Methods and systems for forecasting with model-based PDF estimates

• US 20060116920A1
• Filed: 12/01/2004
• Published: 06/01/2006
• Est. Priority Date: 12/01/2004
• Status: Active Grant

• Current Assignee: Hewlett Packard Enterprise Development LP (Hewlett-Packard Enterprise Company)
• Original Assignee: Hewlett-Packard Development Company, L.P. (HP Inc.)
• Inventors: Shan, Jerry Z.
• Granted Patent: US 8,180,664 B2
• Time in Patent Office: Days
• US Class Current: 705/10
• CPC Class Codes: G06Q 10/04 Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem" market predictions or forecasting for commercial activities G06Q30/0202
• CPC Class Codes: G06Q 10/063 Operations research, analysis or management
• CPC Class Codes: G06Q 30/0202 Market predictions or forecasting for commercial activities

Abstract

Disclosed herein are systems and methods for forecasting with model-based PDF (probability density function) estimates. Some method embodiments may comprise: estimating model parameters for a time series, calculating a PDF for the time series, and generating a forecast from the PDF. The model parameters may comprise a variance for a hidden noise source, and the PDF for the time series may be based at least in part on an estimated variance for the hidden noise source.

Claims

1. A processor-based method comprising:

estimating model parameters of a time series, wherein the model parameters comprise a variance for a hidden noise source;

calculating a probability density function for the time series, wherein the probability density function is based at least in part on the estimated variance; and

generating a forecast from the probability density function.

2. The method of claim 1, wherein the estimating comprises differentiating the time series to obtain a stationary time series.

3. The method of claim 1, wherein the model parameters comprise coefficients of a moving average filter.

4. The method of claim 1, wherein the model parameters comprise coefficients of an autoregressive filter.

5. The method of claim 1, wherein the model parameters comprise an offset value.

6. The method of claim 1, wherein the model accounts for recurring patterns in the time series.

7. The method of claim 1, wherein the model parameters comprise an offset value.

8. The method of claim 1, wherein the probability density function is Gaussian.

9. The method of claim 1, wherein the probability density function is a function of time.

10. The method of claim 1, wherein the time series represents a cumulative value, and wherein the forecast is an end-of-period cumulative value.

11. 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 derive a probability density function for a time series by estimating parameters of a model that comprises a hidden noise source.

12. The computer of claim 11, wherein the software further configures the processor to generate a Bayesian forecast for the time series from the probability density function.

13. The computer of claim 12, wherein the probability density function is a function of time.

14. The computer of claim 13, wherein the software configures the processor to obtain a stationary time series by differentiating an original time series.

15. The computer of claim 14, wherein the original time series represents a cumulative value.

16. The computer of claim 15, wherein the forecast predicts an end-of period value.

17. The computer of claim 11, wherein the model is a seasonal model.

18. The computer of claim 11, wherein the software configures the processor to determine a variance for the hidden noise source, and wherein the software further configures the processor to determine a variance for the probability density function from the variance of the hidden noise source and from estimated filter coefficients.

19. An information carrier medium that communicates software to a computer, said software configuring the computer to:

estimate model parameters for a time series, wherein the model parameters comprise a variance for a hidden noise source; and

determine a probability density function for the time series from the model parameters.

20. The information carrier medium of claim 19, wherein the software further configures the computer to determine a forecast from the probability density function and to display the forecast to a user.

21. The information carrier medium of claim 19, wherein the time series represents a cumulative value.

22. The information carrier medium of claim 21, wherein the forecast relates to an end-of-period value for the time series.

23. The information carrier medium of claim 19, wherein the model parameters comprise auto-regression and moving average filter coefficients.

24. The information carrier medium of claim 23, wherein the probability density function is Gaussian, and wherein the software configures the computer to determine a variance for the probability density function based on the filter coefficients and the variance of the hidden noise source.

25. The information carrier medium of claim 24, wherein the model parameters comprise an offset, and wherein the software configures the computer to determine a mean for the probability density function based on the filter coefficients and the offset.

26. A Bayesian forecasting apparatus that comprises:

modeling means for determining model parameters for a time series;

PDF means for determining unconditional probability density functions of the time series; and

Bayesian forecasting means for forecasting one or more future values of the time series.

27. The apparatus of claim 26, wherein the model parameters comprise moving average filter coefficients.

28. The apparatus of claim 26, wherein the model parameters comprise autoregressive filter coefficients.