Inference in Direct Multi-Step and Long Horizon Forecasting Regressions

This paper proposes and evaluates a new method for inference in direct multi-step and long horizon forecasting regressions. The residuals from both direct multi-step and long horizon forecasting regressions are serially correlated, and can be expressed as a vector moving average (VMA) process of the one step ahead forecast residuals. The proposed estimator imposes the VMA structure on the serially correlated residuals to estimate the covariance matrix of the OLS estimates of direct multi-step and long horizon forecasting regressions. The parameters governing the VMA process are estimated using OLS regressions. A simulation study indicates that the proposed estimator is substantially more accurate and efficient, relative to existing methods that do not impose any structure on the autocorrelation process of the residuals