Dear all
Many thanks to all of those who replied to my request for references re.
generating the transfer function. Here is a list (at the bottom of this
email). I would like to add that Box and Jenkins latest version of
'Time Series Analysis' has an excellent section on the topic.
In addition, I would like to ask for your views on the following which
again refers to input and output time series:
regarding dynamic modelling of the type: Yt = a + v0 Xt + v1
X(t-1)+v2 X(t-2) + b0 Z(t-4) + b1 Z(t-5) + Nt (model 1)
and regression modelling with ARIMA errors of the type ......Yt = a +
b1 Xt + b2 Zt + Nt (Model 2)
What happens if the output series is seasonal and the input series is
seasonal?
Texts seem to always refer to a case where the regression part of the
model is basically a *linear* function. I have read (SAS, ETS; 1994)
that if the model has an input which is related to an output then there
is no requirement for the input series to be stationary, only the
residual has to be stationary....therefore as long as this contraint is
true then this implies that we can retain the 'regression' part of the
model in the (linear) form as it appears in (1) and (2) above.
Is this correct?
My gut reaction when seeing a seasonal series is to replace the 'linear'
form in models (1) and (2) with a 'seasonal' regression part so that we
have the correct form for forecasting purposes but Makridakis et al.
1998 p.396 retain the linear form. If we *do* have to substitute the
regression part in models 1 and 2 with a seasonal form then how does it
effect the transfer function in its quotient/rational form?
Do you have any views on this?
Many thanks for your advice, Best Wishes,
Kim
*******************************************************
Here are the afore-mentioned references....
Pankratz "Forecasting with Dynamic Linear Regresion Models"
Makridakis et al., 1998 "Forecasting"
"SAS for Forecasting Time Series" by Blocklebank & Dickey
Downing, DJ, and Pack, D (1982)
The vanishing transfer function.
In Time Series Analysis, Theory and Practice 1, Ed OD Anderson,
Amsterdam: North Holland
Liu.. LM, and Hanssens, DM
Identiification of multiple input transfer function models.
Communication in Statistics, Theory and Methods, A, 11, 297-314
Liu.. LM, and Hanssens.. D
Identification of multiple input transfer function models via least
squares.
Technical Report No. 58,
BMDP Statistical Software, Los Angeles
"Applied Bayesian Forecasting and Time Series Analysis" by Pole, West
and Harrison.
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