Using randomization to improve performance of a variance estimator of strongly dependent errors

Volume 39 / 2012

Artur Bryk Applicationes Mathematicae 39 (2012), 273-282 MSC: 62G08, 62G20, 62M10. DOI: 10.4064/am39-3-2


We consider a fixed-design regression model with long-range dependent errors which form a moving average or Gaussian process. We introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. We estimate the variance of the errors using the Rice estimator. The estimator is shown to exhibit weak (i.e. in probability) consistency. Simulation results confirm this property for moderate and large sample sizes when randomization is employed.


  • Artur BrykDepartment of Mathematics and Mathematical Economics
    Warsaw School of Economics
    Al. Niepodległości 162
    02-554 Warszawa, Poland

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