## Saturday, October 25, 2014

### Probability Forecasting and Probabilistic Forecasting

Probabilistic energy forecasting is an emerging branch of energy forecasting. I think it's very important to clarify some concepts in the early stage, so that we don't have to run into troubles arguing what the terms mean 10 years later. This post is about probability forecasting and probabilistic forecasting.

With a rich literature developed by the forecasting community, there is no need for me to reinvent the definitions:
A probabilistic forecast takes the form of a predictive probability distribution over future quantities or events of interest... Although probability forecasts for binary events (e.g., an 80% chance of rain today, a 10% chance of a financial meltdown by the end of the year) have been commonly issued for the past several decades, attention has been shifting toward probabilistic forecasts for more general types of variables and events.

Probability forecasting mainly refers to assigning probabilities to binary events in the future, while probabilistic forecasting has a more general coverage beyond just binary events.

Here are some examples in load forecasting:

• the probability that the monthly peak will occur next Thursday
• the probability that the annual peak of next year will be higher than the annual peak of this year
• the probability that tomorrow's daily peak will be lower than 5.5GW if the A/C cycling program is on.
• the probability distribution of the monthly peak this December
• the 1 in 10 year high load of next year
• the probability distribution of tomorrow's daily peak if if the A/C cycling program is on.
In general, probabilistic load forecasts can be in the form of probability distribution functions, quantiles and intervals. Sometimes a probability forecast can be derived from a probabilistic forecast. For instance, we can first figure out the probability distribution of tomorrow's daily peak under the scenario that the A/C cycling program is on. Then we can calculate the probability that the daily peak is lower than 5.5 GW.

Although probabilistic forecasts are often generated based on scenarios, scenario-based forecasts may not be probabilistic forecasts. For instance, we can generate three long term load forecasts based on three scenarios of 0%, 1% and 2% annual GDP growth. These three load forecasts are not probabilistic forecasts unless there are probabilities associated with each GDP growth scenario.

Note that interval forecasts may not be probabilistic forecasts. For instance, we can transform an hourly load series to an interval times series of daily max and min. Directly applying interval time series analysis to this transformed daily interval load data can result in an interval forecast of daily max and min load. Since the forecast does not have any probabilistic meaning, it is not a probabilistic forecast.

The theme of the Global Energy Forecasting Competition 2014 is probabilistic energy forecasting, not probability energy forecasting, because we are asking the participants to provide probability distribution in 99 percentiles (see Quantile, Quartile and Percentile).