#Chapter 4

## TAR example:
n=200 #nr observations
shocks=rnorm(n)

next.obs=function(x,a){ifelse(x<0,-1.5*x+a,0.5*x+a)}

x=0
for (i in 1:n)
{x=c(x,next.obs(x[i],shocks[i]))}

plot(x, type="l")
abline(0,0)

## Neural Network stuff:

# You need to install this library:
library(nnet)

#We use daily intel data
intel.daily=read.csv("DailyINTCfrom2000.csv",header=T)
intel.prices=intel.daily$Adj.Close[length(intel.daily$Adj.Close):1]
library(fBasics)
intel.returns=returns(intel.prices)[-1]

#Separate data:
length(intel.returns)
## The last 60 observations are from April 30 to present -we will use these for testing (because of the crazy last year)
## I am going to use the first 2340 observations for training  and the rest for testing.
pacf(intel.returns[1:2340])
#We will only use the 3 lags as inputs:
intel.x=cbind(intel.returns[1:2337],intel.returns[2:2338],intel.returns[3:2339])
y=intel.returns[4:2340] # the output

# Now we need to build the neural network.
# The size of the hidden layer is not specified. We will use 10 just because it is a round number.
# We want to predict a single number so we need only one node for the output

#In general any neural network algorithm is very slow but the one build in R
#is actually using C routines and it is surprisingly fast

intel.nnet=nnet(intel.x,y, size=10, linout=T, decay=0.01, maxit=1000)
## intel.x is the matrix containing the values for the input nodes as lines
## y is the output node values also as lines
## size specifies the hidden layer size
## linout=T tells R to use linear functions for the second activation function.
## linout=F means use the logistic function
## decay= 0.001 is the step used when learning the weights
## maxit sets up a maximum number of iterations for the convergence of the algorithm

summary(intel.nnet) ## this shows the nodes and the weights

## We can look at the predicted values versus the true values:
plot(y,predict(intel.nnet,intel.x), main="Neural Net Results",xlab="True",ylab="NN predictions")
abline(h=0,v=0); abline(0,1,lty=2) ## the later plots the 45 degree line. The points should have been close to this line

#In general it is better to center the variables before using them in neural networks, however these are adjusted returns and their mean is pretty close to zero.

#How about the sum of squares for the predicted values:

intel.p=cbind(intel.returns[2338:2401],intel.returns[2339:2402],intel.returns[2340:2403])
y.pred=predict(intel.nnet,intel.p)
y.obs=intel.returns[2340:2403] #observed values

# sum of squares:
sum((y.pred-y.obs)^2)

## What about using more inputs (recall the pacf showed evidence of lag 13 and lag 16 being significant too
## What about using more or less nodes in the hidden layer
## What about using a logistic function for the second activation function
## How does this compare with the ARMA models?

## actually about the last question:
intel.ar=ar(intel.returns[1:2339])
intel.ar.pred= predict(intel.ar,n.ahead=64)$pred

sum((y.obs-intel.ar.pred)^2)   ## this is actually better