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.