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In the words of Dr. Chris Chatfield: “Predictions are often given as point forecasts with no guidance as to their likely accuracy (and perhaps even with an unreasonable high number of significant digits implying spurious accuracy!)”.
Our paper sets forth a synergy of existing statistical theories to obtain a clear-cut model for calculating forecasts with prediction intervals, named the “WK1 model”.
Many predictive models calculate a linear or non-linear trend from the historical data and generate a single, discrete forecast value, being a single dot on this defined trend line (i.e. point forecast).
The “WK1 model” increases the power of such a single discrete point forecast by adding its probable accuracy with top and bottom limits. The decision-maker obtains thus different ranges of values, each within several pre-defined prediction intervals to assess for that specific outcome probability.
The first step is obviously to establish the degree of the predicting power between the two variables that will be used, based on the historical data and their statistical fundamentals (covariance and correlation).
Once the predicting power of one variable for another one is proven, the second step of the “WK1 model” will calculate the trend line in the usual way.
Finally, the results of the first two steps are combined with the calculation of the different prediction intervals (e.g. 60% probability, 75%, 90%, 95%, 99%, 99.5%) to provide the decision-maker a forecast supplemented with its prediction intervals (outcome probability), instead of a single point forecast.
These ranges are based on the trend line value, but supplemented with calculated probability margins above and below. By doing so, the “WK1 model” thus includes accuracy and reliability to the point values from the trend line.
For further information, please check www.WK1model.com or contact me.
P.S. In our model, a student T-distribution is applied to your data set (so not required to be Gaussian) and the number of occurrences can be as low as 10 and still be statistically significant.
P.S.S. Our worked out example takes half year sales to forecast year end sales, but as long as one variable is closely enough related to the other one (i.e. covariance > 70%), you can apply the WK1model (e.g. weighted average sales of the last three months to forecast next month's sale).
Martin van Wunnik