## ---------------------------------------------------------------------------------------
# Example to show how the PACF is calculated
set.seed(972)
n <- 1000
x <- arima.sim(list(ar=c(0.5,-0.4)), n=n)
#acf(x)
#pacf(x)
library(onlineforecast)
D <- lagdf(c(x), 0:50)

# A way to calculate the PACF
lag.max <- 10
pacf1 <- numeric(lag.max)
# First, calculate it with the function
val <- pacf(x, lag.max, plot=FALSE)
# Then calc on our own
for(k in 1:lag.max){
  (frml <- pst("k0 ~ 1 + ",pst("k",1:k, collapse=" + ")))
  fit <- lm(frml, D)
  pacf1[k] <- fit$coef[pst("k",k)]
}


## ----fig.height=0.8*figheight-----------------------------------------------------------
# It's very close!
pacf1 - val$acf
plot(val$acf, type="b", xlab="lag", ylab="PACF")
lines(pacf1, type="b", col=2)


## ----acf-nonstat,dev="tikz",echo=FALSE,fig.height=0.9*textheight------------------------
set.seed(29)
acf(arima.sim(model = list(ar = 0.6,order=c(1,1,0)),n= 500),type="covariance")