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Studentizing Weighted Sums Of Linear Processes

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  • Violetta Dalla
  • Liudas Giraitis
  • Hira L. Koul

Abstract

type="main" xml:id="jtsa12056-abs-0001"> This article presents a general method for studentizing weighted sums of a linear process where weights are arrays of known real numbers and innovations form a martingale difference sequence. Asymptotical normality for such sums was established in Abadir et al. (2013). This article centres on the estimation of the standard deviation, to make the normal approximation operational. The proposed studentization is easy to apply and robust against unknown types of dependence (short range and long range) in the observations. It does not require the estimation of the parameters controlling the dependence structure. A finite-sample Monte Carlo simulation study shows the applicability of the proposed methodology for moderate sample sizes. Assumptions for studentization are satisfied by the Nadaraya–Watson kernel type weights used for inference in non-parametric regression settings.

Suggested Citation

  • Violetta Dalla & Liudas Giraitis & Hira L. Koul, 2014. "Studentizing Weighted Sums Of Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(2), pages 151-172, March.
    • Handle: RePEc:bla:jtsera:v:35:y:2014:i:2:p:151-172
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    File URL: http://hdl.handle.net/10.1111/jtsa.12056
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    References listed on IDEAS

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    1. Robinson, P. M., 2005. "Robust covariance matrix estimation : 'HAC' estimates with long memory/antipersistence correction," LSE Research Online Documents on Economics 323, London School of Economics and Political Science, LSE Library.
    2. K Abadir & W Distaso & L Giraitis, "undated". "Two estimators of the long-run variance," Discussion Papers 05/19, Department of Economics, University of York.
    3. Abadir, Karim M. & Distaso, Walter & Giraitis, Liudas, 2009. "Two estimators of the long-run variance: Beyond short memory," Journal of Econometrics, Elsevier, vol. 150(1), pages 56-70, May.
    4. Robinson, P.M., 2005. "Robust Covariance Matrix Estimation: Hac Estimates With Long Memory/Antipersistence Correction," Econometric Theory, Cambridge University Press, vol. 21(1), pages 171-180, February.
    5. P. M. Robinson, 1998. "Inference-Without-Smoothing in the Presence of Nonparametric Autocorrelation," Econometrica, Econometric Society, vol. 66(5), pages 1163-1182, September.
    6. Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
    7. McMurry, Timothy L. & Politis, Dimitris N., 2008. "Bootstrap confidence intervals in nonparametric regression with built-in bias correction," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2463-2469, October.
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    Cited by:

    1. Dalla, Violetta & Giraitis, Liudas & Phillips, Peter C. B., 2022. "Robust Tests For White Noise And Cross-Correlation," Econometric Theory, Cambridge University Press, vol. 38(5), pages 913-941, October.
    2. Liudas Giraitis & Masanobu Taniguchi & Murad S. Taqqu, 2017. "Asymptotic normality of quadratic forms of martingale differences," Statistical Inference for Stochastic Processes, Springer, vol. 20(3), pages 315-327, October.

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