#PROGRAM 6 - SIMULATING AND FORECASTING EWMA
#
# K. Ensor, ensor@rice.edu
# Rice University
#

# Let's first create a time series of length 
# Change the model as you would like by changing the
# set of specifications below. The final list, kmodel
# is the one that feeds into the other routines.

# Plotting function used later

prettyplot<-function(nrow,ncol){
	par(mfrow=c(nrow,ncol),omi=c(.5,1,.5,1))
}

kmodel<-list(ma=c(.2),ndiff=1,period=1) 

x<-rts(arima.sim(200,model=kmodel))
kdescripb(x,"Simulated ARIMA(0,1,1) Realization")

# Construct the one step ahead forecast throughout the series
kmodel.filt<-arima.filt(x,model=kmodel)

#Plot

prettyplot(1,1)
tsplot(1.1x, kmodel.filt$pred)
title(main="EWMA Prediction")

tsplot(x-kmodel.filt$pred)
title(main="One Step Ahead Residuals")

# How would you standardize the residuals?