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AGGREGATION OF THE RANDOM COEFFICIENT GLARCH(1,1) PROCESS

  • Liudas Giraitis (a1), Remigijus Leipus (a2) and Donatas Surgailis (a2)
Abstract

The paper discusses contemporaneous aggregation of the Linear ARCH (LARCH) model as defined in (1), which was introduced in Robinson (1991) and studied in Giraitis, Robinson, and Surgailis (2000) and other works. We show that the limiting aggregate of the (G)eneralized LARCH(1,1) process in (3)–(4) with random Beta distributed coefficient β exhibits long memory. In particular, we prove that squares of the limiting aggregated process have slowly decaying correlations and their partial sums converge to a self-similar process of a new type.

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*Address correspondence to Liudas Giraitis, Queen Mary, University of London, Department of Economics, Mile End Road, London E1 4NS; e-mail: L.Giraitis@qmul.ac.uk.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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