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- W2046009064 abstract "Philippe et al. [9], [10] introduced two distinct time-varying mutually invertible fractionally integrated filters A(d), B(d) depending on an arbitrary sequence d = (d t ) t∈ℤ of real numbers; if the parameter sequence is constant d t ≡ d, then both filters A(d) and B(d) reduce to the usual fractional integration operator (1 − L)−d . They also studied partial sums limits of filtered white noise nonstationary processes A(d)ε t and B(d)ε t for certain classes of deterministic sequences d. The present paper discusses the randomly fractionally integrated stationary processes X = A(d)ε t and X = B(d)ε t by assuming that d = (d t , t ∈ ℤ) is a random iid sequence, independent of the noise (ε t ). In the case where the mean $$bar d = mathbb{E}d_0 in left( {0,1/2} right)$$ , we show that large sample properties of X A and X B are similar to FARIMA(0, $$bar d$$ , 0) process; in particular, their partial sums converge to a fractional Brownian motion with parameter $$bar d + (1/2)$$ . The most technical part of the paper is the study and characterization of limit distributions of partial sums for nonlinear functions h(X ) of a randomly fractionally integrated process X with Gaussian noise. We prove that the limit distribution of those sums is determined by a conditional Hermite rank of h. For the special case of a constant deterministic sequence d t , this reduces to the standard Hermite rank used in Dobrushin and Major [2]." @default.
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- W2046009064 date "2007-01-01" @default.
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- W2046009064 title "Randomly fractionally integrated processes" @default.
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