ETF5200: Applied Time Series Econometrics

  Consider a general time series model of the form Yt = mt + st + et  , (1) where {mt} is the trend component of the form mt = ?0+?1 (t?12)+?2 (t?12)2  with ?i 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.