Methods and systems for cumulative attribute forecasting using a PDF of a current-to-future value ratio

1. A processor-based method comprising:

determining, by a processor, an unconditional probability density function (PDF) for a ratio of a cumulative attribute's current value to an associated future value for the cumulative attribute;

determining, by the processor, an unconditional PDF for a future value of the cumulative attribute;

combining, by the processor, the unconditional PDFs with a current value of the cumulative attribute to obtain a function indicative of a conditional PDF for the future value;

operating, by the processor, on the function to obtain at least one forecast; and

communicating the forecast to a user,

wherein said combining comprises:

finding a set of ratios by dividing the current value of the cumulative attribute by

each of a set of potential future values;

for each potential future value in said set of potential future values,

evaluating the unconditional ratio PDF at the ratio associated with the potential future value;

evaluating the unconditional future value PDF at the potential future value;

multiplying the evaluated unconditional PDFs to determine a product; and

dividing the product of the evaluated unconditional PDFs by the potential future value.

2. The method of claim 1 , wherein said determining of the unconditional PDFs comprises:

connecting to a database having historical records of the cumulative attribute for at least one period prior to a current period;

combining data from multiple periods to estimate the unconditional PDFs.

3. The method of claim 2 , wherein said determining further comprises normalizing a time scale of each period.

4. The method of claim 2 , wherein said determining further comprises fitting a curve to cumulative attribute data from each period prior to the current period.

5. The method of claim 2 , wherein said determining further comprises determining a probability distribution for the cumulative ratio at each time point in the period.

6. The method of claim 2 , wherein the cumulative attribute is of a monetary value, and wherein the periods are fiscal periods.

7. The method of claim 1 , wherein said function is proportional to 1/S T ƒ R t (S t /S T )ƒ S T (S T ), where S t represents the cumulative attribute at a current time t, S T represents potential values of the cumulative attribute at a future time T, ƒ R t (S t /S T ) represents a PDF for ratio R t =S t /S T , and ƒ S T (S T ) represents a PDF for S T .

8. The method of claim 1 , wherein said operating comprises determining a future value that maximizes the function.

9. The method of claim 1 , wherein said operating comprises determining a future value that is the average or median of the function.

10. The method of claim 1 , wherein said operating comprises determining a value indicative of the standard deviation of the function.

11. The method of claim 1 , wherein said operating comprises determining a percentage of area under the function that is associated with a range of potential future values.

12. The method of claim 1 , wherein said communicating comprises displaying the forecast on a screen viewable by a user.

13. A computer comprising:

a display;

a processor coupled to the display; and

a memory coupled to the processor,

wherein the memory stores software that configures the processor to determine a forecast regarding a cumulative attribute's future value, and further configures the processor to show the forecast on the display, and

wherein said forecast is based at least in part on determining a probability density function (PDF) for a ratio of the cumulative attribute's current value to an associated future value, and evaluating said ratio PDF at the ratios between the current attribute's current value and a range of the cumulative attribute's potential future values,

wherein as part of determining the forecast, the software configures the processor to repeat a set of operations for each potential future value in a set of the cumulative attribute's potential future values, wherein the set of operations comprises:

evaluating the ratio PDF at a ratio associated with the potential future value;

evaluating the cumulative attribute's future value PDF at the potential future value; and

dividing a product of the evaluated PDFs by the potential future value, and wherein the repeated set of operations yields a function proportional to the

PDF for the cumulative attribute's future value.

14. The computer of claim 13 , wherein as part of determining the forecast, the software configures the processor to determine one or more values indicative of 1/S T ƒ R t (S t /S T )ƒ S T (S T ), where S t represents the cumulative attribute at a current time t, S T represents potential values of the cumulative attribute at a future time T, ƒ R t (S t /S T ) represents a PDF for ratio S t /S T , and ƒ S T (S T ) represents a PDF for S T .

15. A computer-readable medium storing software executable by a computer, such that execution of said software by the computer causes the computer to:

estimate probability density functions (PDFs) of a cumulative attribute's ratio to an associated future value at different times in a period based on a history of cumulative attribute values in past periods; and

determine a forecast regarding the cumulative attribute's value, wherein said forecast is based at least in part on evaluating a PDF for the cumulative attribute's ratio at the ratios between the current attribute's current value and a range of the cumulative attribute's potential future values,

wherein as part of determining the forecast, the software configures the computer to repeat a set of operations for each potential future value in a set of the cumulative attribute's potential future values, wherein the set of operations comprises:

evaluating the ratio PDF at a ratio associated with the potential future value:

evaluating the cumulative attribute's future value PDF at the potential future value; and

dividing a product of the evaluated PDFs by the potential future value,

and wherein the repeated set of operations yields a function proportional to the PDF for the cumulative attribute's future value.

16. The medium of claim 15 , wherein the cumulative attribute is a measure of business performance.

17. The medium of claim 15 , wherein the cumulative attribute is a monetary value from the set consisting of revenues, costs, and profits.

18. The medium of claim 15 , wherein the software further configures the computer to communicate the forecast to a user.

19. The medium of claim 15 , wherein as part of determining the forecast, the software configures the computer to determine one or more values represented by 1/S T ƒ R t (S t /S T )ƒ S T (S T ), where S t represents the cumulative attribute at a current time t, S T represents potential values of the cumulative attribute at a future time T, ƒ R t (S t /S T ) represents a PDF for ratio S t /S T , and ƒ S T (S T ) represents a PDF for S T .

20. The medium of claim 15 , wherein the forecast comprises a most likely end-of-period value and a confidence interval around the most likely end-of-period value.

21. A cumulative attribute forecasting apparatus comprising:

a processor;

a computer-readable data storage medium storing software that when executed by the processor causes the processor to:

determine an unconditional probability density function (PDF) for a ratio of accumulative attribute's current value to an associated future value for the cumulative attribute;

determine an unconditional PDF for a future value of the cumulative attribute;

combine the unconditional PDFs with a current value of the cumulative attribute to obtain a function indicative of a conditional PDF for the future value;

operate on the function to obtain at least one forecast; and

communicating the forecast to a user, wherein the processor is to combine the unconditional PDFs with the current value by:

finding a set of ratios by dividing the current value of the cumulative attribute by each of a set of potential future values;

for each potential future value in said set of potential future values,

evaluating the unconditional ratio PDF at the ratio associated with the potential future value;

evaluating the unconditional future value PDF at the potential future value;

multiplying the evaluated unconditional PDFs to determine a product; and

dividing the product of the evaluated unconditional PDFs by the potential future value.

22. The apparatus of claim 21 , further comprising a display to communicate the forecast to a user.

23. The apparatus of claim 21 , wherein the conditional PDF is represented by 1/S T ƒ R t (S t /S T )ƒ S T (S T ), where S t represents the cumulative attribute at a current time t, S T represents potential values of the cumulative attribute at a future time T, ƒ R t (S t /S T ) represents a PDF for ratio S t /S T , and ƒ S T (S T ) represents a PDF for S T .