The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Non-linear Time Series Analysis

  • Bruce Mizrach
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2302

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, …, xtp) + σ(xt)εt, where \( {\left\{{x}_t\right\}}_{t=0}^{\infty } \) is a zero mean, covariance stationary process, f : Rp+1R, 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.

Keywords

Chaos Cointegration Ergodicity Forecasting GARCH models Inference Kernel estimators Linear models Lyapunov exponents Markov switching models Nonlinear time series analysis Nonparametric estimation Piecewise linear models Regime dependence Regime switching Representation theory Stochastic volatility models Testing Threshold autoregressions Volterra expansion Wavelets 
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Notes

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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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Bruce Mizrach
    • 1
  1. 1.