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395
A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk
, 1997
"... This article presents a technique for nonparametrically estimating continuoustime di#usion processes which are observed at discrete intervals. We illustrate the methodology by using daily three and six month Treasury Bill data, from January 1965 to July 1995, to estimate the drift and di#usion of t ..."
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Cited by 208 (5 self)
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This article presents a technique for nonparametrically estimating continuoustime di#usion processes which are observed at discrete intervals. We illustrate the methodology by using daily three and six month Treasury Bill data, from January 1965 to July 1995, to estimate the drift and di#usion of the short rate, and the market price of interest rate risk. While the estimated di#usion is similar to that estimated by Chan, Karolyi, Longsta# and Sanders (1992), there is evidence of substantial nonlinearity in the drift. This is close to zero for low and medium interest rates, but mean reversion increases sharply at higher interest rates.
The bootstrap
 In Handbook of Econometrics
, 2001
"... The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an a ..."
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Cited by 174 (2 self)
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The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data. It amounts to treating the data as if they were the population for the purpose of evaluating the distribution of interest. Under mild regularity conditions, the bootstrap yields an approximation to the distribution of an estimator or test statistic that is at least as accurate as the
A test for superior predictive ability
, 2003
"... We propose a new test for superior predictive ability. The new test compares favorable to the reality check for data snooping (RC), because the former is more powerful and less sensitive to poor and irrelevant alternatives. The improvements are achieved by two modifications of the RC. We employ a s ..."
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Cited by 136 (4 self)
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We propose a new test for superior predictive ability. The new test compares favorable to the reality check for data snooping (RC), because the former is more powerful and less sensitive to poor and irrelevant alternatives. The improvements are achieved by two modifications of the RC. We employ a studentized test statistic that reduces the influence of erratic forecasts and we invoke a sample dependent null distribution. The advantages of the new test are confirmed by Monte Carlo experiments and in an empirical exercise, where we compare a large number of regressionbased forecasts of annual US inflation to a simple random walk forecast. The random walk forecast is found to be inferior to regressionbased forecasts and, interestingly, the best sample performance is achieved by models that have a Phillips curve structure.
Variable Length Markov Chains
 Annals of Statistics
, 1999
"... We study estimation in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of higher order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary higher order Markov ..."
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Cited by 130 (5 self)
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We study estimation in the class of stationary variable length Markov chains (VLMC) on a finite space. The processes in this class are still Markovian of higher order, but with memory of variable length yielding a much bigger and structurally richer class of models than ordinary higher order Markov chains. From a more algorithmic view, the VLMC model class has attracted interest in information theory and machine learning but statistical properties have not been explored very much. Provided that good estimation is available, an additional structural richness of the model class enhances predictive power by finding a better tradeoff between model bias and variance and allows better structural description which can be of specific interest. The latter is exemplified with some DNA data. A version of the treestructured context algorithm, proposed by Rissanen (1983) in an information theoretical setup, is shown to have new good asymptotic properties for estimation in the class of VLMC's, even when the underlying model increases in dimensionality: consistent estimation of minimal state spaces and mixing properties of fitted models are given. We also propose a new bootstrap scheme based on fitted VLMC's. We show its validity for quite general stationary categorical time series and for a broad range of statistical procedures. AMS 1991 subject classifications. Primary 62M05; secondary 60J10, 62G09, 62M10, 94A15 Key words and phrases. Bootstrap, categorical time series, central limit theorem, context algorithm, data compression, finitememory sources, FSMX model, KullbackLeibler distance, model selection, tree model. Short title: Variable Length Markov Chain 1 Research supported in part by the Swiss National Science Foundation. Part of the work has been done while visiting th...
Bootstraps for Time Series
, 1999
"... We compare and review block, sieve and local bootstraps for time series and thereby illuminate theoretical facts as well as performance on nitesample data. Our (re) view is selective with the intention to get a new and fair picture about some particular aspects of bootstrapping time series. The ge ..."
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Cited by 112 (4 self)
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We compare and review block, sieve and local bootstraps for time series and thereby illuminate theoretical facts as well as performance on nitesample data. Our (re) view is selective with the intention to get a new and fair picture about some particular aspects of bootstrapping time series. The generality of the block bootstrap is contrasted by sieve bootstraps. We discuss implementational dis/advantages and argue that two types of sieves outperform the block method, each of them in its own important niche, namely linear and categorical processes, respectively. Local bootstraps, designed for nonparametric smoothing problems, are easy to use and implement but exhibit in some cases low performance. Key words and phrases. Autoregression, block bootstrap, categorical time series, context algorithm, double bootstrap, linear process, local bootstrap, Markov chain, sieve bootstrap, stationary process. 1 Introduction Bootstrapping can be viewed as simulating a statistic or statistical pro...
Frequentist properties of Bayesian posterior probabilities of phylogenetic trees under simple and complex substitution models
 SYST. BIOL
, 2004
"... What does die posterior probability of a phylogenetic tree mean? This simulation study shows that Bayesian posterior probabilities have the meaning that is typically ascribed to them; the pt>sterkir probability ot'a tree is the probability that the tree is corwct, assuming th>.it the mo ..."
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Cited by 95 (6 self)
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What does die posterior probability of a phylogenetic tree mean? This simulation study shows that Bayesian posterior probabilities have the meaning that is typically ascribed to them; the pt>sterkir probability ot'a tree is the probability that the tree is corwct, assuming th>.it the model is correct. At the same time, the BayLsian method can be sensitive to model misspecification, and the sensitivity of the Bayesian method appears to be greater than the sensitivity ot " the nonparametric bootstrap method (using maximum likelihood to estimate trees). Although the estimatLs of phylogeny obtained by use of the method of maximum likelihood or the Bayesian method are Ukely to be similar, the assessment of the uncertainty of inferred trees via either bootstriipping (t"or maximum likelihood estimates) or petsterior probabilities (for Bayesian estimates) is not likely to be the same. We suggest that the Bayesian method be implemented with the most complex models of those currently avaiiable, as tliis should reduce the chance that the metliod will concentrate too much probability on tuo few trees. [Bayesian estimation; Markov ch^iin Monte Carlo; posterior probability; prior probability.] Quantify ing the uncertainty of a phylogcneticesti mil te is at least as important a goal as obtaining the phylogenetic estimate itself. Measures of phylogenetic reliability not only point out what parts of a tree can be trusted when interpreting the evolution of a group, but can guide
Stepwise multiple testing as formalized data snooping
 Econometrica
, 2005
"... It is common in econometric applications that several hypothesis tests are carried out at the same time. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. In this paper, we suggest a stepwise multiple testing procedure which asymptotically cont ..."
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Cited by 80 (9 self)
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It is common in econometric applications that several hypothesis tests are carried out at the same time. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. In this paper, we suggest a stepwise multiple testing procedure which asymptotically controls the familywise error rate at a desired level. Compared to related singlestep methods, our procedure is more powerful in the sense that it often will reject more false hypotheses. In addition, we advocate the use of studentization when it is feasible. Unlike some stepwise methods, our method implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect alternative hypotheses. We prove our method asymptotically controls the familywise error rate under minimal assumptions. We present our methodology in the context of comparing several strategies to a common benchmark and deciding which strategies actually beat the benchmark. However, our ideas can easily be extended and/or modified to other contexts, such as making inference for the individual regression coefficients in a multiple regression framework. Some simulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.
Bootstrap Methods in Econometrics: Theory and Numerical Performance
 Eds.), Advances in Economics and Econometrics: Theory and Applications, Seventh World Congress, Vol. III
, 1997
"... 1. ..."
Automatic BlockLength Selection for the Dependent Bootstrap
 Econometric Reviews
, 2004
"... We review the different block bootstrap methods for time series, and present them in a unified framework. We then revisit a recent result of Lahiri [Lahiri, S. N. (1999b). Theoretical comparisons of block bootstrap methods, Ann. Statist. ..."
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Cited by 74 (5 self)
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We review the different block bootstrap methods for time series, and present them in a unified framework. We then revisit a recent result of Lahiri [Lahiri, S. N. (1999b). Theoretical comparisons of block bootstrap methods, Ann. Statist.
A Threestep Method for Choosing the Number of Bootstrap Repetitions
 Econometrica
, 2000
"... This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests, pvalues, and bias correction. For each of these problems, the paper provides a threestep method for choosing B to achieve a ..."
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Cited by 74 (2 self)
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This paper considers the problem of choosing the number of bootstrap repetitions B for bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests, pvalues, and bias correction. For each of these problems, the paper provides a threestep method for choosing B to achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval length, test’s critical value, test’s pvalue, or biascorrected estimate based on B bootstrap simulations from the corresponding ideal bootstrap quantities for which B��. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals. Monte Carlo simulations show that the proposed methods work very well.