title: Generate and estimate models like IGARCH, FIGARCH or HYGARCH
body: <p>my issue is that I'm trying to simulate modifications of GARCH model like <strong>IGARCH, FIGARCH or HYGARCH</strong>.
  I have already found that some of them is possible to generate in R (<em>rugarch</em> or (no more existing) <em>fSeries</em> package) or in Python (<em>arch</em> library). I will organize my questions into the following points:</p>
  
  <p><strong>1. How can I simulate an IGARCH model in Python?</strong></p>
  
  <p>I tried these two ways:</p>
  
  <p>1) used <em>GARCH.simulate</em> with fixed parameters where alfas and betas sum to 1. But there was an error 
        message about non-stationarity and it took intercept in order to initialize the model. And I'm not 
        sure if it is OK and the simulated series is still IGARCH (in my opinion it is only moved by 
        constant so it should have had no crucial effect). 
        I have also programmed my own function for GARCH simulation, and it works also for coefficients 
        that sum to 1. Hopefully, the implementation is good...The only restriction for IGARCH that 
        differentiates it from GARCH is that the sum of coefficients equals 1, right?.</p>
  
  <p>2) used <em>FIGARCH.simulate</em> with fixed parameters where d=1 which is a special case of FIGARCH models 
        which in that case become IGARCH(p,q) models. But the error there was *invalid value encountered in 
        sqrt: data[t] = errors[t] * np.sqrt(sigma2[t])*. </p>
  
  <p><strong>2. Is there any free software in which the HYGARCH is implemented? If not, could somebody advise me how 
           to implement that model in R or Python?</strong></p>
  
  <p>The model is already implemented in Ox Metrics 8, but it is a paid software. I found that the 
     interface to these Ox Metrics functions were implemented in the R package <em>fSeries</em> which, however 
     doesn't exist anymore and I'm not able to install the older version on my R version 3.5.1. And in 
     Python there is no such a model implemented.</p>
  
  <p><strong>3. Corresponds model specification "fgarch" in the function <em>ugarchspec(...)</em> of <em>rugarch</em> package in R to the FIGARCH model? If not, is FIGARCH implemented in the R software?</strong><br>
       My R Code is: </p>
  
  <pre><code> spec=ugarchspec(variance.model=list(model="fGARCH", garchOrder=c(1,1), submodel="GARCH"),
              mean.model=list(armaOrder=c(0,0), include.mean=TRUE), distribution.model="std",
              fixed.pars=list(mu=0.001,omega=0.00001, alpha1=0.05,beta1=0.90,delta = 0.00001,
                              shape=4))
  </code></pre>
  
  <p>I found somewhere on the Internet that there is also possible to specify "figarch" in upper function instead of "fgarch", but in that case I'm not able to simulate the path by using <em>ugarchpath(...)</em>.</p>
  
  <p>Thank you in advance! I need this for my master thesis so I appreciate any recommendations, advises etc.</p>
  
  <p>Domca</p>