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> Another is a standard deviation (i.e. you are pretty much predicting the squared difference between your own point forecast and the outcome). What you probab

> Another is a standard deviation (i.e. you are pretty much predicting the squared difference between your own point forecast and the outcome). What you probably want is the standard error, because you are not interested in how much your data differ from each other but in how much your data differ from the true population.

bo1024 3y ago
I don't see how standard error applies here. You are only going to get one data point, e.g. "violent crime rate in 2023". What I mean is a prediction, not only of what you think the number is, but also of how wrong you think your prediction will be.
- nonameiguess 3y ago
  Standard error is exactly what the statsmodels ARIMA.PredictionResults object actually gives you and the confidence interval in this chart is constructed from a formula that uses the standard error. ARIMA is based on a few assumptions. One, there exists some "true" mean value for the parameter you're trying to estimate, in this case violent crime rate. Two, the value you measure in any given period will be this true mean plus some random error term. Three, the value you measure in successive periods will regress back toward the mean. The "true mean" and error terms are both random variables, not a single value but a distribution of values, and when you add them up to get the predicted measurement for future periods, that is also a random variable with a distribution of values, and it has a standard error and confidence intervals and these are exactly what the article is saying should be included in any graphical report of the model output. This is a characteristic of the model. What you're asking for, "how wrong do you think the model is," is a reasonable thing to ask for, but different and much harder to quantify.
  - bo1024 3y ago
    Thanks for explaining how it works - I don't use R (I assume this is R). This does not seem like a good way to produce "error bars" around a forecast like the one in this case study. It seems more like a note about how much volatility there has been in the past.
    - fjkdlsjflkds 3y ago
      > I don't use R (I assume this is R) Just to clarify... this is Python code, not R.
      - bo1024 3y ago
        Thanks.
  - bo1024 3y ago
    Another import point of discussion: > What you're asking for, "how wrong do you think the model is," is a reasonable thing to ask for, but different and much harder to quantify. This definitely seems to me to be what the original author is motivating: forecasts should have "error bars" in the sense that they should depict how wrong they might be. In other words, when the author writes: > Point forecasts will always be wrong – a more reasonable approach is to provide the prediction intervals for the forecasts. Showing error intervals around the forecasts will show how Richard interpreting minor trends is likely to be misleading. The second sentence does not sound like a good solution to the problem in the first sentence.

bo1024 3y ago

I don't see how standard error applies here. You are only going to get one data point, e.g. "violent crime rate in 2023". What I mean is a prediction, not only of what you think the number is, but also of how wrong you think your prediction will be.

nonameiguess 3y ago
Standard error is exactly what the statsmodels ARIMA.PredictionResults object actually gives you and the confidence interval in this chart is constructed from a formula that uses the standard error. ARIMA is based on a few assumptions. One, there exists some "true" mean value for the parameter you're trying to estimate, in this case violent crime rate. Two, the value you measure in any given period will be this true mean plus some random error term. Three, the value you measure in successive periods will regress back toward the mean. The "true mean" and error terms are both random variables, not a single value but a distribution of values, and when you add them up to get the predicted measurement for future periods, that is also a random variable with a distribution of values, and it has a standard error and confidence intervals and these are exactly what the article is saying should be included in any graphical report of the model output. This is a characteristic of the model. What you're asking for, "how wrong do you think the model is," is a reasonable thing to ask for, but different and much harder to quantify.
- bo1024 3y ago
  Thanks for explaining how it works - I don't use R (I assume this is R). This does not seem like a good way to produce "error bars" around a forecast like the one in this case study. It seems more like a note about how much volatility there has been in the past.
  - fjkdlsjflkds 3y ago
    > I don't use R (I assume this is R) Just to clarify... this is Python code, not R.
    - bo1024 3y ago
      Thanks.
- bo1024 3y ago
  Another import point of discussion: > What you're asking for, "how wrong do you think the model is," is a reasonable thing to ask for, but different and much harder to quantify. This definitely seems to me to be what the original author is motivating: forecasts should have "error bars" in the sense that they should depict how wrong they might be. In other words, when the author writes: > Point forecasts will always be wrong – a more reasonable approach is to provide the prediction intervals for the forecasts. Showing error intervals around the forecasts will show how Richard interpreting minor trends is likely to be misleading. The second sentence does not sound like a good solution to the problem in the first sentence.