Consider the model Yt = βYt-1 + g(Yt-2) + εt for 3 ≤ t ≤ T . Here g is an unknown function,β is an unknown parameter, εt are i.i.d. random errors with mean 0 and variance σ2 and the fourth moment c4, and εt are independent of Ys for all t ≥ 3 and s = 1,2.Pseudo-LS estimators (σ)2T, (α)4T and (D)2T of σ2, α4 and Var(ε23) are respectively constructed based on piecewise polynomial approximator of g. The weak consistency of (α)4T and (D)2T are proved. The asymptotic normality of (α)2T is given, i.e., (√T)((σ)2T- σ2)/(D)T converges in distribution to N(0,1). The result can be used to establish large sample interval estimates of σ2 or to make large sample tests for σ2.
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