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On aggregation of strongly dependent time series

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  • Jan Beran
  • Haiyan Liu
  • Sucharita Ghosh

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:3:p:690-710
    DOI: 10.1111/sjos.12421
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    References listed on IDEAS

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