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1 results

  • Limit Theorems for Aggregated Linear Processes

  • Part of
  • M. Jirak
  • Journal:
    Advances in Applied Probability / Volume 45 / Issue 2 / June 2013
    Published online by Cambridge University Press:
    22 February 2016, pp. 520-544
    Print publication:
    June 2013
    • Article
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  • In this paper we develop an asymptotic theory of aggregated linear processes, and determine in particular the limit distribution of a large class of linear and nonlinear functionals of such processes. Given a sample {Y 1 (N),…,Y n (N)} of the normalized N-fold aggregated process, we describe the limiting behavior of statistics T N,n = T N,n (Y 1 (N),…, Y n (N)) in both of the cases n/N(n) → 0 and N(n)/n → 0, assuming either a ‘limiting long- or short-memory’ condition on the underlying linear process.