# Example R code for STAT 520 HW 2

#1

library(astsa);data(cmort)

temp = tempr-mean(tempr) # center temperature
temp2 = temp^2
trend = time(cmort) # time
fit = lm(cmort~ trend + temp + temp2 + part, na.action=NULL)
summary(fit) # regression results
AIC(fit) # AIC
BIC(fit) # BIC

card.mort = ts.intersect(cmort, temp, temp2, trend, part, partL4=lag(part,-4))
summary(fit1 <- lm(cmort~ temp+ temp2+ trend+ part+ partL4,data=card.mort,na.action=NULL))
AIC(fit1)
BIC(fit1)



#3
library(TSA); data(prescrip)


#(b)
har.=harmonic(prescrip,m=1) 

model.har.pre=lm(prescrip~har.+time(prescrip))


#(g)

lin.trend=lm(prescrip~time(prescrip))

month.=season(prescrip) 

model2=lm(resid(lin.trend)~month.-1) # -1 removes the intercept term 
summary(model2)

AIC(model.har.pre)
BIC(model.har.pre)

AIC(model2)
BIC(model2)