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Recent developments in bootstrap methods for dependent data

Author

Listed:
  • Giuseppe Cavaliere
  • Dimitris N. Politis
  • Anders Rahbek
  • Dominique Dehay
  • Anna E. Dudek

Abstract

type="main" xml:id="jtsa12115-abs-0001"> Let { X ( t ) , t ∈ R } be an almost periodically correlated process and {N(t),t≥0} be a homogeneous Poisson process and {T k ,k≥1} be its jump moments. We assume that { X ( t ) , t ∈ R } and {N(t),t≥0} are independent. Moreover, the process { X ( t ) , t ∈ R } is not observed continuously but only in the time moments {T k ,k≥1}; In this paper, we focus on the estimation of the cyclic means of { X ( t ) , t ∈ R } . The asymptotic normality of the rescaled error of the estimator is shown. Additionally, the bootstrap method based on the circular block bootstrap is proposed. The consistency of the bootstrap technique is proved, and the bootstrap pointwise and simultaneous confidence intervals for the cyclic means are constructed. The results are illustrated by a simulated data example.

Suggested Citation

  • Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Dominique Dehay & Anna E. Dudek, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 327-351, May.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:3:p:327-351
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    References listed on IDEAS

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    1. Łukasz Lenart & Mateusz Pipień, 2013. "Seasonality Revisited - Statistical Testing for Almost Periodically Correlated Stochastic Processes," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 5(2), pages 85-102, June.
    2. ŁUkasz Lenart & Jacek Leśkow & Rafał Synowiecki, 2008. "Subsampling in testing autocovariance for periodically correlated time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(6), pages 995-1018, November.
    3. Hurd, Harry L., 1991. "Correlation theory of almost periodically correlated processes," Journal of Multivariate Analysis, Elsevier, vol. 37(1), pages 24-45, April.
    4. Dominique Dehay & Vincent Monsan, 2007. "Discrete Periodic Sampling with Jitter and Almost Periodically Correlated Processes," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 223-253, October.
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    1. Germán Aneiros & Paula Raña & Philippe Vieu & Juan Vilar, 2018. "Bootstrap in semi-functional partial linear regression under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 659-679, September.

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