Reliable data analysis is one of the hardest tasks in sciences and social
sciences. Often misleading and sometimes puzzling results arise when the
analysis is done without regard for the special features of the data. In this
exposition, I will focus on designing new statistical tools to deal with some
prominent questions in Finance and Economics. In particular, I will talk about
the following. (1) How to characterize the randomness of variables, motivated by
a problem in the pricing of financial options. (2) Uncovering the relation between
interest rates on different maturities, now and in the future; the "term structure
of interest rates". (3) Modelling the unconventional nonlinear long-memory
dynamics that arise from a general-equilibrium economic model, and their
implications for exchange rates, stock market indexes, and all macroeconomic
variables; with recommendations for trading in financial markets, but also for
the design of macroeconomic stabilization policies by governments.