Analysis For Unit Root Model With A Change- Point In Variances

Consider a variance change at an unknown time k0 in the unit root model with an intercept,that is yt=α+ρyt-1+et, et=σ1ξtI{t≤k0}+σ2ξtI{t>k0},t=1.2……T, where I{.} denotes the indicator function and {ξt,t≥1} is a sequence of i.i.d. random variables with mean zeros and variance ones. We derive the limiting distributions of the least squares estimators of p and the statistics tT in this thesis. It is revealed that these limiting distributions are quite different from those with no variance change in the model. In this thesis, we proved that ρ converges to ρ in distributions with a speed of T3/2 and tT converges to a more complicated functional of Wiener process.