Therefore E(Y,-HEt=E(e2) and when j>0, it is obvious that E(Yt-i-uEt=0 Therefore we the results that for j=0 pyo, forj=l and fo That is Beside yo, we need first moment (1) to solve ?o 2.2 The Second-Order Autoregressive Process A stochastic process Yt, tET) is said to be a second order autoregressive process(AR(2)if it can be expressed in the form Yt=c+orYt-1+o2Yt-2+Et where C, 1 and o are constants and Et is a white-noise process 2.2.1 Check Stationarity and Ergodicity Write the AR(2) process is lag operator form: Yt=c+oILY+o2L Yt+ thenTherefore, E(Yt − µ)εt = E(ε 2 t ) = σ 2 , and when j > 0, it is obvious that E(Yt−j − µ)εt = 0. Therefore we the results that γ0 = φγ1 + σ 2 , for j = 0 γ1 = φγ0, for j = 1 and γj = φγj−1, for j > 1. That is γ0 = φφγ0 + σ 2 = σ 2 1 − φ 2 . Beside γ0, we need first moment (γ1) to solve γ0. 2.2 The Second-Order Autoregressive Process A stochastic process {Yt , t ∈ T } is said to be a second order autoregressive process (AR(2)) if it can be expressed in the form Yt = c + φ1Yt−1 + φ2Yt−2 + εt , where c, φ1 and φ2 are constants and εt is a white-noise process. 2.2.1 Check Stationarity and Ergodicity Write the AR(2) process is lag operator form: Yt = c + φ1LYt + φ2L 2Yt + εt , then (1 − φ1L − φ2L 2 )Yt = c + εt . 11