### GAUSSIAN WHITE NOISE
N <- 300   ### try changing sample size N
W <- ts(rnorm(N))
plot(W,type="b",xlab="time")

acf(W,lag.max=100)




### MOVING AVERAGE
coeff <- rep(1,5) 

## `circular=TRUE' prevents NAs at the start of time-series
X <- filter(W,filter=coeff,sides=1,circular=TRUE) 
plot(X,type="b", xlab="time")

acf(X, lag.max=12)



### AUTO-REGRESSIVE
coeff <- 0.95
X <- filter(W,filter=coeff,sides=1,method="recursive",init=1)
plot(X,type="l", xlab="time")

acf(X, lag.max=10000)




### AUTO-REGRESSIVE with cyclic behaviour
coeff <- c(sqrt(2)/1.01,-1/1.01^2)
X <- filter(W,filter=coeff,sides=1,method="recursive",init=c(1,1))
plot(X,type="l", xlab="time")

acf(X, lag.max=50)





#### TEST FOR RANDOM INPUT
X <- sample( c(0,1), 2000, replace=TRUE)
acf(X,lag.max=5)



# use self-typed "random" input
X <- c(0,1,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,1,1,1,1,0,0,1,1,1,0,1,1,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,0,0)
acf(X,lag.max=5)



# easier input via character strings
XC <- "0001101010001011110101010101000010101000110101010011010100101101001000101110010101010010101010100111101010100000010101011110101010101010101010101111111111"
X <- as.numeric( strsplit(XC,"")[[1]])

acf(X,lag.max=5)