H18 - H18 Problem 1 Consider the following model X t = 0.8...

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H18 Problem 1 Consider the following model: 13 4 0.8 0.125 0.1 tt t t t X XX X −− =+ −+ Z . (a) Is the model stationary? (b) Find a state-space representation of the model. Problem 2 Find a state-space representation of the MA(2) process 11 2 2 t t X ZZ Z θ = ++ . Models for Changing Variance . The model is called homoscedastic if the variance is constant, and heteroscedastic when it is not. Example 1 Annual numbers of lynx trapped in the Mackenzie River district of Canada. Example 2 Dow Jones Industrial Index. An autoregressive conditional heteroscedastic (ARCH) model with order is defined as (1 ) p X t σε = and 22 01 1 p 2 t p X X σα α + + , where 0 i are constants, {}~ I ID ( 0 , 1 ) ε t , and t is independent of {, for all t .
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  • Spring '09
  • gUR
  • Stochastic process, Autocorrelation, Stationary process, Autoregressive moving average model, Mathematical terminology, Necessary and sufficient condition

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