Prediction intervals for stationary time series using the sieve bootstrap metod

• Autorzy: Zagdański A.
• Języki publikacji: EN

Abstrakty

EN

We consider the problem of constructing prediction intervals for future observations of stationary time series. Our approach relies on the sieve bootstrap procedure introduced by Blihimann (1997, 1998) which is asymptotically valid for the rich class of linear stationary processes which can be inverted and represented as an autoregressive processes of order infinity (AR(oo)). We extend the results obtained earlier by Stine (1987) for autoregressive time series of known order. A more traditional Gaussian strategy is also presented. We verify accuracy of the proposed methods via numerical comparison including both Gaussian and non-Gaussian data.

Słowa kluczowe

EN

prediction interval; bootstrap

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 2
• Strony: 469--481
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Zagdański A.

• Institute of Mathematics Wrocław University of Technology ul. Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland

Bibliografia

• [1] T. Anderson (1971). The Statistical Analysis of Time Series. Wiley, New York.
• [2] P. Brockwell and R. Davies (1987). Time Series Theory and Method, Springer-Verlag.
• [3] P. Bühlmann (1997). Sieve bootstrap for time series, Bernouli, 3(2), 123-148.
• [4] P. Bühlmann (1998). Sieve bootstrap for smoothing in nonstationary time series, Ann. Statist., 26(1), 48-83.
• [5] E. Carlstein (1992). Resampling techniques for stationary time series: some recent developments, New Directions in Time Series Analysis, Part I, pages 75-85.
• [6] U. Grenander (1981). Abstract Inference, Wiley, New York.
• [7] P. Hall (1988). Theoretical comparison of bootstrap confidence intervals, Ann. Statist., 16, 927-985.
• [8] J. Shao and D. Tu (1995). The Jacknife and Bootstrap, Springer-Verlag, New York.
• [9] R. A. Stine (1987). Estimating properties of autoregressive forecast, J. Amer. Statist. Assoc., 82(400), 1073-1078.