Forecasting with log-linear (S)VAR models: Incorporating annual growth rate conditions
研究了对数或对数差分VAR模型中施加年度增长率条件进行条件预测的方法，提出了线性近似和迭代校正，并提供了MATLAB代码。
This note studies conditional forecasting under conditions on annual growth rates when variables enter a (possibly structural) vector autoregressive (VAR) model in logarithms or logarithmic first differences. Imposing conditions on the annual growth rate of, for example, quarterly real GDP modeled in logarithms is challenging because annual growth rates are nonlinear functions of the log variables. We derive a linear approximation that makes annual growth-rate conditions compatible with standard conditional forecasting methods and complement it with a damped iterative correction that enforces the nonlinear annual-growth restriction up to numerical tolerance. We provide MATLAB companion code 2 that also accepts other types of conditions: (1) conditions on the path of variables entering the VAR, (2) conditions on the path of structural shocks, and (3) conditions on sums of successive variable observations.