Some Bootstrap Tests for Non-linearity and Long Memory in Financial Time Series

Understanding and forecasting financial time series depend crucially on identifying any non-linearity which may be present. Recent developments in tests for non-linearity very commonly display low power, most likely because of over-smoothing and discarding pertinent information. In this presentation, we present some bootstrap tests for non-linearity in a time series, and explain how it can assist in identifying the form of non-linearity. Our methods are based on higher-order moments of the time series of interest, and its bispectrum, being the Fourier transform of the third-order moment. As a by-product of the proposed tests, we identify signature behaviour of long memory, and discuss this observation particularly in the context of high-frequency econometric measurements.