Estimating a gradual parameter change in an AR(1)-process

Marie Hušková (), Zuzana Prášková () and Josef G. Steinebach ()
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Marie Hušková: Charles University
Zuzana Prášková: Charles University
Josef G. Steinebach: University of Cologne

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 7, No 1, 808 pages

Abstract: Abstract We discuss the estimation of a change-point $$t_0$$ t 0 at which the parameter of a (non-stationary) AR(1)-process possibly changes in a gradual way. Making use of the observations $$X_1,\ldots ,X_n$$ X 1 , … , X n , we shall study the least squares estimator $$\widehat{t}_0$$ t ^ 0 for $$t_0$$ t 0 , which is obtained by minimizing the sum of squares of residuals with respect to the given parameters. As a first result it can be shown that, under certain regularity and moment assumptions, $$\widehat{t}_0/n$$ t ^ 0 / n is a consistent estimator for $$\tau _0$$ τ 0 , where $$t_0 =\lfloor n\tau _0\rfloor $$ t 0 = ⌊ n τ 0 ⌋ , with $$0

Keywords: AR(1)-process; Gradual change; Change-point estimator; Consistency; Convergence rate; Asymptotic normality; 62F10; 62F12; 62M10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00844-z

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