Kernel Methods

Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels ArXiv ID: 2410.21858 “View on arXiv” Authors: Unknown Abstract We develop a nonparametric, kernel-based joint estimator for conditional mean and covariance matrices in large and unbalanced panels. The estimator is supported by rigorous consistency results and finite-sample guarantees, ensuring its reliability for empirical applications. We apply it to an extensive panel of monthly US stock excess returns from 1962 to 2021, using macroeconomic and firm-specific covariates as conditioning variables. The estimator effectively captures time-varying cross-sectional dependencies, demonstrating robust statistical and economic performance. We find that idiosyncratic risk explains, on average, more than 75% of the cross-sectional variance. ...

Kernel Three Pass Regression Filter ArXiv ID: 2405.07292 “View on arXiv” Authors: Unknown Abstract We forecast a single time series using a high-dimensional set of predictors. When these predictors share common underlying dynamics, an approximate latent factor model provides a powerful characterization of their co-movements Bai(2003). These latent factors succinctly summarize the data and can also be used for prediction, alleviating the curse of dimensionality in high-dimensional prediction exercises, see Stock & Watson (2002a). However, forecasting using these latent factors suffers from two potential drawbacks. First, not all pervasive factors among the set of predictors may be relevant, and using all of them can lead to inefficient forecasts. The second shortcoming is the assumption of linear dependence of predictors on the underlying factors. The first issue can be addressed by using some form of supervision, which leads to the omission of irrelevant information. One example is the three-pass regression filter proposed by Kelly & Pruitt (2015). We extend their framework to cases where the form of dependence might be nonlinear by developing a new estimator, which we refer to as the Kernel Three-Pass Regression Filter (K3PRF). This alleviates the aforementioned second shortcoming. The estimator is computationally efficient and performs well empirically. The short-term performance matches or exceeds that of established models, while the long-term performance shows significant improvement. ...