Forecasting with Nonlinear and PDL Specifications

As explained above, forecast errors can arise from two sources: coefficient uncertainty and innovation uncertainty. For linear regression models, the forecast standard errors account for both coefficient and innovation uncertainty. However, if the model is specified by expression (or if it contains a PDL specification), then the standard errors ignore coefficient uncertainty. EViews will display a message in the status line at the bottom of the EViews window when forecast standard errors only account for innovation uncertainty.

For example, consider the three specifications:

log(y) c x

y = c(1) + c(2)*x

y = exp(c(1)*x)

y c x pdl(z, 4, 2)

Forecast standard errors from the first model account for both coefficient and innovation uncertainty since the model is specified by list, and does not contain a PDL specification. The remaining specifications have forecast standard errors that account only for residual uncertainty.

Note also that for non-linear dynamic forecasting, EViews produces what Tong and Lim (1980) term the “eventual forecasting function” in which the lagged forecasted values are substituted recursively into the one-step ahead function. If you wish to obtain simulation-based multi-step forecasting, you may create a model from your equation using Proc/Make Model, and then use the resulting model to perform the dynamic stochastic simulation.