The standard square root process introduced by Feller (1951), used by Cox-Ingersoll-Ross (1985) and used for modeling stochastic volatility by Heston (1993) is the following
The Comte-Renault long-memory square root process comes out of two steps. First, they consider
which is equivalent to . Then they consider the long memory process as
where is the fractional integration operator. The variance and autocorrelations of they relate to the variance and autocorrelations of the square root process as follows.
(b) The autocorrelations are and
for small and
for large .
(c) The spectral density of is