Working-Papers (forthcoming and/or submitted)

A novel approach to predictive accuracy testing in nested environments, Econometric Theory, 41, pp. 35-78, 2025. 

Abstract: We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample mean squared error loss differentials between the two competing models, leads to nuisance parameter-free Gaussian asymptotics, and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g., stationary and local to unit root). A local power analysis also establishes their ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes. Funding: ESRC, ES/W000989/1

Out of Sample Predictability in Predictive Regressions with Many Predictor Candidates (with J. Gonzalo), International Journal of Forecasting, 40, pp. 1166-1178, 2024.  

Abstract: We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample MSE loss differentials between the two competing models, leads to nuisance parameter free Gaussian asymptotics and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g. stationary and local to unit root).  A local power analysis also establishes their ability to detect departures from the null in both stationary and persistent settings.  Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes. Funding: ESRC, ES/W000989/1

Direct Multi-Step Forecast based Evaluation of Nested Models via an Encompassing Test, December 2023 [under review]

Abstract: We introduce a novel approach for comparing out-of-sample multi-step forecasts obtained from a pair of nested models that is based on the forecast encompassing principle. Our proposed approach relies on an alternative way of testing the population moment restriction implied by the forecast encompassing principle and that links the forecast errors from the two competing models in a particular way. Its key advantage is that it is able to bypass the variance degeneracy problem afflicting model based forecast comparisons across nested models. It results in a test statistic whose limiting distribution is standard normal and which is particularly simple to construct. Multi-step forecasts are handled through two alternative ways. A standard approach that relies on a HAC type studentization of our test statistic and an alternative self-normalization based approach which bypasses the need to estimate long-run variances. All our inferences are shown to be able to accommodate a variety of predictor types including stationary, highly-persistent and purely deterministic predictors without affecting the way inferences are implemented.  Funding: ESRC, ES/W000989/1  

Serial-Dependence and Persistence Robust Inference in Predictive Regressions, February 2025

Abstract: This paper introduces a new method for testing the statistical significance of estimated parameters in predictive regressions. The approach features a new family of test statistics that are robust to the degree of persistence of the predictors. Importantly, the method accounts for serial correlation and conditional heteroskedasticity without requiring any corrections or adjustments. This is achieved through a mechanism embedded within the test statistics that effectively decouples serial dependence present in the data. The limiting null distributions of these test statistics are shown to follow a chi-square distribution, and their asymptotic power under local alternatives is derived. A comprehensive set of simulation experiments illustrates their finite sample size and power properties. Funding: ESRC, ES/W000989/1

Detecting Sparse Cointegration (with J. Gonzalo), January 2025

Abstract:: We propose a two-step procedure to detect cointegration in high-dimensional settings, focusing on sparse relationships. First, we use the adaptive LASSO to identify the small subset of integrated covariates driving the equilibrium relationship with a target series, ensuring model-selection consistency. Second, we adopt an information-theoretic model choice criterion to distinguish between stationarity and nonstationarity in the resulting residuals, avoiding dependence on asymptotic distributional assumptions. Monte Carlo experiments confirm robust finite-sample performance, even under endogeneity and serial correlation.. Funding: ESRC, ES/W000989/1