Abstract
We have seen in Sect. 2.1.4 that nonlinear processes, due to their dependence on initial conditions, often magnify error causing unstable behavior. Even when stationary solutions exist, this noise magnification and dependence on initial conditions reflects on the tails of the stationary distribution, as well as on how large values cluster.
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Notes
- 1.
Extensions of Goldie and Grbel’s results, namely the connection between the tails of R and the behavior of A near 1, can be found in Hitczenko and Wesolowski (2009).
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Turkman, K.F., Scotto, M.G., de Zea Bermudez, P. (2014). Extremes of Nonlinear Time Series. In: Non-Linear Time Series. Springer, Cham. https://doi.org/10.1007/978-3-319-07028-5_3
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