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

• Authors: Hušková Marie , Prášková Zuzana , Steinebach Josef G.
• Languages of publication: EN

Abstracts

EN

The authors discuss the estimation of a change-point 𝑡0 at which the parameter of a (non-stationary) AR(1)-process possibly changes in a gradual way. Making use of the observations 𝑋1, … , 𝑋𝑛 , we study the least squares estimator 𝑡̂0 for 𝑡0, which is obtained by minimizing the sum of squares of the residuals with respect to the given parameters. As the first result it can be shown that, under certain regularity and moment assumptions, 𝑡̂0/𝑛 is a consistent estimator for 𝜏0, where 𝑡0 = ⌊𝑛𝜏0⌋, with 0 < 𝜏0 < 1, i.e., 𝑡̂0/𝑛 →𝑃 𝜏0 (𝑛 → ∞). Based on the rates obtained in the proof of the consistency result, a rough convergence rate statement can also be given. Some possible further investigations are briefly discussed, including the weak limiting behaviour of the (suitably normalized) estimator.

Keywords

EN

gradual change; change-point estimation; least squares estimator; AR(1)-process

• Publisher: Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
• Journal: Śląski Przegląd Statystyczny
• Year: 2020
• Issue: 18 (24)
• Pages: 254-262

Contributors

author

Hušková Marie

• Charles University in Prague, the Czech Republic

author

Prášková Zuzana

• Charles University in Prague, the Czech Republic

author

Steinebach Josef G.

• University of Cologne, Germany

References

• Hušková M., Prášková Z., Steinebach J.G., 2019, Estimating a gradual parameter change in an AR(1)-process. Preprint (2019), Charles University in Prague and the University of Cologne.