### Smoothing Class.


### Attach the dataset
attach(FinMark)
par(mfrow=c(1,1))

### Plot 1. Monthly returns.
plot(Time, VW.Return,main="Monthly returns")
 
### Plot 2. Monthly returns squared.
plot(Time, VW.Return.Sq, main="Monthly returns squared")

### Plot 3. log Monthly returns squared.
eps <- 0.00000001
plot(Time, log(VW.Return.Sq + eps),main="Log of the squared returns")

### Plot 4. The spline smooth to log Monthly returns squared.
plot(Time, log(VW.Return.Sq + eps),main="Log of the squared returns with spline smooth")
par(col=2,lwd=4)
lines(smooth.spline(Time, log(VW.Return.Sq + eps)))
par(col=1,lwd=1)

### Plot 5. A variety of smooths.
par(mfrow=c(3,3))
for(i in 1:9)
{
plot(smooth.spline(Time, log(VW.Return.Sq + eps),df=2^i),xlab="Date",
ylab="Volatility",type="n",main=paste("Spline smooth with e.d.f. = ",2^i))
lines(smooth.spline(Time, log(VW.Return.Sq + eps),df=2^i))
}

par(mfrow=c(1,1))


### Make a function to do Tukey's smoother.

t.smooth <- function(x,w=1)
	{
		y <- x
                option.width <- w
		for(i in (1+w):(length(x) - w))
			{
				y[i] <- median(c(x[(i-w):(i+w)]))	
			}
	if(sum((y-x)^2) < 0.00000001){return(y);break()}
                t.smooth(y, option.width)
}	

par(col=1,lwd=1)
par(mfrow=c(1,1))
### Plot 6, Tukey's smooth.
plot(Time,t.smooth(log(VW.Return.Sq + eps),w=1),main="Tukey's smooth,w=1")
par(col=2,lwd=2)
lines(Time,t.smooth(log(VW.Return.Sq + eps),w=1))

### Plot 7. Another Tukey smooth.
par(col=1,lwd=1)
plot(Time,t.smooth(log(VW.Return.Sq + eps),w=10),main="Tukey's smooth,w=10")
par(col=2,lwd=2)
lines(Time,t.smooth(log(VW.Return.Sq + eps),w=10))
par(col=1,lwd=1)


### Another version of Tukey's smooth built into S-Plus
### Graph 8
plot(Time,smooth(log(VW.Return.Sq + eps)),main="S-Plus Tukey smooth")
par(col=2,lwd=2)
lines(Time,smooth(log(VW.Return.Sq + eps)))
par(col=1,lwd=1)



### Graph 9. Lowess smoothing. (Robust local linear fits)

plot(Time,log(VW.Return.Sq + eps),main="Lowess smooth, default")
par(col=2,lwd=4)
lines(lowess(Time,log(VW.Return.Sq + eps)))
par(col=1,lwd=1)



### Plot 10. A variety of lowess smooths.
par(mfrow=c(3,3))
for(i in 0:8)
{
plot(lowess(Time, log(VW.Return.Sq + eps),f=1/(2^i)),xlab="Date",
ylab="Volatility",main=paste("Lowess smooth, span = 1/",(2^i)),type="n")
lines(lowess(Time, log(VW.Return.Sq + eps),f=1/(2^i)))
}

par(mfrow=c(1,1))
### Plot 11. Finally the super-smoother. Locally adaptive band-width
plot(Time,log(VW.Return.Sq + eps),main="Super smooth, default")
par(col=2,lwd=4)
lines(supsmu(Time,log(VW.Return.Sq + eps)))
par(col=1,lwd=1)



### Plot 12. A variety of supsmu smooths.
par(mfrow=c(3,3))
for(i in 0:8)
{
plot(supsmu(Time, log(VW.Return.Sq + eps),span=1/(2^i)),xlab="Date",
ylab="Volatility",main=paste("Super smooth, span=1/",(2^i)),type="n")
lines(supsmu(Time, log(VW.Return.Sq + eps),span=1/(2^i)))
}