Nonlinear Time Series Modeling by LPTime, Nonparametric Empirical Learning
Subhadeep Mukhopadhyay, Emanuel Parzen · arXiv (Cornell University) · 2013
We describe a new comprehensive approach to nonlinear time series analysis and modeling based on recently developed theory on unied algorithms of data science via LP modeling. We introduce novel data-specic mid-distribution based Legendre Polynomial(LP) like nonlinear transformations of the original time series fY (t)g that enables us to adapt all the existing stationary linear Gaussian time series modeling strategy and made it applicable for 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 describe each stage of the model building process, associated theoretical concepts and illustrate with daily S&P 500 return data between Jan/2/1963 - Dec/31/2009. Our proposed LPTime algorithm systematically discovers all the ‘stylized facts’ of the nancial time series automatically all at once, which were previously noted by many researchers one at a time.