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A Class of Stochastic Processes
Chapter 3 Asymptotic Normality of the Autoregressive
3 other sections not shown
a a R(k-j A=N+l arbitrary implies assumed that f Asymptotic Normality asymptotic variance autoregressive spectral estimator bias error Borel sets Chapter Choose an arbitrary coincides a.e. conjugate transpose continuous function convergence is uniform covariance averaging kernel Covariance Function covariance-stationary Define Doctor of Philosophy E E E E E E E equations error and asymptotic exists a positive exists a sequence Finite Order Autoregressive fixed fM(X Furthermore Hence implies fM implies there exists imply 00 integer iterated limit J-it j=l J j=l Lebesgue measure lim lim multivariate normal distribution oo oo Order Autoregressive Processes P^v+N+l p=N+l pair T,M Parzen positive and bounded positive real number proof of Lemma radius of convergence Section 3.1 stationary process Stochastic Process strictly positive definite T-l Q-v Q-v T-l T Q T+v Q+v Theorem 3.9 true unit circle windowed spectral estimator zero-mean