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110
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 175 (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
The Impact of Bootstrap Methods on Time Series Analysis
 Statistical Science
, 2003
"... Sparked by Efron’s seminal paper, the decade of the 1980s was a period of active research on bootstrap methods for independent data— mainly i.i.d. or regression setups. By contrast, in the 1990s much research was directed towards resampling dependent data, for example, time series and random field ..."
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Cited by 51 (6 self)
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Sparked by Efron’s seminal paper, the decade of the 1980s was a period of active research on bootstrap methods for independent data— mainly i.i.d. or regression setups. By contrast, in the 1990s much research was directed towards resampling dependent data, for example, time series and random fields. Consequently, the availability of valid nonparametric inference procedures based on resampling and/or subsampling has freed practitioners from the necessity of resorting to simplifying assumptions such as normality or linearity that may be misleading.
Bootstrap methods for time series
 International Statist. Review
, 2003
"... The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one’s data or a model estimated from the data. The methods that are available for implementing the bootstrap and the accuracy of bootstrap estimates depend on whether the data are a random sampl ..."
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Cited by 44 (0 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 or a model estimated from the data. The methods that are available for implementing the bootstrap and the accuracy of bootstrap estimates depend on whether the data are a random sample from a distribution or a time series. This paper is concerned with the application of the bootstrap to timeseries data when one does not have a finitedimensional parametric model that reduces the data generation process to independent random sampling. We review the methods that have been proposed for implementing the bootstrap in this situation and discuss the accuracy of these methods relative to that of firstorder asymptotic approximations. We argue that methods for implementing the bootstrap with timeseries data are not as well understood as methods for data that are sampled randomly from a distribution. Moreover, the performance of the bootstrap as measured by the rate of convergence of estimation errors tends to be poorer with time series than with random samples. This is an important problem for applied research because firstorder asymptotic approximations are often inaccurate and misleading with timeseries data and samples of the sizes encountered in applications. We conclude that there is a need for further research in the application of the bootstrap to time series, and we describe some of the important unsolved problems.
A Sieve Bootstrap for the Test of a Unit Root
, 2001
"... In this paper, we consider a sieve bootstrap for the test of a unit root in models driven by general linear processes. The given model is first approximated by a finite autoregressive integrated process of order increasing with the sample size, and then the method of bootstrap is applied for the app ..."
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Cited by 32 (3 self)
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In this paper, we consider a sieve bootstrap for the test of a unit root in models driven by general linear processes. The given model is first approximated by a finite autoregressive integrated process of order increasing with the sample size, and then the method of bootstrap is applied for the approximated autoregression to obtain the critical values for the usual unit root tests. The resulting tests, which may simply be viewed as the bootstrapped versions of AugmentedDickeyFuller (ADF) unit root tests by Said and Dickey (1984), are shown to be consistent under very general conditions. The asymptotic validity of the bootstrap ADF unit root tests is thus established. Our conditions are significantly weaker than those used by Said and Dickey. Simulations show that bootstrap provides substantial improvements on finite sample sizes of the tests.
Inference of Trends in Time Series
 J. the Royal Statistical Society: Series B (Statistical Methodology
, 2007
"... Summary. We consider statistical inference of trends in mean nonstationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically cor ..."
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Cited by 32 (13 self)
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Summary. We consider statistical inference of trends in mean nonstationary models. A test statistic is proposed for the existence of structural breaks in trends. On the basis of a strong invariance principle of stationary processes, we construct simultaneous confidence bands with asymptotically correct nominal coverage probabilities. The results are applied to global warming temperature data and Nile river flow data. Our confidence band of the trend of the global warming temperature series supports the claim that the trend is increasing over the last 150 years.
The design and analysis of benchmark experiments
 J Comp Graph Stat
, 2005
"... The assessment of the performance of learners by means of benchmark experiments is an established exercise. In practice, benchmark studies are a tool to compare the performance of several competing algorithms for a certain learning problem. Crossvalidation or resampling techniques are commonly used ..."
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Cited by 30 (14 self)
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The assessment of the performance of learners by means of benchmark experiments is an established exercise. In practice, benchmark studies are a tool to compare the performance of several competing algorithms for a certain learning problem. Crossvalidation or resampling techniques are commonly used to derive point estimates of the performances which are compared to identify algorithms with good properties. For several benchmarking problems, test procedures taking the variability of those point estimates into account have been suggested. Most of the recently proposed inference procedures are based on special variance estimators for the crossvalidated performance. We introduce a theoretical framework for inference problems in benchmark experiments and show that standard statistical test procedures can be used to test for differences in the performances. The theory is based on well defined distributions of performance measures which can be compared with established tests. To demonstrate the usefulness in practice, the theoretical results are applied to regression and classification benchmark studies based on artificial and real world data.
Block length selection in the bootstrap for time series
 Comput. Statist. Data Anal
, 1999
"... The blockwise bootstrap is a modification of Efron's bootstrap designed to give correct results for dependent stationary observations. One drawback of the method is that it depends critically on a block length which had to be chosen by the user. Here we propose a fully datadriven method to sel ..."
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Cited by 28 (3 self)
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The blockwise bootstrap is a modification of Efron's bootstrap designed to give correct results for dependent stationary observations. One drawback of the method is that it depends critically on a block length which had to be chosen by the user. Here we propose a fully datadriven method to select this block length. It is based on the equivalence of the blockwise bootstrap variance to a lag weight estimator of a spectral density at the origin. The relevant spectral density is the one of the process given by the influence function of the statistic to be bootstrapped. In this equivalence the block length is the inverse of the bandwidth. We thus apply a recently developed local bandwidth selection procedure to the time series given by the estimated influence function. Simulations show that this procedure gives good results in a wide range of situations.
European Central Bank
, 2008
"... New Keynesian Phillips Curves (NKPC) have been extensively used in the analysis of monetary policy, but yet there are a number of issues of concern about how they are estimated and then related to the underlying macroeconomic theory. The first is whether such equations are identified. To check ident ..."
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Cited by 27 (0 self)
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New Keynesian Phillips Curves (NKPC) have been extensively used in the analysis of monetary policy, but yet there are a number of issues of concern about how they are estimated and then related to the underlying macroeconomic theory. The first is whether such equations are identified. To check identification requires specifying the process for the forcing variables (typically the output gap) and solving the model for inflationintermsoftheobservables. Inpractice,theequationisestimatedby GMM, relying on statistical criteria to choose instruments. This may result in failure of identification or weak instruments. Secondly, the NKPC is usually derived as a part of a DSGE model, solved by loglinearising around a steady state and the variables are then measured in terms of deviations from the steady state. In practice the steady states, e.g. for output, are usually estimated by some statistical procedure such as the HodrickPrescott (HP) filter that might not be appropriate. Thirdly, there are arguments that other variables, e.g. interest rates, foreign inflation and foreign output gaps should enter the Phillips curve. This paper examines these three issues and argues that all three benefit from a global perspective. The global perspective provides additional instruments to alleviate the weak instrument problem, yields a theoretically consistent measure of the steady state and provides a natural route for foreign inflation or output gap to enter the NKPC. Keywords: Global VAR (GVAR), identification, New Keynesian Phillips Curve, TrendCycle decomposition.
Bootstrap methods in econometrics
 Economic Record
, 2006
"... Bootstrap methods involve estimating a model many times using simulated data. Then quantities computed from the simulated data are used to make inferences from the actual data. Why have bootstrap methods become popular? ..."
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Cited by 24 (6 self)
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Bootstrap methods involve estimating a model many times using simulated data. Then quantities computed from the simulated data are used to make inferences from the actual data. Why have bootstrap methods become popular?
Bootstrap Tests for Simple Structure in Nonparametric Time Series Regression, working paper
, 1998
"... Bootstrap tests for simple structures in nonparametric time series regression Article (Accepted version) ..."
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Cited by 21 (7 self)
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Bootstrap tests for simple structures in nonparametric time series regression Article (Accepted version)