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On aggregation of strongly dependent time series
Author(s) -
Beran Jan,
Liu Haiyan,
Ghosh Sucharita
Publication year - 2020
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12421
Subject(s) - mathematics , estimator , series (stratigraphy) , autocorrelation , nonparametric statistics , statistical physics , statistical inference , rate of convergence , convergence (economics) , econometrics , statistics , computer science , paleontology , computer network , channel (broadcasting) , physics , economics , biology , economic growth
We consider cross‐sectional aggregation of time series with long‐range dependence. This question arises for instance from the statistical analysis of networks where aggregation is defined via routing matrices. Asymptotically, aggregation turns out to increase dependence substantially, transforming a hyperbolic decay of autocorrelations to a slowly varying rate. This effect has direct consequences for statistical inference. For instance, unusually slow rates of convergence for nonparametric trend estimators and nonstandard formulas for optimal bandwidths are obtained. The situation changes, when time‐dependent aggregation is applied. Suitably chosen time‐dependent aggregation schemes can preserve a hyperbolic rate or even eliminate autocorrelations completely.