title: How to simulate Arima-Garch models in R?
body: <p>I was trying to find how may I simulate (i.e. generate ARIMA in the mean model and a GARCh in the variance model) in R. </p>
  
  <p>I tried searching online but I only found how to fit such a model using </p>
  
  <pre><code>spec &lt;- ugarchspec( variance.model = list(   
                                              model = "sGARCH", 
                                               garchOrder = c(1, 1),
                                               submodel = NULL, 
                                               external.regressors = NULL, 
                                               variance.targeting = FALSE),
  
                                               mean.model = list(  armaOrder = c(1, 1), 
                                                                   include.mean = TRUE, 
                                                                   archm = FALSE,
                                                                   archpow = 1, 
                                                                   arfima = FALSE, 
                                                                   external.regressors = NULL, 
                                                                   archex = FALSE),
                                                                   distribution.model = "norm", 
                                                                   start.pars = list(), 
                                                                   fixed.pars = list()
                      )
  </code></pre>
  
  <p>Then I write </p>
  
  <pre><code>garch &lt;- ugarchfit(spec = spec, data = data, solver.control = list(trace=0))
  </code></pre>
  
  <p>This is obviously fitting and not simulating i.e. generating random variables.</p>