Marcelo C. Medeiros

The forecasting combination puzzle is a well-known phenomenon in forecasting literature, stressing the challenge of outperforming the simple average when aggregating forecasts from diverse methods. This study proposes a Reinforcement Learning - based framework as a dynamic model selection approach to address this puzzle. Our framework is evaluated through extensive forecasting exercises using simulated and real data. Specifically, we analyze the M4 Competition dataset and the Survey of Professional Forecasters (SPF). This research introduces an adaptable methodology for selecting and combining forecasts under uncertainty, offering a promising advancement in resolving the forecasting combination puzzle.

We propose a model to forecast large realized covariance matrices of returns, applying it to the constituents of the S&P 500 daily. To address the curse of dimensionality, we decompose the return covariance matrix using standard firm-level factors (e.g., size, value, and profitability) and use sectoral restrictions in the residual covariance matrix. This restricted model is then estimated using vector heterogeneous autoregressive models with the least absolute shrinkage and selection operator. Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of minimum variance portfolios.

We propose a model to forecast large realized covariance matrices of returns, applying it to the constituents of the S\&P 500 daily. To address the curse of dimensionality, we decompose the return covariance matrix using standard firm-level factors (e.g., size, value, and profitability) and use sectoral restrictions in the residual covariance matrix. This restricted model is then estimated using vector heterogeneous autoregressive (VHAR) models with the least absolute shrinkage and selection operator (LASSO). Our methodology improves forecasting precision relative to standard benchmarks and leads to better estimates of minimum variance portfolios.

In this paper, we apply statistical methods for functional data to explore the heterogeneity in the registered number of deaths of COVID‐19, over time. The cumulative daily number of deaths in regions across Brazil is treated as continuous curves (functional data). The first stage of the analysis applies clustering methods for functional data to identify and describe potential heterogeneity in the curves and their functional derivatives. The estimated clusters are labeled with different “levels of alert” to identify cities in a possible critical situation. In the second stage of the analysis, we apply a functional quantile regression model for the death curves to explore the associations with functional rates of vaccination and stringency and also with several scalar geographical, socioeconomic and demographic covariates. The proposed model gave a better curve fit at different levels of the cumulative number of deaths when compared to a functional regression model based on ordinary least squares. Our results add to the understanding of the development of COVID‐19 death counts.

Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimensions. However, they are seemingly mutually exclusive. We propose a lifting method that combines the merits of these two models in a supervised learning methodology that allows for efficiently exploring all the information in high-dimensional datasets. The method is based on a flexible model for high-dimensional panel data, called factor-augmented regression model with observable and/or latent common factors, as well as idiosyncratic components. This model not only includes both principal component regression and sparse regression as specific models but also significantly weakens the cross-sectional dependence and facilitates model selection and interpretability. The method consists of several steps and a novel test for (partial) covariance structure in high dimensions to infer the remaining cross-section dependence at each step. We develop the theory for the model and demonstrate the validity of the multiplier bootstrap for testing a high-dimensional (partial) covariance structure. The theory is supported by a simulation study and applications.

We provide a new theory for nodewise regression when the residuals from a fitted factor model are used. We apply our results to the analysis of the consistency of Sharpe ratio estimators when there are many assets in a portfolio. We allow for an increasing number of assets as well as time observations of the portfolio. Since the nodewise regression is not feasible due to the unknown nature of idiosyncratic errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix of errors which is consistent even when number of assets, p, exceeds the time span of the portfolio, n. In another new development, we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors and p>n. We show that: (1) with p>n, the Sharpe ratio estimators are consistent in global minimum-variance and mean-variance portfolios; and (2) with p>n, the maximum Sharpe ratio estimator is consistent when the portfolio weights sum to one; and (3) with p<<n, the maximum-out-of-sample Sharpe ratio estimator is consistent.