where {at} ∼ W N (0, σ2), in which ‘WN’ means white noise.Whatis the unconditional mean and unconditional variance of the series {Xt}?
Due on November 3th before class
{23.32 32.33 32.88 28.98 33.16 26.33 29.88
32.69 18.98 21.23 26.66 29.89}
Question: Calculate the lag-k sample autocorrelation of the time series for k = 1, 2, 3.
Xt = at + αat−1,
where {at} ∼ W N (0, σ2), in which ‘WN’ means white noise.
(a) rt − 0.5rt−1 = at,
(b) rt − 1.3rt−1 + 0.4rt−2 = at.
i.i.d. N (0, 1).
(a)rt= at − at−3,
(b)rt= t + at,
(c)rt= a2.
/or invertible:
(a) (1 − 0.8B)rt = (1 − 0.5B)at,
(b) (1 − 0.6B)rt = (1 − 1.2B + 0.2B2)at.
(a) (1 − 0.9B)(rt − 10) = at,
(b) rt = 10 − 0.9at−1 + at,
where at ∼ N (0, σ2) with σ2 = 2. Given r1 = 1.2 and r2 = 0.1, find the
l−step ahead forecast values and 95% forecast intervals for l = 1, 2, 3, 4.