Title: Simulate ARFIMA process with custom initial values
Tags: r
Question: My question deals with the fracdiff.sim function in R (in the fracdiff package) for which the help document, just like for arima.sim, is not really clear concerning initial values.
It's ok that stationary processes do not depend on their initial values when time grows, but my aim is to see in my simulations the return of my long memory process (fitted with arfima) to its mean.
Therefore, I need to input at least the p final values of my in-sample process (and eventually q innovations) if it is ARFIMA(p,d,q). In other words, I would like to set the burn-in period's length to 0 and give starting values instead.
Nevertheless, I'm currently not able to do this. I know that fracdiff.sim makes it possible for the user to chose the length of a burning period (which leads to the stationnary behavior) and the mean of the simulated process (it is simulated and then translated to make the means match). There is also a condition: the length of the burn-in period must be >= p+q. What I suppose is that there is something to do with the innov argument but I'm really not sure.
This idea is inspired by the arima.sim function which has a start.innov argument. However, even if my aim was to simulate an ARMA(p,q), I'm not sure of the exact use of this argument (the help is quite poor) : must we input only q innovations ? put with them the p last values of the in-sample process ? In which order ?
To sum up, I want to simulate ARFIMA processes starting from a specific value and having a specific mean in order to see the return to the mean and not only the long term behavior. I fund beginnings of solutions for arima.sim on the internet but nobody clearly answered, and if the solution uses start.innov, how to solve the problem for ARFIMA processes (fracdiff.sim doesn't have the start.innov argument) ?
Hopping I have been clear enough,
Comment: I know this is like 3 months too late, but you should try posting on: http://stats.stackexchange.com/



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