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we have set of historical data of different price forecasts and the real prices.

When assessing "which forecasts are best", what parts of the analysis should one never miss out? We are at a very start of our investigation, using forecast error mean, forecast error standard deviation, forecast error 90% percentiles, error distribution skewness. We calculate the same quantities for absolute values of the errors.

What quantities might we miss out? Are some procedures crucial for determining what price forecast systems to utilize? Are there any practical sources on such analysis?

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Hi: Based on your question, it sounds like the Diebold-Mariano test might be perfect for your case. It doesn't require any sophisticated assumptions about models or processes etc. All one needs are the two sets of forecasts and the actuals. I can't find the actual paper but below is the reference to it. I imagine that, if you google hard enough, the paper itself is probably somewhere on the internet ( besides from the publisher ).

https://amstat.tandfonline.com/doi/abs/10.1080/07350015.1995.10524599#.XpjzqvkpDCI

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