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Aggregation Of The Random Coefficient Glarch(1,1) Process

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  • Giraitis, Liudas
  • Leipus, Remigijus
  • Surgailis, Donatas

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.

Suggested Citation

  • Giraitis, Liudas & Leipus, Remigijus & Surgailis, Donatas, 2010. "Aggregation Of The Random Coefficient Glarch(1,1) Process," Econometric Theory, Cambridge University Press, vol. 26(2), pages 406-425, April.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:02:p:406-425_10
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    Cited by:

    1. Jan Beran & Haiyan Liu & Sucharita Ghosh, 2020. "On aggregation of strongly dependent time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 690-710, September.
    2. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2015. "Joint aggregation of random-coefficient AR(1) processes with common innovations," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 73-82.

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