Statsmodel mixes confidence interval and prediction interval terminology despite the two having different definitions. For example, the statsmodels.tsa.arima.model.ARIMAResults.get_forecast function is defined as “Out-of-sample forecasts and prediction intervals” but returns “...out-of-sample forecasts and results including confidence intervals.” Correspondingly, the summary_frame method from get_forecast, outputs mean values and CIs (confidence intervals).
Confidence intervals get me intervals around a parameter. What I really care about is quantifying the probability of my forecasts laying within a specified interval (aka prediction intervals). What exactly is being presented here from statsmodel? Are the mean values of the forecast point predictions given by statsmodel forecast representing the average value of the distribution of potential values, or do they represent some other mean value?
To add even more confusion other models such as ETS models have a summary_frame method that outputs mean and prediction intervals instead of mean and confidence intervals like in ARIMA. Why the change in intervals between the two methods? If the confidence intervals in ARIMA forecasts are actually confidence intervals and not prediction intervals, then how can I interpret it given that it isn’t telling me anything about the variability in the point forecasts.
The difference between confidence and prediction intervals is explained here by Rob Hyndman https://robjhyndman.com/hyndsight/intervals/
Here is an additional post by him stating that “There is almost no use for a confidence interval in forecasting.” https://stats.stackexchange.com/questions/62188/confidence-or-prediction-limits-for-significant-difference-between-forecast-and/62197#62197
ETS model documentation showcasing prediction intervals instead of confidence
Statsmodel mixes confidence interval and prediction interval terminology despite the two having different definitions. For example, the statsmodels.tsa.arima.model.ARIMAResults.get_forecast function is defined as “Out-of-sample forecasts and prediction intervals” but returns “...out-of-sample forecasts and results including confidence intervals.” Correspondingly, the summary_frame method off of get_forecast outputs mean values and CIs (confidence intervals).
Confidence intervals get me intervals around a parameter. What I really care about is quantifying the probability of my forecasts laying within a specified interval (aka prediction intervals). What exactly is being presented here? Are the mean values of the forecast point predictions given by statsmodel forecast representing the average value of the distribution of potential values, or do they represent some other mean value?
Statsmodel mixes confidence interval and prediction interval terminology despite the two having different definitions. For example, the statsmodels.tsa.arima.model.ARIMAResults.get_forecast function is defined as “Out-of-sample forecasts and prediction intervals” but returns “...out-of-sample forecasts and results including confidence intervals.” Correspondingly, the summary_frame method off of get_forecast outputs mean values and CIs (confidence intervals).
Confidence intervals get me intervals around a parameter. What I really care about is quantifying the probability of my forecasts laying within a specified interval (aka prediction intervals). What exactly is being presented here? Are the mean values of the forecast point predictions given by statsmodel forecast representing the average value of the distribution of potential values, or do they represent some other mean value?
To add even more confusion other models such as ETS models have a summary_frame method that outputs mean and prediction intervals instead of mean and confidence intervals like in ARIMA. Why the change in intervals between the two methods? If the confidence intervals in ARIMA forecasts are actually confidence intervals and not prediction intervals, then how can I interpret it given that it isn’t telling me anything about the variability in the point forecasts.
The difference between confidence and prediction intervals is explained here by Rob Hyndman https://robjhyndman.com/hyndsight/intervals/
Here is an additional post by him stating that “There is almost no use for a confidence interval in forecasting.” https://stats.stackexchange.com/questions/62188/confidence-or-prediction-limits-for-significant-difference-between-forecast-and/62197#62197
ETS model documentation showcasing prediction intervals instead of confidence
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In v0.13, you can only get the second version.
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