Shrinkage Estimation in High Dimensional Dynamic Factor Models

Description

Both shrinkage estimation and high dimensional factor models become increasingly popular in econometrics and statistics during recent years. On the one hand, the shrinkage estimation is a method that tends to shrink estimates towards zero. It is especially useful when the model has a large number of unknown parameters that demonstrate sparsity, namely, many of the parameters are zeros. Various shrinkage estimators are developed so that the estimators will be exactly zeros for unknown zero parameters and will converge to the parameters' true values for unknown nonzero parameters. This means that the shrinkage method allows people to conduct estimation as if they know the true model in advance. This is known as the oracle property. On the other hand, factor models are commonly used in macroeconomics and finance where the data sets have large cross section and time dimensions. Usually, it is technically cumbersome to directly estimate high dimensional models. The factor model assumes that the high dimensional data are driven by a small number of common factors and many idiosyncratic noises. In many applications, a few common factors can explain a substantial amount of variation in high dimensional data sets. Hence, factor models provide a useful way of conducting dimension reduction which leads to low dimensional models without loss of important information.This project will propose a shrinkage type of estimator for high dimensional factor models so that model selection and factor loading estimation can be accomplished simultaneously. In a conventional factor model, unobservable factors are estimated by principal components (PC), and then the number of factors is determined by some information criteria. Subsequently, factor loadings are estimated by conventional OLS, given the PC estimates of factors. The advantage of the shrinkage estimation method is that it can combine the selection and estimation into one step. Also, the literature mainly focuses on determining the number of factors, which is a special case of model selections in factor models. In contrast, we will deal with more general model selection problems based on the oracle property of the shrinkage estimator. For example, we can select the overidentifying restrictions for the factor-augmented VAR models. We will propose a class of shrinkage estimators, establish their asymptotic properties, and provide the conditions under which these estimators can select the correct model with a probability converging to one. The finite sample performance of the proposed estimator will be explored using Monte Carlo simulation.