Probability & Forecasts

Question

I am doing a forecast on turnover and would like to know how i can work out the probability that the next sales figure will be over a certain amount given that we have all the data from previous years. How is this possible? e.g. Year 1 100 Year 2 110 Year 3 125 Year 4 145 Year 5 170 Year 6 209 Year 7 245 Year 8 286 Year 9 354 Year 10 452

What is the probability that Year 11 will for example exceed 540? How do I work this out?

Answer 1

While I agree with Willie Wong that you will need to make some assumptions to get a probability, some models will be more "assumption heavy" than others. If you have enough data to assume a particular model for your sales (e.g., linear trend with normally distributed errors) then you will be able to get a more precise estimate.

However, if you simply assume that your past sales growth is representative of sales growth in the near future, then you can get a rough probability estimate by using the following nonparametric approach:

1. Calculate the difference between each squential pair of the N successive annual revenues (e.g., $T_2-T_1$), you will get N-1 differences (i.e., $d_i$).
2. Assign a probability of $\frac{1}{N-1}$ to each difference (this assumes that the early data is as relevant as later data, hence the equal weighting of each difference).
3. Calculate N-1 future revenue predictions by adding each difference to the last known annual revenue: $Prediction_i=T_N+d_i$.
4. The resulting probability mass distribution will be an approximation of the distribution of possible future revenue in period $T_{N+1}$ You can use this approximate distribution to get coarse probability estimates for questions like the one you posed. However, this will be dependent on the truth of the assumptions underlying the model.

You may not like the discreteness and coarseness of the results, but without further knowledge of the details of the process, which would suggest a more precise model, you really can't expect to be able to express your uncertainty with much precision either...you get out what you are able to put in...statistics cannot generate knowledge from ignorance.