This dissertation focuses on the mean reversion in macroeconomic and financial data using nonparametric estimation method. The first essay studies the recent attempts to solve the second form of the Purchasing Power Parity (PPP) puzzle (usually expressed as a half-life of 3∼5 years), mostly by using non-linear stochastic models of real exchange rates. Despite the introduction of non-linearities, the literature has continued to focus on the notion of "half-life" as a measure of persistence. We argue the half-life measure is only appropriate in linear settings, failing to capture the richness of non-linear dynamics introduced in the more recent literature. We conclude that depending on the models and criteria selected for investigating the PPP puzzle, the puzzle may be in the eye of the beholder. The second essay studies the convergence of per capita income across the world. The recent literature on "convergence" of cross-country per capita incomes has been dominated by the two hypotheses of "global convergence" vs. "club-convergence". Utilizing new measures of "stochastic stability", we establish two stylized facts that question the fruitfulness of the literature's focus on asymptotic income distributions. The first stylized fact is non-stationarity of transition dynamics, in the sense of changing transition kernels, thus making "convergence" hypotheses less meaningful. In the meantime, we find statistical support for a second stylized fact of emergence, disappearance, and re-emergence of a "stochastically stable" middle-income group. Moreover, the probability of escaping a low-income poverty-trap appears to depend significantly on the existence of such a stable middle-income group. The third essay studies the individual income convergence issue. The recent literature on 'global income distribution' has recently focused on 'individual income inequality' to account for the so-called China effect. We examine the robustness of various population weighting schemes that account for different country sizes in the study of income distribution dynamics. We apply our test of stochastic stability to within as well as between country income distribution dynamics, and find that the middle-income group's role in income distribution dynamics vanishes when we allow for very higher population weights for China and India.