acf(yres1)
pacf(yres1)
##pacf disappears suggests an AR model

#fit ARMA model to data  MEAN =FALSE MEANS MEAN SET TO ZERO, COEFFICIENTS SHOULD BE LARGER THAN STANDARD ERRORS TO SHOW SIGNIFICANTLY DIFFERENT THAN ZERO
co2=arima(yres1,order=c(4,0,2),include.mean=FALSE)
co2
##check this is appropraite
#First Check diagnostics/ white-noiseness of residuals
tsdiag(co2)
# residuals are like white noise, as the sample acf is close to zero at lag 1 - middle plot
# bottom plot shows Ljung-Box statistics to lag 10 - set of p-values. These are high so residuals look like white noise.
#can run Ljung-box to different lag:
x=co2$residuals
p = rep(0, 10)
for (i in 1:10) {
  p[i] = Box.test(x, i, type = "Ljung-Box" )$p.value
}
p.min = .05 # level of significance
plot(p, ylim=c(0,1),main="p values for Ljung-Box statistic", xlab="lag",ylab="p value")
abline(h=p.min,col=4,lty=2)