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Transfer function model. Y(t) =  +  u a(t-u) X(u) +  (t)

Transfer function model. Y(t) =  +  u a(t-u) X(u) +  (t) dZ Y (  ) = A(  ) dZ X (  ) + dZ  (  ) Y(t) =  exp{it } dZ Y (  ) Gas furnace data - Box & Jenkins Sampling interval 9 sec., observations for 296 pairs of data points

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Transfer function model. Y(t) =  +  u a(t-u) X(u) +  (t)

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  1. Transfer function model. Y(t) =  + u a(t-u) X(u) + (t) dZY() = A() dZX() + dZ( ) Y(t) =  exp{it}dZY() Gas furnace data - Box & Jenkins Sampling interval 9 sec., observations for 296 pairs of data points X: 0.60 of input - 0.04 (input gas rate in cuft/min) Y: % CO2 in outlet gas

  2. Time side inference. Comparing alternate models. Supose there are J AICj = -2 log L(Ĝj ) + 2 sj sj is the number of paremeters in Gj There is also BICj = -2 log L(Ĝj ) + sj log nj Fundamental contributions of statistics

  3. bootstrap-like

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