# Sum of Random Forest prediction intervals?

I'm using a Random Forest model for prediction, where the value I'm interested in is the aggregate of these predictions (that is, the total sum of all predicted values). I want to also derive confidence intervals for this aggregated value.

Using the quantregForest package I've managed to derive 95% confidence limits for each of my Random Forest predicted values. From what I've read from posts concerning linear regression (e.g. The "sum" of prediction intervals), I can't just sum the limits of the confidence interval for each of the predictions to produce an overall estimate. How do I then go about producing an 'overall' confidence interval for my aggregated values?

Thanks!

Edit: Specifically, I'm using a RF to predict values spatially (e.g. country-wide), where the sum I'm interested in is the value of predictions within a certain area.

I will explain how AUTOBOX ( a piece of multivariate time series software that I have helped to develop) implemented a procedure to accomplish this and perhaps that will help you. Given a model which partitions observation to signal and noise ( hopefully white but not necessarily so ! ) for this discussion. Make a 1 period prediction and then bootstrap the residuals and incorporate any auto-projective structure to obtain a probability distribution. Now compute a second period out probability distribution. Note that no assumption about normality is required here .. the probability distributions are what they are.

One can then sum the elements of the two probability distributions to obtain a probability distribution of the sum.

If one has causal series that need to be predicted in order to predict the outcome series this can easily be included by incorporating the elements of each forecast for each series into this composite. In this way more realistic limits can be found for the dependent series which explicitly incorporate the uncertainty in the user specified predictor/causal series and not naively assumimg particular values for them.

I don't use Random Forest but prefer a more classical disciplined model building approach leading to an ARMAX model incorporating identifiable memory structure and latent deterministic structure waiting to be identified .

If Random Forest is not amenable to the aforementioned strategy i.e. re-sampling et al then you might want to look elsewhere for a viable solution.

"Strengths and weaknesses. Random forest runtimes are quite fast, and they are able to deal with unbalanced and missing data. Random Forest weaknesses are that when used for regression they cannot predict beyond the range in the training data, and that they may over-fit data sets that are particularly noisy."

so it would appear that no forecasting is possible using RF .

• I appreciate your response, thank you! Rather than forecasting, what I'm doing is using a Random Forest model to predict values across an area (spatially) and want to derive a confidence interval for this sum - is this still likely to be unachievable using RF? – Ollie_B Mar 17 at 9:41
• as far as I know ... – IrishStat Mar 17 at 18:12