This study analyzes the impact of the COVID-19 pandemic on currency circulation in Brazil by comparing actual data from 2000 to 2023 with counterfactual projections using the \textbf{SARIMA(3,1,1)(3,1,4)\textsubscript{12}} model. The model was selected based on an extensive parameter search, balancing accuracy and simplicity, and validated through the metrics MAPE, RMSE, and AIC. The results indicate a significant deviation between projected and observed values, with an average difference of R\$ 47.57 billion (13.95\%). This suggests that the pandemic, emergency policies, and the introduction of \textit{Pix} had a substantial impact on currency circulation. The robustness of the SARIMA model was confirmed, effectively capturing historical trends and seasonality, though findings emphasize the importance of considering exogenous variables, such as interest rates and macroeconomic policies, in future analyses. Future research should explore multivariate models incorporating economic indicators, long-term analysis of post-pandemic currency circulation trends, and studies on public cash-holding behavior. The results reinforce the need for continuous monitoring and econometric modeling to support decision-making in uncertain economic contexts.

The fast paced progress of artificial intelligence (AI) through scaling laws connecting rising computational power with improving performance has created tremendous technological breakthroughs. These breakthroughs do not translate to corresponding user satisfaction improvements, resulting in a general mismatch. This research suggests that hedonic adaptation the psychological process by which people revert to a baseline state of happiness after drastic change provides a suitable model for understanding this phenomenon. We argue that user satisfaction with AI follows a logarithmic path, thus creating a longterm "satisfaction gap" as people rapidly get used to new capabilities as expectations. This process occurs through discrete stages: initial excitement, declining returns, stabilization, and sporadic resurgence, depending on adaptation rate and capability introduction. These processes have far reaching implications for AI research, user experience design, marketing, and ethics, suggesting a paradigm shift from sole technical scaling to methods that sustain perceived value in the midst of human adaptation. This perspective reframes AI development, necessitating practices that align technological progress with people's subjective experience.

This paper proposes econometric methods for studying how economic variables respond to function-valued shocks. Our methods are developed based on linear projection estimation of predictive regression models with a function-valued predictor and other control variables. We show that the linear projection coefficient associated with the functional variable allows for the impulse response interpretation in a functional structural vector autoregressive model under a certain identification scheme, similar to well-known Sims' (1972) causal chain, but with nontrivial complications in our functional setup. A novel estimator based on an operator Schur complement is proposed and its asymptotic properties are studied. We illustrate its empirical applicability with two examples involving functional variables: economy sentiment distributions and functional monetary policy shocks.

The theory of optimal transportation has developed into a powerful and elegant framework for comparing probability distributions, with wide-ranging applications in all areas of science. The fundamental idea of analyzing probabilities by comparing their underlying state space naturally aligns with the core idea of causal inference, where understanding and quantifying counterfactual states is paramount. Despite this intuitive connection, explicit research at the intersection of optimal transport and causal inference is only beginning to develop. Yet, many foundational models in causal inference have implicitly relied on optimal transport principles for decades, without recognizing the underlying connection. Therefore, the goal of this review is to offer an introduction to the surprisingly deep existing connections between optimal transport and the identification of causal effects with observational data -- where optimal transport is not just a set of potential tools, but actually builds the foundation of model assumptions. As a result, this review is intended to unify the language and notation between different areas of statistics, mathematics, and econometrics, by pointing out these existing connections, and to explore novel problems and directions for future work in both areas derived from this realization.

In this article, we propose a novel logistic quasi-maximum likelihood estimation (LQMLE) for general parametric time series models. Compared to the classical Gaussian QMLE and existing robust estimations, it enjoys many distinctive advantages, such as robustness in respect of distributional misspecification and heavy-tailedness of the innovation, more resiliency to outliers, smoothness and strict concavity of the log logistic quasi-likelihood function, and boundedness of the influence function among others. Under some mild conditions, we establish the strong consistency and asymptotic normality of the LQMLE. Moreover, we propose a new and vital parameter identifiability condition to ensure desirable asymptotics of the LQMLE. Further, based on the LQMLE, we consider the Wald test and the Lagrange multiplier test for the unknown parameters, and derive the limiting distributions of the corresponding test statistics. The applicability of our methodology is demonstrated by several time series models, including DAR, GARCH, ARMA-GARCH, DTARMACH, and EXPAR. Numerical simulation studies are carried out to assess the finite-sample performance of our methodology, and an empirical example is analyzed to illustrate its usefulness.