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Distant long-range dependent sums and regression estimation

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  • Csörgo, Sándor
  • Mielniczuk, Jan

Abstract

Consider a stationary sequence G(Z0), G(Z1), ..., where G(·) is a Borel function and Z0, Z1, ... is a sequence of standard normal variables with covariance function E(Z0Zj) = j-[alpha]L(j), j = 1, 2, ..., where E(G(Z0)) = 0, E(G2(Z0)) 0 and sequences of gap-lengths l1,n, ..., lk,n such that l1,n --> [infinity] and lj,n - lj-1,n --> [infinity], j = 2, ..., k, arbitrary slowly, the vector process , 0

Suggested Citation

  • Csörgo, Sándor & Mielniczuk, Jan, 1995. "Distant long-range dependent sums and regression estimation," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 143-155, September.
    • Handle: RePEc:eee:spapps:v:59:y:1995:i:1:p:143-155
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    References listed on IDEAS

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    1. Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
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    Cited by:

    1. Deo, R. S., 1997. "Nonparametric regression with long-memory errors," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 89-94, April.
    2. Marinucci, D. & Robinson, P. M., 2000. "Weak convergence of multivariate fractional processes," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 103-120, March.
    3. 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.
    4. Surgailis, Donatas & Teyssière, Gilles & Vaiciulis, Marijus, 2008. "The increment ratio statistic," Journal of Multivariate Analysis, Elsevier, vol. 99(3), pages 510-541, March.

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