Volatility processes and volatility forecast with long memory

  title={Volatility processes and volatility forecast with long memory},
  author={Gilles Zumbach},
We introduce a new family of processes that include the long memory (power law) in the volatility correlation. This is achieved by measuring the historical volatilities on a set of increasing time horizons and by computing the resulting effective volatility by a sum with power law weights. The processes have 2 parameters (linear processes) or 4 parameters (affine processes). In the limit where only one component is included, the processes are equivalent to GARCH(1,1) and I-GARCH(1). Volatility… CONTINUE READING