Factor-augmented Regression Models Research Articles

Testing for sparse idiosyncratic components in factor-augmented regression models

We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative model augmented with sparse idiosyncratic components. The asymptotic properties of the test are established under time series dependence and polynomial tails. We outline a data-driven rule to select the tuning parameter and prove its theoretical validity. In simulation experiments, our procedure exhibits high power against sparse alternatives and low power against dense deviations from the null. Moreover, we apply our test to various datasets in macroeconomics and finance and often reject the null. This suggests the presence of sparsity — on top of a dense component — in commonly studied economic applications. The R package ‘FAS’ implements our approach.

Bridging Factor and Sparse Models

Factor and sparse models are two widely used methods to impose a low-dimensional structure in high-dimension. They are seemingly mutually exclusive. In this paper, we propose a simple lifting method that combines the merits of these two models in a supervised learning methodology that allows to efficiently explore all the information in high-dimensional datasets. The method is based on a flexible model for panel data, called factor-augmented regression model with both observable, latent common factors, as well as idiosyncratic components as high-dimensional covariate variables. This model not only includes both factor regression and sparse regression as specific models but also significantly weakens the cross-sectional dependence and hence facilitates model selection and interpretability. The methodology consists of three steps. At each step, the remaining cross-section dependence can be inferred by a novel test for covariance structure in high-dimensions. We developed asymptotic theory for the factor-augmented sparse regression model and demonstrated the validity of the multiplier bootstrap for testing high-dimensional covariance structure. This is further extended to testing high-dimensional partial covariance structures. The theory and methods are further supported by an extensive simulation study and applications to the construction of a partial covariance network of the financial returns and a prediction exercise for a large panel of macroeconomic time series from FRED-MD database.

Forecasting using cross-section average–augmented time series regressions

Summary There is a large and growing body of literature concerned with forecasting time series variables by the use of factor-augmented regression models. The workhorse of this literature is a two-step approach in which the factors are first estimated by applying the principal components method to a large panel of variables, and the forecast regression is then estimated, conditional on the first-step factor estimates. Another stream of research that has attracted much attention is concerned with the use of cross-section averages as common factor estimates in interactive effects panel regression models. The main justification for this second development is the simplicity and good performance of the cross-section averages when compared with estimated principal component factors. In view of this, it is quite surprising that no one has yet considered the use of cross-section averages for forecasting. Indeed, given the purpose to forecast the conditional mean, the use of the cross-sectional average to estimate the factors is only natural. The present paper can be seen as a reaction to this. The purpose is to investigate the asymptotic and small-sample properties of forecasts based on cross-section average–augmented regressions. In contrast to most existing studies, the investigation is carried out while allowing the number of factors to be unknown.

On factor models with random missing: EM estimation, inference, and cross validation

We consider the estimation and inference in approximate factor models with random missing values. We show that with the low rank structure of the common component, we can estimate the factors and factor loadings consistently with the missing values replaced by zeros. We establish the asymptotic distributions of the resulting estimators and those based on the EM algorithm. We also propose a cross-validation-based method to determine the number of factors in factor models with or without missing values and justify its consistency. Simulations demonstrate that our cross validation method is robust to fat tails in the error distribution and significantly outperforms some existing popular methods in terms of correct percentage in determining the number of factors. An application to the factor-augmented regression models shows that a proper treatment of the missing values can improve the out-of-sample forecast of some macroeconomic variables.

On testing for structural break of coefficients in factor-augmented regression models

This paper considers testing for structural break of factor-augmented regression models with unknown change point. In this case, the classical structural break tests proposed by Andrews (1993) and Andrews and Ploberger (1994) are infeasible due to the presence of unobservable factors. This paper develops the feasible two-step tests based on their structural break tests. We prove that the asymptotic null distributions of the proposed two-step tests remain to be the same as those of their infeasible tests. The Monte Carlo simulations confirm the theoretical results and show that the two-step tests perform well in finite sample.

Factor-augmented regression models with structural change

This paper considers a factor-augmented regression model in the presence of structural change. We propose a two-step procedure to estimate the coefficients of explanatory variables. We show that when the number of units (N) and the number of periods (T) are large and comparable, the proposed two-step estimator is T-consistent and has the same limiting distribution as if the unobservable factors were observed. Monte Carlo simulations confirm our theoretical results and show good finite sample performance of the two-step estimator.