Higher-order spectral based tests of Gaussianity, linearity, and stationarity in stock returns

This paper presents empirical examinations of three important aspects of stock returns: Gaussianity, linearity, and stationarity by applying time series tests based upon the higher-order spectra. If the stationary time series is Gaussian, the second order spectrum contains all the useful information present in the series. If the series is non-Gaussian, the second order spectrum will not adequately characterize the series. Therefore, it is necessary to consider higher order spectral analysis. The tests are applied using daily stock market returns from Taiwan and Korea, weekly stock returns of five Thai companies, weekly stock market returns from Thailand, and lastly trade-by-trade stock returns of fifteen U.S. companies. We find that stationarity is rejected for trade-by-trade unaliased returns, and the aliasing problem should be considered more seriously when daily or weekly data is used in time series applications.