The RATS Software Forum

ac_1 wrote:Yes, the forecast errors are highly correlated: 0.94798 to 0.99933 (and obviously 1). But I do not want to ‘fit’ to the OOS forecasts; and then there’s TOOS forecasts where forecast errors cannot be calculated - which is why I'd like to use the n component models forecast STDERRS.

As you say: The problem is that there is simply not enough information as I need to calculate covariance matrices at each data point OOS.

You are completely misunderstanding what STDERRS is giving you. It's computing the theoretical out-of-sample standard errors assuming the model is correct. Your whole process assumes the models aren't correct. (If you knew one was correct, you wouldn't be taking averages; you would just use the correct one). The calculations described above don't make any assumptions about that; they simply look at what the sample performance is of the different forecasts.

ac_1 wrote: The aim is to have combination models applicable for:
- one-step ahead forecasts
- multi-step ahead forecasts
mean forecasts and PI's:
- not only for OOS 1 to 50 points (as in this example)
- but also for TOOS (true-out-of-sample) i.e. from the 51st point onwards.

ac_1 wrote: Back to the question: how to calculate Combination forecast PI's (equally weighted or optimized), OOS and TOOS taking into account the forecast errors, without 'fitting' to the OOS forecasts?

Note I am assuming the 7 models above all have OOS and TOOS PI’s generated, and the idea is to analytically aggregate them, as I cannot simply average quantiles (e.g. compute an average of 7 medians)!

An idea: How about calculating the 'in-sample' fitted-errors (fitn(t) - actual(t)), for n component models. Then, estimate the covariances between the different 'in-sample' fitted-errors. After that use a multivariate GARCH model, which can forecast means, variances and covariances. The variance expression, a linear combination of n component models, used for the PI equations, is: x'Vx, where V is the forecast (one-step or multi-step) covariance matrix, x are equal weights; and x'Vx should increase at each step for multi-step OOS and TOOS.

Is the idea/method possible?