Forecast evaluation

Dear all,

I have a few questions regarding the forecasting performance and I hope this is the right place to ask as the questions are not related to Dynare.

I am comparing a few model specifications in terms of their forecasting performance. I have computed predictions for 1 to 8 quarters ahead using recursive forecasting scheme. I have calculated some univariate measures to evaluate the variables using RMSFE. My first question is:

1) What is the easiest way to determine whether these errors are significant and how should I do that?

I would like to also use some multivariate measures. In the literature, I have come across the following for the point forecasts:

  • Log determinant statistic
  • Trace statistic

2) How can I compute these statistics (with relation to Dynare output)?

And finally a similar question regarding the density forecasts:

3) How can I get the log predictive density score (again with relation to Dynare output)?

I don’t have much experience with forecasting so I would be really grateful for any advice. Thank you in advance.