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Title: Efficient estimation of large approximate factor models using constrained principal components regression Authors:  Rachida Ouysse - University of New South Wales (Australia) [presenting]
Abstract: The aim is to develop a new approach to the estimation of the number of factors, factors and factor loadings in large dimensional factor models. Principal components analysis (PCA) provides consistent estimation of the factor structure. For efficient estimation it is essential to estimate a large error covariance matrix when $N$ is large. The proposed method does not assume conditional sparsity, and proposes two approaches to estimating the common factors and factor loadings; both are based on solving a constrained principal component regression problem. The method solves a PCA problem under the constraint of bounded $\frac{1}{N}\sum_{i=1}^{N}\sum_{j=1}^{N}|E(e_{it}e_{jt})|$, which identifies the factor space. Regularisation is achieved by shrinking the off diagonal elements of the covariance matrix to zero. We present results for the main constrained problem and its dual problem which can be viewed as a lasso applied to the off diagonal elements of the covariance matrix. The results from a series of Monte carlo simulations are appreciable for estimating the factor space, estimating the number of factors, but less significant in terms of forecasts performance. The performance of a one-step estimator, which endogenizes the shrinkage estimator and the cross-section bound, are illustrated in a series of monte carlo simulations. We illustrate the method in the context of factor-augmented forecasts of U.S. inflation and growth rate of output.