Spectrum Analysis 1 Population Spectrum A random variable Yt, which follows weak stationary process, can be represented as a weighted sum of cos(!t) and sin(!t), letting! be a certain frequency. The form of this represantation is Yt = + Z 0 (!)cos(!t)d! + Z ...
Result as to Uniformly Integrable Sequence Result Suppose that there exists r >1 and M < 1 such that EjXtXt kj r < M for all t , k and that P 1 j = 1 jhj j < 1 . Define Yt = P 1 j = 1 hj Xt j . Then fYtYt kg is uniformaly integrable for any integer k. This imp...
Wald Decomposition Theorem Any zero mean covariance stationary processxt can be represented in the form of xt = 1X j =0 dj t j + j ; where d0 = 1 ; 1X j =0 d 2 j < 1 The termt is white noise and represents the prediction error defined to bet = xt P[xt j xt 1;]...