April 2008
Intermediate
832 pages
26h 2m
English
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Problems and Computer Projects
PROBLEMS
Problem X.1 (Forward and backward residuals) Assume the regressors have shift structure and use the following updates for the conversion factor from Table 40.1,
to establish the identity
Problem X.2 (Conversion factor) Show that 
.
Problem X.3 (Prediction vectors) Assume the regressors {uM,j} have shift structure. Use the discussion in Sees. 40.2–40.4, and the results of Lemmas 32.1 and 32.2, to argue that the weight prediction vectors 
satisfy the relations
Problem X.4 (Prediction errors) Introduce the shift operator q–lu(i) = u(i – 1). Applying an operator 
to a sequence u(i) results in 
. Show that the forward and backward prediction errors of order ...
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