For example, for an MA(2) process 1+61+2] 1+B261]a2 0 For any value of (01, 82,,0g), the MA(q) process is thus weakly-stationary 1.2.2 Check Ergodicity It is clear that the condition ∑hl<∞ satisfied. Thus the MA(g process is ergodic 1.2.3 The Dependence Structure The autocorrelation function is zero after q lags. See the plots of p 50 1.3 The Infinite-Order Moving Average Process A stochastic process Yt, tET) is said to be an infinite-order moving average process (MA(oo)) if it can be expressed in this form Y=+∑9=1=1+901+91-1+2-2+ are constants with o=l and Et is a white-noise process 1.3.1 Is This a Well Defined Random Sequence? A sequence pi lio is said to be square-summable if ∑y<∞For example, for an MA(2) process, γ0 = [1 + θ 2 1 + θ 2 2 ]σ 2 γ1 = [θ1 + θ2θ1]σ 2 γ2 = [θ2]σ 2 γ3 = γ4 = .... = 0 For any value of (θ1, θ2, ..., θq), the MA(q) process is thus weakly-stationary. 1.2.2 Check Ergodicity It is clear that the condition X∞ j=0 |γj | < ∞ is satisfied. Thus the MA(q) process is ergodic. 1.2.3 The Dependence Structure The autocorrelation function is zero after q lags. See the plots of p.50. 1.3 The Infinite-Order Moving Average Process A stochastic process {Yt , t ∈ T } is said to be an infinite-order moving average process (MA(∞)) if it can be expressed in this form Yt = µ + X∞ j=0 ϕjεt−j = µ + ϕ0εt + ϕ1εt−1 + ϕ2εt−2 + ..... where µ, ϕ0, ϕ1, ϕ2, ..., are constants with ϕ0 = 1 and εt is a white-noise process. 1.3.1 Is This a Well Defined Random Sequence? A sequence {ϕj} ∞ j=0 is said to be square-summable if X∞ j=0 ϕ 2 j < ∞, 4