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A new comprehensive approach to nonlinear time series analysis and modelingis developed in the present paper. We introduce novel data-specificmid-distribution based Legendre Polynomial (LP) like nonlinear transformationsof the original time series Y(t) that enables us to adapt all the existingstationary linear Gaussian time series modeling strategy and made it applicablefor non-Gaussian and nonlinear processes in a robust fashion. The emphasis ofthe present paper is on empirical time series modeling via the algorithmLPTime. We demonstrate the effectiveness of our theoretical framework usingdaily S&P 500 return data between Jan/2/1963 - Dec/31/2009. Our proposed LPTimealgorithm systematically discovers all the `stylized facts' of the financialtime series automatically all at once, which were previously noted by manyresearchers one at a time.

Nonlinear Time Series Modeling: A Unified Perspective, Algorithm, and Application