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

the exact distribution of the hansen jagannathan bound under the assumption of multivariate normality of asset returns this paper presents a geometric interpretation and the finite sample distributions of the sample hansen jagannathan bounds on the variance of admissible stochastic discount factors with and without the nonnegativity constraint on the stochastic discount factors in addition since the sample hansen jagannathan bounds can be very volatile we propose a simple method to construct confidence intervals for the population hansen jagannathan bounds finally we show that the analytical results in the paper are robust to departures from the normality assumption

estimating information rates with confidence intervals in neural spike trains information theory provides a natural set of statistics to quantify the amount of knowledge a neuron conveys about a stimulus a related work kennel shlens abarbanel chichilnisky 2005 demonstrated how to reliably estimate with a bayesian confidence interval the entropy rate from a discrete observed time series we extend this method to measure the rate of novel information that a neural spike train encodes about a stimulus the average and specific mutual information rates our estimator makes few assumptions about the underlying neural dynamics shows excellent performance in experimentally relevant regimes and uniquely provides confidence intervals bounding the range of information rates compatible with the observed spike train we validate this estimator with simulations of spike trains and highlight how stimulus parameters affect its convergence in bias and variance finally we apply these ideas to a recording from a guinea pig retinal ganglion cell and compare results to a simple linear decoder

theoretical comparisons of block bootstrap methods in this paper we compare the asymptotic behavior of some common block bootstrap methods based on nonrandom as well as random block lengths it is shown that asymptotically bootstrap estimators derived using any of the methods considered in the paper have the same amount of bias to the first order however the variances of these bootstrap estimators may be different even in the first order expansions for the bias the variance and the mean squared error of different block bootstrap variance estimators are obtained it follows from these expansions that using overlapping blocks is to be preferred over nonoverlapping blocks and that using random block lengths typically leads to mean squared errors larger than those for nonrandom block lengths

subsampling for heteroskedastic time series abstract in this article a general theory for the construction of confidence intervals or regions in the context of heteroskedastic dependent data is presented the basic idea is to approximate the sampling distribution of a statistic based on the values of the statistic computed over smaller subsets of the data this method was first proposed by politis and romano 1994b for stationary observations we extend their results to heteroskedastic observations and prove a general asymptotic validity result under minimal conditions in contrast the usual bootstrap and moving blocks bootstrap are typically valid only for asymptotically linear statistics and their justification requires a case by case analysis our general asymptotic results are applied to a regression setting with dependent heteroskedastic errors

markov chain monte carlo in stastical mechanics the appearance of the article by n metropolis a w rosenbluth m n rosenbluth a h teller and e teller marked the birth of the monte carlo method for the study of statistical mechanical systems and of a specific form of importance sampling namely markov chain monte carlo after nearly 40 years of statistical usage this technique has had a profound impact on statistical theory on both bayesian and classical statistics markov chain monte carlo is used essentially to estimate integrals in high dimensions this article addresses the accuracy of such estimation through computer experiments performed on the two dimensional ising model we compare the most common method for error estimates in statistical mechanics it appears that the moving block bootstrap outperforms other methods based on subseries values when the number of observations is relatively small and the time correlation between successive configurations decays slowly moreover the moving block bootstrap enables estimates of the sta

forecasting the yield curve in a data rich environment a no arbitrage factor augmented var approach this paper suggests a term structure model which parsimoniously exploits a broad macroeconomic information set the model uses the short rate and the common components of a large number of macroeconomic variables as factors precisely the dynamics of the short rate are modeled with a factor augmented vector autoregression and the term structure is derived using parameter restrictions implied by no arbitrage the model has economic appeal and provides better out of sample yield forecasts at intermediate and long horizons than a number of previously suggested approaches the forecast improvement is highly significant and particularly pronounced for short and medium term maturities

towards estimating extremal serial dependence via the bootstrapped extremogram abstract davis and mikosch 2009a introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series there we showed some standard statistical properties of the sample extremogram a major difficulty was the construction of credible confidence bands for the extremogram in this paper we employ the stationary bootstrap to overcome this problem the use of the stationary bootstrap for the extremogram and the resulting interpretations are illustrated with several financial time series

inference on the tail process with application to financial time series modeling abstract to draw inference on serial extremal dependence within heavy tailed markov chains drees et al 2015 proposed nonparametric estimators of the spectral tail process the methodology can be extended to the more general setting of a stationary regularly varying time series the large sample distribution of the estimators is derived via empirical process theory for cluster functionals the finite sample performance of these estimators is evaluated via monte carlo simulations moreover two different bootstrap schemes are employed which yield confidence intervals for the pre asymptotic spectral tail process the stationary bootstrap and the multiplier block bootstrap the estimators are applied to stock price data to study the persistence of positive and negative shocks

modeling spatial processes with unknown extremal dependence class abstractmany environmental processes exhibit weakening spatial dependence as events become more extreme well known limiting models such as max stable or generalized pareto processes cannot capture this which can lead to a preference for models that exhibit a property known as asymptotic independence however weakening dependence does not automatically imply asymptotic independence and whether the process is truly asymptotically in dependent is usually far from clear the distinction is key as it can have a large impact upon extrapolation that is the estimated probabilities of events more extreme than those observed in this work we present a single spatial model that is able to capture both dependence classes in a parsimonious manner and with a smooth transition between the two cases the model covers a wide range of possibilities from asymptotic independence through to complete dependence and permits weakening dependence of extremes even under asymptotic dependence censored likelihood based

forecasting volatility of fuel oil futures in china garch type sv or realized volatility models abstract in most previous works on forecasting oil market volatility squared daily returns were taken as the proxy of unobserved actual volatility however as demonstrated by andersen and bollerslev 1998 22 this proxy with too high measurement noise could be perfectly outperformed by a so called realized volatility rv measure calculated by the cumulative sum of squared intraday returns with this motivation we further extend earlier works by employing intraday high frequency data to compare the performance of three typical volatility models in the daily out of sample volatility forecasting of fuel oil futures on the shanghai futures exchange shfe the garch type stochastic volatility sv and realized volatility models by taking rv as the proxy of actual daily volatility and then computing forecasting errors we find that the realized volatility model based on intraday high frequency data produces significantly more accurate volatility forecasts than the garch type and sv models based on daily returns furthermore the sv model outperforms many linear and nonlinear garch type models that capture long memory volatility and or the asymmetric leverage effect in volatility these results also prove that abundant volatility information is available in intraday high frequency data and can be used to construct more accurate oil volatility forecasting models

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

the dependent wild bootstrap we propose a new resampling procedure the dependent wild bootstrap for stationary time series as a natural extension of the traditional wild bootstrap to time series setting the dependent wild bootstrap offers a viable alternative to the existing block based bootstrap methods whose properties have been extensively studied over the last two decades unlike all of the block based bootstrap methods the dependent wild bootstrap can be easily extended to irregularly spaced time series with no implementational difficulty furthermore it preserves the favorable bias and mean squared error property of the tapered block bootstrap which is the state of the art block based method in terms of asymptotic accuracy of variance estimation and distribution approximation the consistency of the dependent wild bootstrap in distribution approximation is established under the framework of the smooth function model in addition we obtain the bias and variance expansions of the dependent wild bootstrap variance estimat

a data driven smooth test of symmetry in this paper we propose a data driven smooth test of symmetry we first transform the raw data via the probability integral transformation according to a symmetrized empirical distribution and show that under the null hypothesis of symmetry the transformed data has a limiting uniform distribution reducing testing for symmetry to testing for uniformity employing neyman s smooth test of uniformity we show that only odd ordered orthogonal moments of the transformed data are required in constructing the test statistic we present a standardized smooth test that is distribution free asymptotically and derive the asymptotic behavior of the test and establish its consistency extension to dependent data case is discussed we investigate the finite sample performance of the proposed tests on both homogeneous and mixed distributions with unobserved heterogeneity an empirical application on testing symmetry of wage adjustment process based on heterogeneous wage contracts with different durations is provided

bootstrap technology and applications bootstrap resampling methods have emerged as powerful tools for constructing inferential procedures in modern statistical data analysis although these methods depend on the availability of fast inexpensive computing they offer the potential for highly accurate methods of inference moreover they can even eliminate the need to impose a convenient statistical model that does not have a strong scientific basis in this article we review some bootstrap methods emphasizing applications through illustrations with some real data special attention is given to regression problems with dependent data and choosing tuning parameters for optimal performance

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

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

the pseudo true score encompassing test for non nested hypotheses abstract well known encompassing tests are usually difficult to implement because it is difficult to compute the pseudo true value of the quasi maximum likelihood estimator in this paper we propose a more operational encompassing test that does not involve such pseudo true value and is asymptotically equivalent to the wald and score encompassing tests instead the proposed test relies on the pseudo true score which is relatively easy to evaluate this test is not restricted to testing conditional mean specifications and hence extends the applicability of the conditional mean encompassing test of wooldridge j econom 45 1990b 331 the proposed test is particularly useful when data characteristics can be fully incorporated into the likelihood function our simulations confirm that this test compares favorably with the j and ja tests in testing conditional mean specifications and outperforms the cox test in testing conditional variance specifications

models for estimating bayes factors with applications to phylogeny and tests of monophyly summary bayes factors comparing two or more competing hypotheses are often estimated by constructing a markov chain monte carlo mcmc sampler to explore the joint space of the hypotheses to obtain ecien t bayes factor estimates carlin and chib 1995 suggest adjusting the prior odds of the competing hypotheses so that the posterior odds are approximately one then estimating the bayes factor by simple division a byproduct is that one often produces several independent mcmc chains only one of which is actually used for estimation we extend this approach to incorporate output from multiple chains by proposing three statistical models the rst assumes independent sampler draws and models the hypothesis indicator function using logistic regression for various choices of the prior odds the two more complex models relax the independence assumption by allowing for higherlag dependence within the mcmc output these models allow us to estimate the uncertainty in our bayes factor calculation and to fully use several dieren t mcmc chains even when the prior odds of the hypotheses vary from chain to chain we apply these methods to calculate bayes factors for tests of monophyly in two phylogenetic

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

consistent specification tests for semiparametric nonparametric models based on series estimation methods abstract this paper considers the problem of consistent model specification tests using series estimation methods the null models we consider in this paper all contain some nonparametric components a leading case we consider is to test for an additive partially linear model the null distribution of the test statistic is derived using a central limit theorem for hilbert valued random arrays the test statistic is shown to be able to detect local alternatives that approach the null models at the order of op n 1 2 we show that the wild bootstrap method can be used to approximate the null distribution of the test statistic a small monte carlo simulation is reported to examine the finite sample performance of the proposed test we also show that the proposed test can be easily modified to obtain series based consistent tests for other semiparametric nonparametric models

distance ideals of graphs abstract we introduce the concept of distance ideals of graphs which can be regarded as a generalization of the smith normal form and the spectra of the distance matrix and the laplacian distance matrix of a graph we also obtain a classification of the graphs with at most one trivial distance ideal

a general resampling scheme for triangular arrays of alpha mixing random variables with application to the problem of spectral density estimation in 1989 kunsch introduced a modified bootstrap and jackknife for a statistic which is used to estimate a parameter of the m dimensional joint distribution of stationary and alpha mixing observations the modification amounts to resampling whole blocks of consecutive observations or deleting whole blocks one at a time liu and singh independently proposed in 1988 the same technique for observations that are m dependent however many time series statistics notably estimators of the spectral density function involve parameters of the whole infinite dimensional joint distribution and hence do not fit in this framework in this report we generalize the moving blocks resampling scheme of kunsch and liu and singh a still modified version of the nonparametric bootstrap and jackknife is seen to be valid for general linear statistics that are asymptotically normal and consistent for a parameter of the whole joint distribution we then apply this result to the problem of estimation of the spectral density

simultaneous multiple change point and factor analysis for high dimensional time series abstract we propose the first comprehensive treatment of high dimensional time series factor models with multiple change points in their second order structure we operate under the most flexible definition of piecewise stationarity and estimate the number and locations of change points consistently as well as identifying whether they originate in the common or idiosyncratic components through the use of wavelets we transform the problem of change point detection in the second order structure of a high dimensional time series into the relatively easier problem of change point detection in the means of high dimensional panel data also our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change points by adopting a screening procedure we further show that consistent factor analysis is achieved over each segment defined by the change points estimated by the proposed methodology in extensive simulation studies we observe that factor analysis prior to change point detection improves the detectability of change points and identify and describe an interesting spillover effect in which substantial breaks in the idiosyncratic components get naturally enough identified as change points in the common components which prompts us to regard the corresponding change points as also acting as a form of factors our methodology is implemented in the r package factorcpt available from cran

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

the moving blocks bootstrap and robust inference for linear least squares and quantile regressions abstract this paper presents the moving blocks bootstrap mbb as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms the mbb covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent hac standard errors for least squares ls and quantile regression qr coefficient estimators the mbb covariance estimator is shown to be asymptotically equivalent to the bartlett kernel estimator suggested by newey and west 1987 and the asymptotically optimal choice of the blocksize is discussed a monte carlo study is included showing that the mbb fares well in comparison to standard hac inference procedures considering strong mixing data generating processes the paper extends existing asymptotic results for the qr estimator the analogy to the ls case is stressed the paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new grenander like conditions for the latter case the use of the mbb approach is illustrated for a practical example using a standard econometric package