmed that educational level is a good marker for cognitive reserve

tests for white noise against alternatives with both seasonal and nonseasonal serial correlation summary this paper considers tests for seasonal and nonseasonal serial correlation in time series and in the errors of regression models the problem of testing for white noise against

valuation rings in finite dimensional division algebras a subring b of a division algebra d is called a valuation ring of d if x or x 1 is contained in b for every x in d x 0 such a ring is called an extension of the valuation ring b of k the centre of d if b k b let d be a division algebra finite dimensional over its centre k d k n2 b a valuation ring of k and b bi iei the set of all extension of b in d theorem 1 b possesses at most n extensions in d i e b n theorem 2 any two extensions of b in d are conjugate in d theorems 3 and 4 the set t of elements in d which are integral over b is a subring of d if and only if b 1 in this case t bi bi in b

generalised density forecast combinations density forecast combinations are becoming increasingly popular as a means of improving forecast accuracy as measured by a scoring rule in this paper we generalise this literature by letting the combination weights follow more general schemes sieve estimation is used to optimise the score of the generalised density combination where the combination weights depend on the variable one is trying to forecast specific attention is paid to the use of piecewise linear weight functions that let the weights vary by region of the density we analyse these schemes theoretically in monte carlo experiments and in an empirical study our results show that the generalised combinations outperform their linear counterparts

testing when a parameter is on the boundary of the maintained hypothesis this paper considers testing problems where several of the standard regularity conditions fail to hold we consider the case where i parameter vectors in the null hypothesis may lie on the boundary of the maintained hypothesis and ii there may be a nuisance parameter that appears under the alternative hypothesis but not under the null the paper establishes the asymptotic null and local alternative distributions of quasi likelihood ratio rescaled quasi likelihood ratio wald and score tests in this case the results apply to tests based on a wide variety of extremum estimators and apply to a wide variety of models examples treated in the paper are i tests of the null hypothesis of no conditional heteroskedasticity in a garch 1 1 regression model and ii tests of the null hypothesis that some random coefficients have variances equal to zero in a random coefficients regression model with possibly correlated random coefficients

robust inference for threshold regression models abstract this paper considers robust inference in threshold regression models when the practitioners do not know whether at the threshold point the true specification has a kink or a jump nesting previous works that assume either continuity or discontinuity at the threshold we find that the parameter values under the kink restriction are irregular points of the hessian matrix destroying the asymptotic normality and inducing the cube root convergence rate for the threshold estimate however we are able to obtain the same asymptotic distribution as hansen 2000 for the quasi likelihood ratio statistic for the unknown threshold we propose to construct confidence intervals for the threshold by bootstrap test inversion finite sample performances of the proposed procedures are examined through monte carlo simulations and an economic empirical application is given

testing for observation dependent regime switching in mixture autoregressive models abstract testing for regime switching when the regime switching probabilities are specified either as constants mixture models or are governed by a finite state markov chain markov switching models are long standing problems that have also attracted recent interest this paper considers testing for regime switching when the regime switching probabilities are time varying and depend on observed data observation dependent regime switching specifically we consider the likelihood ratio test for observation dependent regime switching in mixture autoregressive models the testing problem is highly nonstandard involving unidentified nuisance parameters under the null parameters on the boundary singular information matrices and higher order approximations of the log likelihood we derive the asymptotic null distribution of the likelihood ratio test statistic in a general mixture autoregressive setting using high level conditions that allow for various forms of dependence of the regime switching probabilities on past observations and we illustrate the theory using two particular mixture autoregressive models the likelihood ratio test has a nonstandard asymptotic distribution that can easily be simulated and monte carlo studies show the test to have good finite sample size and power properties

testing for two regime threshold cointegration in vector error correction models this paper examines a two regime vector error correction model with a single cointegrating vector and a threshold effect in the error correction term we propose a relatively simple algorithm to obtain maximum likelihood estimation of the complete threshold cointegration model for the bivariate case we propose a suplm test for the presence of a threshold we derive the null asymptotic distribution show how to simulate asymptotic critical values and present a bootstrap approximation we investigate the performance of the test using monte carlo simulation and find that the test works quite well applying our methods to the term structure model of interest rates we find strong evidence for a threshold effect

estimation and model selection based inference in single and multiple threshold models this paper evaluates the properties of a joint and sequential estimation procedure for estimating the parameters of single and multiple threshold models we initially proceed under the assumption that the number of regimes is known a priori but subsequently relax this assumption via the introduction of a model selection based procedure that allows the estimation of both the unknown parameters and their number to be performed jointly theoretical properties of the resulting estimators are derived and their finite sample properties investigated

consistent hypothesis testing in semiparametric and nonparametric models for econometric time series abstract in this paper we modify the general hypothesis studied by robinson 1989 for semi nonparametric time series models and present a consistent testing procedure for the modified hypothesis as examples we provide consistent tests for the portfolio conditional mean variance efficiency hypothesis for theomitted variables in a multivariate nonparametric time series regression model and for the two original examples in robinson the asymptotic distributions under the null and pitman local alternatives are established by invoking central limit theorems for hilbert valued dependent random arrays to approximate the critical values of the general test we modify the conditional monte carlo approach of hansen 1996 and the stationary bootstrap of politis and romano 1994a b and show that both work asymptotically

testing for a linear ma model against threshold ma models this paper investigates the conditional quasi likelihood ratio test for the threshold in ma models under the hypothesis of no threshold it is shown that the test statistic converges weakly to a function of the centred gaussian process under local alternatives it is shown that this test has nontrivial asymptotic power the results are based on a new weak convergence of a linear marked empirical process which is independently of interest this paper also gives an invertible expansion of the threshold ma models

exact and asymptotic tests for possibly non regular hypotheses on stochastic volatility models abstract we study the problem of testing hypotheses on the parameters of one and two factor stochastic volatility models sv allowing for the possible presence of non regularities such as singular moment conditions and unidentified parameters which can lead to non standard asymptotic distributions we focus on the development of simulation based exact procedures whose level can be controlled in finite samples as well as on large sample procedures which remain valid under non regular conditions we consider wald type score type and likelihood ratio type tests based on a simple moment estimator which can be easily simulated we also propose a c type test which is very easy to implement and exhibits relatively good size and power properties besides usual linear restrictions on the sv model coefficients the problems studied include testing homoskedasticity against a sv alternative which involves singular moment conditions under the null hypothesis and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors which raises identification difficulties three ways of implementing the tests based on alternative statistics are compared asymptotic critical values when available a local monte carlo or parametric bootstrap test procedure and a maximized monte carlo mmc procedure the size and power properties of the proposed tests are examined in a simulation experiment the results indicate that the c based tests built upon the simple moment estimator available in closed form have good size and power properties for regular hypotheses while monte carlo tests are much more reliable than those based on asymptotic critical values further in cases where the parametric bootstrap appears to fail for example in the presence of identification problems the mmc procedure easily controls the level of the tests moreover mmc based tests exhibit relatively good power performance despite the conservative feature of the procedure finally we present an application to a time series of returns on the standard and poor s composite price index

testing for regime switching we analyze use of a quasi likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a markov regime switching context this test exploits mixture properties implied by the regime switching process but ignores certain implied serial correlation properties when formulated in the natural way the setting is nonstandard involving nuisance parameters on the boundary of the parameter space nuisance parameters identified only under the alternative or approximations using derivatives higher than second order we exploit recent advances by andrews 2001 and contribute to the literature by extending the scope of mixture models obtaining asymptotic null distributions different from those in the literature we further provide critical values for popular models or bounds for tail probabilities that are useful in constructing conservative critical values for regime switching tests we compare the size and power of our statistics to other useful tests for regime switching via monte carlo methods and find relatively good performance we apply our methods to reexamine the classic cartel study of porter 1983 and reaffirm porter s findings

higher order approximations for testing neglected nonlinearity we illustrate the need to use higher order specifically sixth order expansions in order to properly determine the asymptotic distribution of a standard artificial neural network test for neglected nonlinearity the test statistic is a quasi likelihood ratio qlr statistic designed to test whether the mean square prediction error improves by including an additional hidden unit with an activation function violating the no zero condition in cho ishida and white 2011 this statistic is also shown to be asymptotically equivalent under the null to the lagrange multiplier lm statistic of luukkonen saikkonen and terasvirta 1988 and terasvirta 1994 in addition we compare the power properties of our qlr test to one satisfying the no zero condition and find that the latter is not consistent for detecting a dgp with neglected nonlinearity violating an analogous no zero condition whereas our qlr test is consistent

testing for neglected nonlinearity in regression models based on the theory of random fields abstract within a flexible regression model j d hamilton econometrica 69 3 2001 537 we offer a battery of new lagrange multiplier statistics that circumvent the problem of unidentified nuisance parameters under the null hypothesis of linearity and that are robust to the specification of the covariance function that defines the random field these advantages are the result of i switching from the l 2 to the l 1 norm and ii assuming that the random field is sufficiently smooth for its covariance function to be locally approximated by a high order taylor expansion a monte carlo simulation suggests that our statistics have superior power performance on detecting bilinear neural network and smooth transition autoregressive specifications we also provide an application to the industrial production index of sixteen oecd countries

bootstrap conditional distribution tests in the presence of dynamic misspecification abstract in this paper we show the first order validity of the block bootstrap for kolmogorov type conditional distribution tests under dynamic misspecification and parameter estimation error our approach is unique because we construct statistics that allow for dynamic misspecification under both hypotheses we consider two tests the ck test of andrews 1997 a conditional kolmogorov test econometrica 65 1097 1128 and a version of the dgt test of diebold gunther and tay 1998a evaluating density forecasts with applications to finance and management international economic review 39 863 883 test limiting distributions are gaussian processes with covariance kernels that reflect dynamic misspecification and parameter estimation error critical values are based on an extension of the empirical process version of the block bootstrap to the case of nonvanishing parameter estimation error monte carlo experiments are also carried out

empirically relevant critical values for hypothesis tests a bootstrap approach tests of statistical hypotheses can be based on either of two critical values the type i critical value or the size corrected critical value the former usually depends on unknown population parameters and cannot be evaluated exactly in applications but it can often be estimated very accurately by using the bootstrap the latter does not depend on unknown population parameters but is likely to yield a test with low power the critical values used in most monte carlo studies of the powers of tests are neither type i nor size corrected they are irrelevant to empirical research

simulation based finite sample tests for heteroskedasticity and arch effects tests for heteroskedasticity in linear regressions are typically based on asymptotic approximations we show that the size of such tests can be perfectly controlledin nite samples through monte carlo test techniques with both gaussian and non gaussian heavy tailed disturbance distributions the procedures studied include standard heteroskedasticity tests e g glejser bartlett cochran hartley breusch pagan godfrey white szroeter as well as tests for arch type heterosked asticity sup type andcombinedtests are also proposedto allow for unknown breakpoints in the variance the fact that the proposedproced ures achieve size control andhave goodpower is demonstrated in a monte carlo simulation c 2003 elsevier b v all rights reserved

asymptotic analysis of the squared estimation error in misspecified factor models abstract in this paper we obtain asymptotic approximations to the squared error of the least squares estimator of the common component in large approximate factor models with possibly misspecified number of factors the approximations are derived under both strong and weak factors asymptotics assuming that the cross sectional and temporal dimensions of the data are comparable we develop consistent estimators of these approximations and propose to use them for model comparison and for selection of the number of factors we show that the estimators of the number of factors that minimize these loss estimators are asymptotically loss efficient in the sense of shibata 1980 li 1987 and shao 1997

evaluating garch models in this paper a unified framework for testing the adequacy of an estimated garch model is presented parametric lagrange multiplier lm or lm type tests of no arch in standardized errors linearity and parameter constancy are proposed the asymptotic null distributions of the tests are standard which makes application easy versions of the tests that are robust against nonnormal errors are provided the finite sample properties of the test statistics are investigated by simulation the robust tests prove superior to the nonrobust ones when the errors are nonnormal they also compare favourably in terms of power with misspecification tests previously proposed in the literature

valuation rings in ore extensions abstract extensions of valuation rings v of a skew field k are considered in the skew field f k x for a monomorphism of k at least two such extensions exist if is an automorphism but no extension may exist if is a monomorphism only there exist extensions r a of v in f with xr a ar a for every non zero a in k if and only if v is invariant and is compatible with v

testing for structural change in conditional models in the past decade we have seen the development of a new set of tests for structural change of unknown timing in regression models most notably the supf statistic of andrews 1993 econometrica 61 825 856 the expf and avef statistics of andrewsploberger 1994 econometrica 62 1383 1414 and the statistic of nyblom 1989 journal of american statistical association 84 223 230 the distribution theory used for these tests is primarily asymptotic and has been derived under the maintained assumption that the regressors are stationary this excludes structural change in the marginal distribution of the regressors as a result these tests technically cannot discriminate between structural change in the conditional and marginal distributions this paper attempts to remedy this de ciency by deriving the large sample distributions of the test statistics allowing for structural change in the marginal distribution of the regressors we nd that the asymptotic distributions of the supf expf avef and statistics are not invariant to structural change in the regressors to solve the size problem we introduce a xed regressor bootstrap which achieves the rst order asymptotic distribution and appears to possess reasonable size properties in small samples our bootstrap theory allows for arbitrary structural change in the regressors including structural shifts polynomial trends and exogenous stochastic trends it allows for lagged dependent variables and heteroskedastic error processes 2000 elsevier science s a all rights reserved

bootstrapping structural change tests this paper demonstrates the asymptotic validity of methods based on the wild recursive and wild fixed bootstraps for testing hypotheses about discrete parameter change in linear models estimated via two stage least squares the framework allows for the errors to exhibit conditional and or unconditional heteroscedasticity and for the reduced form to be unstable simulation evidence indicates the bootstrap tests yield reliable inferences in the sample sizes often encountered in macroeconomics if the errors exhibit unconditional heteroscedasticity and or the reduced form is unstable then the bootstrap methods are particularly attractive because the limiting distributions of the test statistics are not pivotal

testing for granger causality in large mixed frequency vars abstract we analyze granger causality testing in a mixed frequency var where the difference in sampling frequencies of the variables is large implying parameter proliferation problems in case we attempt to estimate the model unrestrictedly we propose several tests based on reduced rank restrictions including bootstrap versions thereof to account for factor estimation uncertainty and improve the finite sample properties of the tests and a bayesian var extended to mixed frequencies we compare these methods to a test based on an aggregated model the m a x test ghysels et al 2016a and an unrestricted var based test ghysels et al 2016b using monte carlo simulations an empirical application illustrates the techniques

testing linearity using power transforms of regressors we develop a method of testing linearity using power transforms of regressors allowing for stationary processes and time trends the linear model is a simplifying hypothesis that derives from the power transform model in three different ways each producing its own identification problem we call this modeling difficulty the trifold identification problem and show that it may be overcome using a test based on the quasi likelihood ratio qlr statistic more specifically the qlr statistic may be approximated under each identification problem and the separate null approximations may be combined to produce a composite approximation that embodies the linear model hypothesis the limit theory for the qlr test statistic depends on a gaussian stochastic process in the important special case of a linear time trend regressor and martingale difference errors asymptotic critical values of the test are provided test power is analyzed and an empirical application to crop yield distributions is provided the paper also considers generalizations of the box cox transformation which are associated with the qlr test statistic

testing for unit roots in bounded time series abstract many key economic and financial series are bounded either by construction or through policy controls conventional unit root tests are potentially unreliable in the presence of bounds since they tend to over reject the null hypothesis of a unit root even asymptotically so far very little work has been undertaken to develop unit root tests which can be applied to bounded time series in this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds we present new augmented dickey fuller type tests as well as new versions of the modified m tests developed by ng and perron ng s perron p 2001 lag length selection and the construction of unit root tests with good size and power econometrica 69 1519 1554 and demonstrate how these tests combined with a simulation based method to retrieve the relevant critical values make it possible to control size asymptotically a monte carlo study suggests that the proposed tests perform well in finite samples moreover the tests outperform the phillips perron type tests originally proposed in cavaliere cavaliere g 2005 limited time series with a unit root econometric theory 21 907 945 an illustrative application to u s interest rate data is provided

a consistent test for nonlinear out of sample predictive accuracy abstract in this paper we draw on both the consistent specification testing and the predictive ability testing literatures and propose an integrated conditional moment type predictive accuracy test that is similar in spirit to that developed by bierens j econometr 20 1982 105 econometrica 58 1990 1443 and bierens and ploberger econometrica 65 1997 1129 the test is consistent against generic nonlinear alternatives and is designed for comparing nested models one important feature of our approach is that the same loss function is used for in sample estimation and out of sample prediction in this way we rule out the possibility that the null model can outperform the nesting generic alternative model it turns out that the limiting distribution of the icm type test statistic that we propose is a functional of a gaussian process with a covariance kernel that reflects both the time series structure of the data as well as the contribution of parameter estimation error as a consequence critical values that are data dependent and cannot be directly tabulated one approach in this case is to obtain critical value upper bounds using the approach of bierens and ploberger econometrica 65 1997 1129 here we establish the validity of a conditional p value method for constructing critical values the method is similar in spirit to that proposed by hansen econometrica 64 1996 413 and inoue econometric theory 17 2001 156 although we additionally account for parameter estimation error in a series of monte carlo experiments the finite sample properties of three variants of the predictive accuracy test are examined our findings suggest that all three variants of the test have good finite sample properties when quadratic loss is specified even for samples as small as 600 observations however non quadratic loss functions such as linex loss require larger sample sizes of 1000 observations or more in order to ensure reasonable finite sample performance

superconsistent estimation and inference in structural econometric models using extreme order statistics abstract data generating processes whose distributions supports depend on unknown parameters arise naturally in empirical applications in such situations the maximum likelihood estimator is often difficult to calculate and usually has a nonstandard limiting distribution that depends on nuisance parameters we propose an alternative estimation strategy that is typically simpler to implement than the likelihood approach and allows one to conduct inference using simulation methods our proposed estimators are based on the analog estimation principle and bear a striking resemblance to generalized method of moments estimators although here the estimators are generally parameter consistent at rate t rather than the usual rate t

model selection for sinusoids in noise statistical analysis and a new penalty term detection of the number of sinusoids embedded in noise is a fundamental problem in statistical signal processing most parametric methods minimize the sum of a data fit likelihood term and a complexity penalty term the latter is often derived via information theoretic criteria such as minimum description length mdl or via bayesian approaches including bayesian information criterion bic or maximum a posteriori map while the resulting estimators are asymptotically consistent empirically their finite sample performance is strongly dependent on the specific penalty term chosen in this paper we elucidate the source of this behavior by relating the detection performance to the extreme value distribution of the maximum of the periodogram and of related random fields based on this relation we propose a combined detection estimation algorithm with a new penalty term our proposed penalty term is sharp in the sense that the resulting estimator achieves a nearly constant false alarm rate a series of simulations support our theoretical analysis and show the superior detection performance of the suggested estimator

hypothesis testing in mixture regression models summary we establish asymptotic theory for both the maximum likelihood and the maximum modified likelihood estimators in mixture regression models moreover under specific and reasonable conditions we show that the optimal convergence rate of n 1 4 for estimating the mixing distribution is achievable for both the maximum likelihood and the maximum modified likelihood estimators we also derive the asymptotic distributions of two log likelihood ratio test statistics for testing homogeneity and we propose a resampling procedure for approximating the p value simulation studies are conducted to investigate the empirical performance of the two test statistics finally two real data sets are analysed to illustrate the application of our theoretical results