BIOL 335 Lecture Notes - Lecture 13: Moving-Average Model, White Noise, Correlogram
Document Summary
Suppose {zt} is white noise with mean zero and variance 2. We have seen that a process {xt} is said to be a moving average process of order q, denoted ma(q), if. Xt = 0zt + 1zt 1 + + qzt q for some constants 0, 1, . This activity concerns a special case of the model above with q , 0 = 1 and i = i for i 1, speci cally. | |< 1, otherwise the sum diverges: show that xt = xt 1 + zt. Zt =xt (cid:0) zt 1 + 2zt 2 + (cid:1) =xt (zt 1 + zt 2 + ) =xt xt 1: we call {xt} an autoregressive process of order 1, denoted ar(1) . Each value in the series is modelled as the previous value plus noise. E (xt) =e(cid:0)zt + z (t 1) + 2zt 2 + (cid:1) =e (zt) + e ( zt 1) + e(cid:0) 2zt 2(cid:1) + .
