  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 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 demonstrate the effectiveness of our theoretical framework using
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 financial
time series automatically all at once, which were previously noted by many
researchers one at a time.
