# Integer valued AR 1 

INAR = function(lambda,phi,n0,n){

         m = (n+n0)
    
      	y <- rep(0,m)
	w <- rpois(m,lambda)
        tmp <- rep(0,m)
         
        for(i in c(2:m)){

            tmp[i] = rbinom(n=1,size=y[i-1],p=phi)

            y[i] = tmp[i] + w[i]

        }

         y = y[-c(1:n0)]
          
         return(y)

     }
            

# For the INAR2 you need to be careful how to specify the parameters phi1 and phi2

INAR2 = function(lambda,phi1,phi2,n0,n){

         m = (n+n0)
    
      	y <- c(1,1,rep(0,(m-2)))
	w <- rpois(m,lambda)
        tmp <- rep(0,m)
        tmp2 <-rep(0,m)
         
        for(i in c(3:m)){

            tmp[i] = rbinom(n=1,size=y[i-1],p=phi1)

            tmp2[i] = rbinom(n=1,size=y[i-2],p=phi2)
            
            y[i] = (tmp[i] + tmp2[i] + w[i])

        }

         y = y[-c(1:n0)]
          
         return(y)

     }
      


test1 = INAR(lambda = 5,phi = 0.1, n0=100, n=100)

test2 = INAR(lambda = 5,phi = 0.5, n0=100, n=100)

test3 = INAR(lambda = 5,phi = 0.95, n0=100, n=100)

test4 = INAR2(lambda=5, phi1=0.5, phi2=0.5, n0=100,n=100)

# Make acf plots to check the correlation

#par(mfrow=c(2,1))

plot(c(1:100),test1)

plot(c(1:100),test2)

plot(c(1:100),test3)