English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Fractionally integrated generalized autoregressive conditionalheteroskedasticity (FIGARCH) arises in modeling of financial time series.FIGARCH is essentially governed by a system of nonlinear stochastic differenceequations ${u_t}$ = ${z_t}$ $(1-\sum\limits_{j=1}^q \beta_j L^j)\sigma_{t}^2 =\omega+(1-\sum\limits_{j=1}^q \beta_j L^j - (\sum\limits_{k=1}^p \varphi_k L^k)(1-L)^d) u_t^2$, where $\omega\in$ R, and $\beta_j\in$ R are constantparameters, $\{u_t\}_{{t\in}^+}$ and $\{\sigma_t\}_{{t\in}^+}$ are the discretetime real valued stochastic processes which represent FIGARCH (p,d,q) andstochastic volatility, respectively. Moreover, L is the backward shiftoperator, i.e. $L^d u_t \equiv u_{t-d}$ (d is the fractional differencingparameter 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 (FalseNearest Neighbour), the Lyapunov exponents, and for both the stochasticdifference equation given above and for the financial time series. We haveobserved that maximal Lyapunov exponents are negative, therefore, it can besuggested that FIGARCH (p,d,q) is not deterministic chaotic process.

Chaos in Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastic Processes