On the range of validity of the autoregressive sieve bootstrap

Kreiß, Jens-Peter; Paparoditis, Efstathios; Politis, Dimitris N.

doi:10.1214/11-aos900

Cited by 116 publications

(155 citation statements)

References 32 publications

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“…With caveats concerning invertibility, the Wold theorem therefore extends validity to the general covariance stationary case. The issues arising here are carefully analysed, in the bootstrap context, by Kreiss, Paparoditis, and Politis (2011). They show that Gaussianity of the series is certainly sufficient and this is, in any case, an assumption adopted for our subsequent asymptotic analysis and imposed in our experiments.…”

Section: The Bias-corrected Estimatormentioning

confidence: 95%

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A Test of the Long Memory Hypothesis Based on Self-Similarity

Davidson¹,

Rambaccussing²

2015

Journal of Time Series Econometrics

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A test of the long memory hypothesis based on self-similarityDavidson, James; Rambaccussing, Dooruj Davidson, J., & Rambaccussing, D. (2015). A test of the long memory hypothesis based on self-similarity. Journal of Time Series Econometrics, 7(2), 115-141. [7]. DOI: 10.1515DOI: 10. /jtse-2013 General rights Copyright and moral rights for the publications made accessible in Discovery Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from Discovery Research Portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain.• You may freely distribute the URL identifying the publication in the public portal. Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract: This paper develops a new test of true versus spurious long memory, based on log-periodogram estimation of the long memory parameter using skipsampled data. A correction factor is derived to overcome the bias in this estimator due to aliasing. The procedure is designed to be used in the context of a conventional test of significance of the long memory parameter, and a composite test procedure is described that has the properties of known asymptotic size and consistency. The test is implemented using the bootstrap, with the distribution under the null hypothesis being approximated using a dependentsample bootstrap technique to approximate short-run dependence following fractional differencing. The properties of the test are investigated in a set of Monte Carlo experiments. The procedure is illustrated by applications to exchange rate volatility and dividend growth series.

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Section: The Bias-corrected Estimatormentioning

confidence: 95%

“…Politis and Romano (1994) and the sieve autoregression method of Bühlmann (1997). Note that the latter calculation is also used to obtain expression [7], and the same remarks apply regarding the validity of the sieve AR method in this context; see Kreiss, Paparoditis, and Politis (2011). 2.…”

Section: The Bootstrap Testmentioning

confidence: 99%

A Test of the Long Memory Hypothesis Based on Self-Similarity

Davidson¹,

Rambaccussing²

2015

Journal of Time Series Econometrics

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“…Under very mild conditions and without having to assume any autoregressive structure of the underlying process, they were able to show that the AR sieve remains valid whenever the so-called companion process mimics the proper limiting distribution, which constitutes a simple and general check criterion. Recently, Meyer and Kreiss (2014+) extended the results of Kreiss, Paparoditis and Politis (2011) to the multivariate case. To generalize their concept, as a second main contribution of this paper, we introduce a spatial AR sieve methodology in the spirit of Kreiss, Paparoditis and Politis (2011) and provide rigorous theory.…”

Section: Introductionmentioning

confidence: 99%

“…However, while all the aforementioned results were derived under the explicit assumption of an underlying AR(∞) process, Kreiss, Paparoditis and Politis (2011) extended the range of applicability of the AR sieve significantly. Under very mild conditions and without having to assume any autoregressive structure of the underlying process, they were able to show that the AR sieve remains valid whenever the so-called companion process mimics the proper limiting distribution, which constitutes a simple and general check criterion.…”

Section: Introductionmentioning

confidence: 99%

Baxter’s inequality and sieve bootstrap for random fields

Meyer¹,

Jentsch²,

Kreiß³

2017

Bernoulli

Self Cite

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Abstract. The concept of the autoregressive (AR) sieve bootstrap is investigated for the case of spatial processes in Z 2 . This procedure fits AR models of increasing order to the given data and, via resampling of the residuals, generates bootstrap replicates of the sample. The paper explores the range of validity of this resampling procedure and provides a general check criterion which allows to decide whether the AR sieve bootstrap asymptotically works for a specific statistic of interest or not. The criterion may be applied to a large class of stationary spatial processes. As another major contribution of this paper, a weighted Baxter-inequality for spatial processes is provided. This result yields a rate of convergence for the finite predictor coefficients, i.e. the coefficients of finite-order AR model fits, towards the autoregressive coefficients which are inherent to the underlying process under mild conditions.The developed check criterion is applied to some particularly interesting statistics like sample autocorrelations and standardized sample variograms. A simulation study shows that the procedure performs very well compared to normal approximations as well as block bootstrap methods in finite samples.

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“…With regard to the former, the VAR bootstrap scheme becomes infeasible in panel data where the number of cross-sectional units is large and the dimension of the system is too high. With regard to the latter, Palm (1977) shows that any VAR model can be written as a system of ARMA equations for each unit; starting from this consideration and using the results of Kreiss et al (2011), Smeeks and Urbain (2011) describe the AR sieve bootstrap algorithm for panel data. Chang (2004) has proven the validity of the AR sieve bootstrap in the context of panel data if there is only one contemporaneous source of dependence between the units; however, this 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 3 condition is likely to be violated in many empirical applications.…”

Section: Introductionmentioning

confidence: 99%

Computational framework for longevity risk management

D’Amato

Haberman²,

Piscopo

et al. 2013

Comput Manag Sci

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract: Longevity risk threatens the financial stability of private and government sponsored defined benefit pension systems as well as social security schemes, in an environment already characterized by persistent low interest rates and heightened financial uncertainty. Permanent repository linkThe mortality experience of countries in the industrialized world would suggest a substantial age-time interaction, with the two dominant trends affecting different age groups at different times. From a statistical point of view, this indicates a dependence structure. It is observed that mortality improvements are similar for individuals of contiguous ages (Wills and Sherris 2008). Moreover, considering the dataset by single ages, the correlations between the residuals for adjacent age groups tend to be high (as noted in Denton et al 2005). This suggests that there is value in exploring the dependence structure, also across time, in other words the inter-period correlation.In this research, we focus on the projections of mortality rates, contravening the most commonly encountered dependence property which is the "lack of dependence" . By taking into account the presence of dependence across age and time which leads to systematic over-estimation or under-estimation of uncertainty in the estimates (Liu and Braun 2010), the paper analyzes a tailor-made bootstrap methodology for capturing the spatial dependence in deriving prediction intervals for mortality projection rates. We propose a method which leads to a prudent measure of longevity risk, avoiding the structural incompleteness of the ordinary simulation bootstrap methodology which involves the assumption of independence.Response to Reviewers: Dear Referees, we thank you for your reports, which were useful for us, in order to increase the value of our work. Please find below, the description of how we have changed the paper according to your suggestions.Reviewer #1: General comments Powered by Editorial Manager® and Preprint Manager® from Aries Systems CorporationThe manuscript "Computational framework for longevity risk management" introduces a Panel Sieve Bootstrapping technique in the Lee-Carter setting to capture the spatial dependence across age and time in deriving prediction intervals for mortality projection rates. The manuscript is well written and the information provided is so interesting. The use of bootstrapping method to explore the dependency nature of residuals looks very promising for me. However, I found some difficulties to prove the accurate projection with reducing dependency nature of the residual using bootstrapping technique. The authors started nicely to describe the procedure; however, failed to prove the evidence of forecast accuracy using their techniques.We have added some comments on forecast accuracy at the end of the section 4. In particular, we have enriched the numerical application with the calculation and comments ...

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On the range of validity of the autoregressive sieve bootstrap

Cited by 116 publications

References 32 publications

A Test of the Long Memory Hypothesis Based on Self-Similarity

A Test of the Long Memory Hypothesis Based on Self-Similarity

Baxter’s inequality and sieve bootstrap for random fields

Computational framework for longevity risk management

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