Bootstrapping Autoregressive Processes with Possible Unit Roots

Inoue, Atsushi; Kilian, Lutz

doi:10.1111/1468-0262.00281

Cited by 86 publications

(78 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This algorithm is motivated by the …ndings in Inoue and Kilian (2002b) regarding how to bootstrap persistent processes of unknown order of integration. They demonstrate that the standard bootstrap algorithm for unrestricted autoregressions is asymptotically valid for many I (1) processes.…”

Section: Direct Sieve Bootstrap (Dsb) Algorithmmentioning

confidence: 99%

Sieve bootstrap -tests on long-run average parameters

Fuertes

2008

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractPanel estimators can provide consistent measures of a long-run average parameter even if the individual regressions are spurious. However, the t-test on this parameter is fraught with problems because the limit distribution of the test statistic is nonstandard and rather complicated, particularly in panels with mixed (non)stationary errors. A sieve bootstrap framework is suggested to approximate the distribution of the t -statistic. An extensive Monte Carlo study demonstrates that the bootstrap is quite useful in this context.

show abstract

Section: Direct Sieve Bootstrap (Dsb) Algorithmmentioning

confidence: 99%

Sieve bootstrap -tests on long-run average parameters

Fuertes

2008

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

show abstract

“…Horowitz (2001) considers a nonparametric bootstrap for Markov processes that utilizes a nonparametric estimator of the transition densities of the process. Bose (1988) and Inoue and Kilian (1999) consider a residual-based bootstrap for AR processes that relies on transforming the data to obtain approximately iid residuals. Bühlmann (1998), Park (1999), and Chang and Park (1999) consider sieve bootstraps for linear time series processes.…”

Section: Introductionmentioning

confidence: 99%

Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes

Andrews

Lieberman

Marmer³

2006

Journal of Econometrics

View full text Add to dashboard Cite

This paper provides bounds on the errors in coverage probabilities of maximum likelihood-based, percentile-t, parametric bootstrap conÞdence intervals for Markov time series processes. These bounds show that the parametric bootstrap for Markov time series provides higher-order improvements (over conÞdence intervals based on Þrst order asymptotics) that are comparable to those obtained by the parametric and nonparametric bootstrap for iid data and are better than those obtained by the block bootstrap for time series. Similar results are given for Wald-based conÞdence regions.The paper also shows that k-step parametric bootstrap conÞdence intervals achieve the same higher-order improvements as the standard parametric bootstrap for Markov processes. The k-step bootstrap conÞdence intervals are computationally attractive. They circumvent the need to compute a nonlinear optimization for each simulated bootstrap sample. The latter is necessary to implement the standard parametric bootstrap when the maximum likelihood estimator solves a nonlinear optimization problem.

show abstract

“…The finite order autoregressive model can also be considered as a special case within our framework. In particular, it is rather straightforward to show that the result by Inoue and Kilian (2002) continues to hold for weakly integrated processes. Undoubtedly, the bootstrap would provide refinements for more general models as well.…”

Section: Bootstrap Refinements For General Modelsmentioning

confidence: 95%

A bootstrap theory for weakly integrated processes

Park

2006

Journal of Econometrics

View full text Add to dashboard Cite

This paper develops a bootstrap theory for models including autoregressive time series with roots approaching to unity as the sample size increases. In particular, we consider the processes with roots converging to unity with rates slower than n −1 . We call such processes weakly integrated processes. It is established that the bootstrap relying on the estimated autoregressive model is generally consistent for the weakly integrated processes. Both the sample and bootstrap statistics of the weakly integrated processes are shown to yield the same normal asymptotics. Moreover, for the asymptotically pivotal statistics of the weakly integrated processes, the bootstrap is expected to provide an asymptotic refinement and give better approximations for the finite sample distributions than the first order asymptotic theory. For the weakly integrated processes, the magnitudes of potential refinements by the bootstrap are shown to be proportional to the rate at which the root of the underlying process converges to unity. The order of boostrap refinement can be as large as o(n −1/2+ ) for any > 0. Our theory helps to explain the actual improvements observed by many practitioners, which are made by the use of the bootstrap in analyzing the models with roots close to unity.

show abstract

Bootstrapping Autoregressive Processes with Possible Unit Roots

Cited by 86 publications

References 24 publications

Sieve bootstrap -tests on long-run average parameters

Sieve bootstrap -tests on long-run average parameters

Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes

A bootstrap theory for weakly integrated processes

Contact Info

Product

Resources

About