Latent Variable Autoregression with Exogenous Inputs

Abstract: This paper introduces a new least squares regression methodology called (C)LARX: a (constrained) latent variable autoregressive model with exogenous inputs. Two additional contributions are made as a side effect: First, a new matrix operator is introduced for matrices and vectors with blocks along one dimension; Second, a new latent variable regression (LVR) framework is proposed for economics and finance. The empirical section examines how well the stock market predicts real economic activity in the United States. (C)LARX models outperform the baseline OLS specification in out-of-sample forecasts and offer novel analytical insights about the underlying functional relationship.