title: ARIMA(2,0,1) with Monte Carlo Simulation in R, always show zero initial values, why?
body: <p>I have the following R code for using Monte Carlo simulation with ARIMA(2,0,1), but the code is not working, can someone please help out? Many thanks!</p>
  
  <p>I want to simulate 52 weeks ahead for 1000 times.</p>
  
  <pre><code>ar1 = 0.4857
  ar2 = 0.0173
  ma1 = -0.8054
  r0 &lt;-  0.002937432
  
  r.sims &lt;- matrix(rep(0,1000*52),nrow=52, ncol=1000)
  e &lt;- rnorm(52*1000, mean =  0.002976873, sd = 0.1056021)
  
  r.sims[1] &lt;- ar1*r0 + e[1] + ma1*e[0]
  r.sims[2] &lt;- ar1*r.sims[1] + ar2*r0 + e[2] + ma1*e[1]
  
  
  for(j in 1:1000){
      for(i in 1:52){
  
          r.sims[i] &lt;- r.sims[i-1]*ar1 + r.sims[i-2]*ar2 + e[i] + e[i-1]
  
  
  }
  }
  </code></pre>
  
  <p>Hi everyone, I have modified the R-code, they seem to run, but slight problems with initial values being zeros, can anyone help please?</p>
  
  <pre><code>r.sims &lt;- matrix(rep(0,1000*52),nrow=52, ncol=1000)
  e.sims &lt;- matrix( rnorm(52*1000, mean =  0.002976873, sd = 0.1056021), 52, 1000) 
  
  r.sims[1] &lt;- ar1*r0 + e.sims[1] + ma1*e0
  r.sims[2] &lt;- ar1*r.sims[1] + ar2*r0 + e.sims[2] + ma1*e.sims[1]
  
  for(j in 1:1000){
  
                for(i in 3:52)
  
                  r.sims[i,] &lt;- r.sims[i-1,]*ar1 + r.sims[i-2,]*ar2 + e.sims[i,] + e.sims[i-1,]
  
  }
  
  
            [,996]       [,997]       [,998]        [,999]      [,1000]
   [1,]  0.000000000  0.000000000  0.000000000  0.0000000000  0.000000000
   [2,]  0.000000000  0.000000000  0.000000000  0.0000000000  0.000000000
   [3,]  0.010016382  0.062227948  0.091050851  0.2800012622  0.066996876
   [4,]  0.176391453  0.209624874 -0.085862618  0.1604297614  0.096992283
   [5,]  0.083494205  0.353051231 -0.292593785 -0.1443630697  0.200975961
   [6,] -0.011723566  0.477519286 -0.415555028 -0.2725228872  0.199274345
   [7,]  0.148164653  0.509141653 -0.202830713 -0.2986390235 -0.013175047
   [8,] -0.022379916  0.431266718 -0.020794588 -0.1296328172 -0.038491656
   [9,] -0.161865835  0.231474893 -0.043960056  0.2651309362  0.053714510
  [10,] -0.218850909  0.038706080  0.162595635  0.2791854517 -0.029590991
  </code></pre>