Change-point Analysis In AR(1) Model For Panel Data

In this paper,we revisit the AR(1)model with a single structural break in an unknown time. Chong(2001)investigated the consistency of the least squares estimators of the AR parameters and the break fraction for time series data.In this paper, we study the Change-point problems for panel data.We consider the model yit=β1yi,t-1I{t≤κ0}+β2yi,t-1I{t>κ0}+εit (i=1,2,...,N; t=1,2,...,T),where I{·} denotes the indicator function,εit～i.i.d.(0,σ2)(?)i,t,0<σ2<∞.In three cases, including:Case 1:|β1|<1 and |β2|<1; case 2:|β1|<1 and β2=1；Case 3:β1=1 and |β2|<1.We discuss the consistency of the least squares estimators of β1、β2 and τ0(τ0=κ0/T),we also derives the limiting distributions of β1 and β2.chong(2001) pointed out that the asymptotic distributions of β1 and β2 are not all normally distributed under different situations.As for panel data,the results are quite different from those of time series date.The results in this paper reveal that β1 and β2 all are normally distributed under the above three cases.