Chaos in Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastic Processes

2016/01/29 by Yilmaz, Adil, Unal, Gazanfer
#37D45 #39A50 #62M10 #91G80 #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Other Statistics (stat.OT) #Statistical Finance (q-fin.ST)

paper · doi:10.48550/arxiv.1601.08099

Abstract

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-∑_j=1^q β_j L^j)σ_t² = ω+(1-∑_j=1^q β_j L^j - (∑_k=1^p φ_k L^k) (1-L)^d) u_t², where ω∈ R, and β_j∈ R are constant parameters, \u_t\_t∈⁺ and \σ_t\_t∈⁺ 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 ≡ u_t-d (d is the fractional differencing parameter 0

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