Research & Projects

Working paper 1 (Job Market paper)

High Dimensional Supervised Forecasting for Conditional Quantiles: Quantile-Covariance Three-Pass Regression Filter

Abstract

We propose a supervised method that predicts the conditional quantile of a univariate time series under a high dimensional setting. We call it the Quantile-Covariance Three-Pass Regression Filter (Qcov3PRF). Inspired by the Three-Pass Regression Filter (3PRF) of Kelly and Pruitt (2015), this method selects the relevant unobservable common factors from a large set of predictors that forecast the conditional quantile of a target variable. By specifying the number of these relevant factors, Qcov3PRF forecasts are consistent for the infeasible best forecast when both the time dimension and cross section dimension become large. Qcov3PRF is related to Partial Least Squares (PLS) modifications that consider quantile regression in the prediction stage and, in contrast to other supervised methods, it successfully allows the estimation of more than one relevant factor by incorporating a concept of quantile covariance. We also show that Qcov3PRF possess good finite sample properties compared to competitive alternatives through simulations. We confirm the good performance of the method with three empirical applications: forecasting Industrial Production Growth based on the components of the National Finance Conditions Index, forecasting the global temperature growth index with country specific carbon dioxide emissions, and forecasting the real GDP with systemic risk measures.

Working paper 2

Vulnerable economic growth as a result of financial conditions and forecasting macroeconomic risks in Mexico in a supervised setting

Abstract

In this work we apply the Quantile-Covariance Three-Pass Regression Filter (Qcov-3PRF) estimation method to study the effects of financial conditions in Mexico and the US on Mexican economic activity. This supervised method focuses on predicting the conditional quantile of a target variable by estimating a set of unobservable factors, relevant for the target, contained in a very large set of predictors. In particular, we obtain relevant effects from financial conditions on predicting the left tail of the distribution of economic growth in Mexico, i.e., we obtain evidence of Growth at Risk (GaR). This result is robust with both in-sample and out-of sample analysis based on different extensions of Qcov-3PRF, across different horizons and often superior to competitive alternatives. Also, our findings indicate that the relevant latent factors that forecast shorter horizons are different from the ones used to predict longer horizons. Our results suggest significant effects from variables such as interest rates and financial indicators from the US when predicting longer horizons of economic activity in the left tail of its distribution, whereas variables such as exchange rates, country risk, and financial indicators from the US are more important for shorter horizons.

Working paper 3

Sufficient Dimension Reduction in Supervised Forecasting with Many Predictors

Abstract

We propose a supervised forecasting method that estimates the conditional mean of a time series target variable non-linearly under the presence of a large set of highly correlated covariates. The target variable follows a multi-index model that depends explicitly on the latent factors from the set of predictors. The indices and the relevant unobservable common factors are estimated consistently using the Three Pass Regression Filter (3PRF) of Kelly and Pruitt (2015), given that the number of indices and of the relevant factors for each index are specified. Therefore, our approach considers two stages to reduce the dimensionality of the covariates: first, through latent factors, and second, through sufficient dimension reduction, i.e., the projected indices. Our method extends the sufficient dimension reduction to high-dimensional regimes by reducing the cross-sectional information through factor models in a supervised setting. We first generate artificial targets following the Sliced Inverse Regression (SIR), then we implement the 3PRF for each target. Our approach correctly estimates projection indices of the underlying factors even in the presence of a non-parametric forecasting function. The resulting conditional mean forecasts are consistent for the nonlinear sufficient infeasible best forecast when both the time dimension and cross section dimension become large. We provide asymptotic results and show the good finite sample performance through simulations. We confirm the forecasting performance relative to alternatives with empirical applications.

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