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CONTEMPORANEOUS AGGREGATION OF TRIANGULAR ARRAY OF RANDOM‐COEFFICIENT AR(1) PROCESSES
Author(s) -
Philippe Anne,
Puplinskaite Donata,
Surgailis Donatas
Publication year - 2014
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12045
Subject(s) - mathematics , mixing (physics) , consistency (knowledge bases) , limit (mathematics) , exponent , distribution (mathematics) , estimator , combinatorics , space (punctuation) , mathematical analysis , triangular array , law of large numbers , statistical physics , pure mathematics , statistics , discrete mathematics , random variable , linguistics , philosophy , physics , quantum mechanics
We discuss contemporaneous aggregation of independent copies of a triangular array of random‐coefficient processes with i.i.d. innovations belonging to the domain of attraction of an infinitely divisible law W . The limiting aggregated process is shown to exist, under general assumptions on W and the mixing distribution, and is represented as a mixed infinitely divisible moving average { X ( t ) } in (4). Partial sums process of { X ( t ) } is discussed under the assumption E W 2 < ∞ and a mixing density regularly varying at the ‘unit root’ x = 1 with exponent β > 0. We show that the previous partial sums process may exhibit four different limit behaviors depending on β and the Lévy triplet of W . Finally, we study the disaggregation problem for { X ( t ) } in spirit of Leipus et al. (2006) and obtain the weak consistency of the corresponding estimator of ϕ ( x ) in a suitable L 2 space.