Abstract
Since the early 1980s, there has been a growing interest in stochastic nonlinear dynamical systems of the form xt+1 = f (xt, xt−1, …, xt−p) + σ(xt)εt, where \( {\left\{{x}_t\right\}}_{t=0}^{\infty } \) is a zero mean, covariance stationary process, f : Rp+1 → R, σ is the conditional volatility, and \( {\left\{{\varepsilon}_t\right\}}_{t=0}^{\infty } \) is an independent and identically distributed noise process. The major recent developments in nonlinear time series are described using this canonical model: (a) representation theory; (b) nonparametric modelling; (c) ergodic properties; (d) piecewise linear models; (e) volatility modelling; (f) hypothesis testing for linearity and normality; (g) forecasting.
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Acknowledgment
I would like to thank Cees Diks, James Hamilton, Sebastiano Manzan, Simon Potter, Phil Rothman, Dick van Dijk and Steven Durlauf for helpful comments.
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Mizrach, B. (2018). Non-linear Time Series Analysis. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2302
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2302
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