Consider a general time series model of the form

Yt = mt + st + et  , (1)

where {mt} is the trend component of the form mt = θ0+θ1 (t−12)+θ2 (t−12)2  with θi 6= 0 (i = 0, 1, 2) being unknown parameters, {st} is the seasonal component satisfying st+12 = st and P12 j=1 sj = 0, and {et} is a sequence of stationary residuals with E[e1] = 0 and E[e1]

(a) Is {Yt} stationary ? Give your reasoning.

(b) Is the first–order differenced version of Yt, Zt = 512Yt = Yt − Yt−12,stationary ? Give your detailed reasoning.

(c) Is the second–order differenced version of Yt,Wt stationary ? Give your detailed reasoning.

 

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