L does not equal 1.
L is the lag operator with specific properties.
Example:
c:constant, L*c=c
Yt: time series , L*Yt=Yt-1 etc (see any time series textbook for these)
Regarding your question since c(2) is a constant we write c(2)*L=c(2).
This applies to polynomials as well. If A(L)=1-a1*L-a2*L^2 then
A(L)*c=.=A(1)*c
Now if in the denominator c/(1-a*L)=c/(1-a).
Further, if |a|<1 then c/(1-a)=c*sum(a^j) for j=0 to infinity (series
property). Thus c/(1-a)= c*sum(a^j)=c*sum((aL)^j)=c*sum(a^j*L^j)
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Dr Ioannis A. Venetis
Assistant Professor
University of Patras, Department of Economic Sciences
University Campus, Rio, 26504, Greece
Tel: +30 2610 969 964
Ιωάννης Α. Βενέτης
Επίκουρος Καθηγητής
Τμήμα Οικονομικών Επιστημών, Πανεπιστήμιο Πατρών
Πανεπιστημιούπολη, Ρίο 26504
Τηλ: 2610 969 964
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