ASYMPTOTIC NORMALITY OF PSEUDO-LS ESTIMATOR FOR PARTLY LINEAR AUTOREGRESSION MODELS

Consider the model Y-t=beta(t-1)+g(Y-t-2)+epsilon(t) for t greater than or equal to 3. Here g is an unknown function, beta is an unknown parameter to be estimated and epsilon(t) are i.i.d, random error with zero 0 and variance sigma(2) and epsilon(t) are independent of Y-s for all t greater than or equal to 3 and s=1,2. A class of asymptotically normal estimators of beta are directly obtained based on piecewise polynomial approximator g(T)(.) of g and the model Y-t-1=beta Y-t-1+g(T)(Y-t-2)+epsilon(t). The asymptotic normality of pseudo-LS (PLS) estimator beta(T) of beta and an estimator sigma(T)(2), of sigma 2 are investigated.