Nonlinear time series modeling: A unified perspective, algorithm and application

A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution-based Legendre Polynomial (LP)-like nonlinear transformations of the original time series {Y(t)} that enable us to adapt all the existing stationary linear Gaussian time series modeling strategies and make them applicable to non-Gaussian and nonlinear processes in a robust fashion. The emphasis of the present paper is on empirical time series modeling via the algorithm LPTime. We demonstrate the effectiveness of our theoretical framework using daily S&P 500 return data between 2 January 1963 and 31 December 2009. Our proposed LPTime algorithm systematically discovers all the 'stylized facts' of the financial time series automatically, all at once, which were previously noted by many researchers one at a time.