  Fractionally integrated generalized autoregressive conditional
heteroskedasticity (FIGARCH) arises in modeling of financial time series.
FIGARCH is essentially governed by a system of nonlinear stochastic difference
equations ${u_t}$ = ${z_t}$ $(1-\sum\limits_{j=1}^q \beta_j L^j)\sigma_{t}^2 =
\omega+(1-\sum\limits_{j=1}^q \beta_j L^j - (\sum\limits_{k=1}^p \varphi_k L^k)
(1-L)^d) u_t^2$, where $\omega\in$ R, and $\beta_j\in$ R are constant
parameters, $\{u_t\}_{{t\in}^+}$ and $\{\sigma_t\}_{{t\in}^+}$ are the discrete
time real valued stochastic processes which represent FIGARCH (p,d,q) and
stochastic volatility, respectively. Moreover, L is the backward shift
operator, i.e. $L^d u_t \equiv u_{t-d}$ (d is the fractional differencing
parameter 0$<$d$<$1).
  In this work, we have studied the chaoticity properties of FIGARCH (p,d,q)
processes by computing mutual information, correlation dimensions, FNNs (False
Nearest Neighbour), the Lyapunov exponents, and for both the stochastic
difference equation given above and for the financial time series. We have
observed that maximal Lyapunov exponents are negative, therefore, it can be
suggested that FIGARCH (p,d,q) is not deterministic chaotic process.
