Asymptotic theory for regression models with fractional local to unity root errors

Kris Brabanter () and Farzad Sabzikar ()
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Kris Brabanter: Iowa State University
Farzad Sabzikar: Iowa State University

Metrika: International Journal for Theoretical and Applied Statistics, 2021, vol. 84, issue 7, No 3, 997-1024

Abstract: Abstract This paper develops the asymptotic theory for parametric and nonparametric regression models when the errors have a fractional local to unity root (FLUR) model structure. FLUR models are stationary time series with semi-long range dependence property in the sense that their covariance function resembles that of a long memory model for moderate lags but eventually diminishes exponentially fast according to the presence of a decay factor governed by a an exponential tempering parameter. When this parameter is sample size dependent, the asymptotic theory for these regression models admit a wide range of stochastic processes with behavior that includes long, semi-long, and short memory processes.

Keywords: Tempered linear processes; Semi-long range dependence; Non-parametric regression; Piecewise polynomial regression; Tempered fractional calculus; 60G22; 60G50; 62F12; 62G08 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00184-021-00812-7

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