TY - GEN
A1 - Hušková, Marie
A1 - Prášková, Zuzana
A1 - Steinebach, Josef G.
PB - Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
N2 - 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.
L1 - http://www.dbc.wroc.pl/Content/109574/Huskova_Praskova_Steinebach_Estimating_a_gradual_parameter.pdf
CY - Wrocław
L2 - http://www.dbc.wroc.pl/Content/109574
T1 - Estimating a gradual parameter change in an AR(1)-process
UR - http://www.dbc.wroc.pl/dlibra/publication/edition/109574
T2 - Silesian Statistical Review
ER -