A Nonlinear Time Series Workshop: A Toolkit for Detecting and Identifying Nonlinear Serial Dependence

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The complex dynamic behaviour exhibited by many nonlinear systems - chaos, episodic volatility bursts, stochastic regimes switching - has attracted a good deal of attention. This text aims to provide the reader with both the statistical background and the software tools necessary for detecting nonlinear behaviour in time series data. The most useful existing detection techniques are described, including Engle’s LaGrange Multiplier test for conditional hetero-skedasticity and tests based on the correlation dimension and on the estimated bispectrum. These techniques are illustrated using actual data from fields such as economics, finance, engineering, and geophysics.