# Method to combine quantile regression forecasts

I am predicting electricity usage for customers which is highly skewed. Regular regression models did not fit well due to skewed distribution, hence I tried quantile regression. I'm obtaining the models for 0.1, 05 and 0.9 quantiles. So I have 3 set of predictions for the three models optimized at the quantiles specified above. All the three models perform very well for the quantiles optimized but the performance decreases for other quantiles as one would expect. Regular averaging would give equal weights to all three model outputs and hence does not represent true distribution. Can anyone suggest what would be the best method for model averaging for quantile regression method?

• 1. Where you have "05" do you intend "0.5"? 2. What are you trying to obtain by averaging these quantiles? What's the purpose and what properties are you seeking? – Glen_b Apr 1 '19 at 22:59
• @Glen_b 1. yes that was by mistake, I meant 0.5. 2. The overall goal of averaging is to obtain weights in such a way that the relationships of the dependent variable with independent variable at different quantiles is preserved instead of giving equal weights to all predictions. but obtain one prediction instead of 3 different predictions. – iprof0214 Apr 2 '19 at 17:05
• I understand that you want one prediction instead of three; we can generally take that much as a given when you cay "combine". I'm not quite sure what you mean by "the relationships of the dependent variable with independent variable at different quantiles is preserved" (particularly if whatever it is isn't a property of an ordinary average at any given set of x-values). Can you say something about the differences between models in your question? – Glen_b Apr 2 '19 at 21:34