Gaussian Analysis of Non-Gaussian Time Series

A framework is proposed for the analysis of non-Gaussian time series under the Gaussian assumption. The analysis is based on the Gaussian autocorrelation computed from the transform of the sample autocorrelation. It is shown that this approach improves the linear autoregressive fit. We also use it to generate time series that preserve the original autocorrelation and marginal distribution and develop a combined test that discriminates whether a linear stochastic time series is a monotonic or non-monotonic transform of a Gaussian time series. The usefulness of the proposed analysis is demonstrated on stock exchange volumes of several world markets.