Detecting Nonlinearity in Time Series: Surrogate and Bootstrap Approaches

Detecting nonlinearity in financial time series is a key point when the main interest is to understand the generating process. One of the main tests for testing linearity in time series is the Hinich Bispectrum Nonlinearity Test (HINBIN). Although this test has been succesfully applied to a vast number of time series, further improvement in the size power of the test is possible. A new method that combines the bispectrum and the surrogate method and bootstrap is then presented for detecting nonlinearity, gaussianity and time reversibility. Simulated and real data examples are given to demonstrate the efficacy of the new tests.