# 1.2 Linear Filtering of Time Series (Solution to Homework)

 
# Ex. 1.9 (Public Expenditures Data) West Germany's public expenditures (in billion D-Marks) 
# between 1961 and 1990. Compute simple moving averages of order 3 and 5 to estimate a possible
# trend. Plot the original data as well as the filtered ones and compare the curves.
pubexpen <- ts(read.table("pubexpen.txt")[,2],start=1961)
pubexpen
pubexpen.star.3 <- filter(pubexpen,filter=c(1,1,1)/3)
pubexpen.star.5 <- filter(pubexpen,filter=c(1,1,1,1,1)/5)
plot(pubexpen)
lines(pubexpen.star.3,col="red")
lines(pubexpen.star.5,col="blue")