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Prediction intervals are the most valuable statistical tools available to hotel investment decision-makers. However, they are not used as frequently as they should be. Lodging analysts, such as PwC, CBRE, and STR traditionally provide forecasts that are point estimates – that is, single-parameter estimates of occupancy, ADR, and RevPAR, etc. But point forecasts provide no indication of the uncertainty in the number, and uncertainty is an important consideration in decision making.

As single numbers, point estimates are almost always above or below the parameters they are supposed to estimate. Without additional information, point estimates are less than optimal for making hotel investment decisions! Prediction interval estimates are very likely to be true, and the prediction level specifies and controls the probability that the interval estimates are true.

A prediction interval is a standard way of describing the precision of a measurement of some parameter, such as a RevPAR forecast. There are two common ways of stating prediction intervals both of which provide exactly the same information, for example, 1) Total U.S. RevPAR is forecast to grow by 5% plus or minus 2% with 90% confidence. 2) Total U.S. RevPAR is forecast to grow by between 3% and 7%, with 90% confidence.

The difference between a point and probabilistic forecast is illustrated in the fan chart below. The point forecast is the RevPAR forecast growing from \$100.49 in 2014 to \$104.09 in 2015 and \$113.51 in 2021. The outside forecasts represent the 5% and 95% prediction intervals, while the inner forecasts represent the 35% and 65% intervals. Clearly, the wider the interval, the greater uncertainty we have about RevPAR in the future.

The prediction level provides information about how sure you are that the true value of the parameter you have an interest in lies between the upper and lower bounds. This is not a subjective indication of confidence: one doesn’t merely substitute the number 90% for the phrase “I’m quite sure.” Instead, the prediction interval is calculated using statistical techniques that ensure that the confidence level is objective.

Recognizing and dealing with possible numbers around the most probable number is a major function of hotel investment risk analysis and is the reason we believe that no major investment decision should be made without the benefit of prediction intervals! Providing uncertainty information can result in better decisions.

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