Information criterion-based systems and methods for constructing combining weights for multimodel forecasting and prediction

• US 8,374,903 B2
• Filed: 06/20/2008
• Issued: 02/12/2013
• Est. Priority Date: 06/20/2008
• Status: Active Grant

• Current Assignee: SAS Institute Incorporated
• Original Assignee: SAS Institute Incorporated
• Inventors: Little, Mark Roland
• Primary Examiner(s): Choi, Peter
• Assistant Examiner(s): CHONG CRUZ, NADJA N
• Application Number:
  US12/143,116
• Publication Number:
  US 20090319310A1
• Time in Patent Office: 1,698 Days
• Field of Search: 705/7.31, 705/7.37
• US Class Current: 705/7.31
• 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 30/0202 Market predictions or forecasting for commercial activities

Abstract

Systems and methods are provided for a computer-implemented method for automatically generating a weighted average forecast model that includes receiving a plurality of forecasting models and time series data. At least one parameter of each of the received forecasting models is optimized utilizing the received time series data. A weighting factor is generated for each of the plurality of optimized forecasting models utilizing an information criteria value indicating fit quality of each of the optimized forecasting models, and the generated weighting factors are stored.

Claims

1. A computer-implemented method for generating a weighted average forecast model, comprising:

receiving, using one or more processors, a plurality of forecasting models;

receiving, using the one or more processors, time series data;

optimizing, using the one or more processors, one or more parameters for each of the received forecasting models, wherein optimizing a parameter includes using the received time series data;

determining, using the one or more processors, an information criteria value for each of the optimized forecasting models, wherein the information criteria value indicates fit quality and complexity;

determining, using the one or more processors, a lowest calculated information criteria value;

determining, using the one or more processors, an information criteria delta value for each of the optimized forecasting models, wherein a delta value indicates a difference between an information criteria value for an optimized forecasting model and the lowest calculated information criteria value;

determining, using the one or more processors, raw weights for each of the optimized forecasting models using the information criteria delta values;

determining, using the one or more processors, normalized weighting factors for each of the optimized forecasting models using the raw weights;

generating, using the one or more processors, a weighted average forecast model using the optimized forecasting models and the normalized weighting factors; and

generating a forecast using the weighted average forecast model.

2. The method of claim 1, further comprising:

generating a forecasted output for each of the optimized forecasting models; and

generating a weighted average of the forecasted outputs using the normalized weighting factors.

3. The method of claim 2, further comprising:

receiving updated time series data;

generating an updated forecasted output for each of the optimized forecasting models utilizing the updated time series data; and

generating an updated weighted average of the updated forecasted outputs using the normalized weighting factors.

4. The method of claim 2, wherein the weighted average indicates forecasted monthly sales of a product.

5. The method of claim 2, further comprising:

generating additional weighted averages for a plurality of stock keeping units.

6. The method of claim 1, wherein the time series data includes data associated with operation of a physical system over a period of time.

7. The method of claim 6, wherein the physical system is a manufacturing system, a grocery store chain, or a retail store chain.

8. The method of claim 1, further comprising optimizing the one or more parameters according to a least squares regression.

9. The method of claim 1, further comprising using an Akaike Information Criterion for the information criteria value.

10. The method of claim 9, further comprising calculating the Akaike Information Criterion (AIC) according to:

AIC=−

2ln(L)+2·

P,

wherein L is a likelihood value corresponding to the optimized forecasting model; and

wherein P is a number of fitted parameters in the optimized forecasting model.

11. The method of claim 9, further comprising calculating the Akaike Information Criterion (AIC) according to:

AIC=n·

ln(mse)+2·

P,

wherein mse is a mean squared error;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

12. The method of claim 1, wherein the information criteria value is an adjusted Akaike Information Criterion (AICc), the method further comprising calculating the adjusted Akaike Information Criterion (AICc) according to:

AICc=AIC+(2·

P·

(P+1))/(n−

P−

1),

wherein AIC is an Akaike Information Criterion for the optimized forecasting model;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

13. The method of claim 1, wherein the information criteria value is a Bayesian Information Criterion (BIC), the method further comprising calculating the Bayesian Information Criterion (BIC) according to:

BIC=−

2·

ln(L)+ln(n)·

P,

wherein L is a likelihood value corresponding to the optimized forecasting model;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

14. The method of claim 1, further comprising computing the raw weights (wraw) according to:

wraw=exp(−

Δ

/2),

wherein Δ

is the information criteria delta value.

15. The method of claim 1, further comprising computing the raw weights (wraw) according to:

wraw=exp(λ

·

−

λ

/2),

wherein Δ

is the information criteria delta value; and

wherein λ

is an adjustment factor.

16. The method of claim 15, wherein the adjustment factor is predetermined.

17. The method of claim 1, further comprising storing the weighted average forecast model, and wherein the normalized weighting factors are stored in a random access memory.

18. The method of claim 2, wherein the weighted average is a forecasted future value for monetary sales of a product, a quantity of sales of a product, a monetary value of market demand of a product, a physical quantity of market demand for a product, inventory needs at a retail outlet, a quantity of order by an identified customer, a quantity of a resource needed for a production process, a volume of traffic, transportation logistics, quantity of service requests, a stock price, a stock trading volume, a commodity trading volume, a commodity usage, a product consumption, a population change, an average income, an average wealth, a likelihood of default on a loan, a currency exchange rate, a tax rate, a volume of open market activity of U.S. Federal Reserve system, an average temperature, or an average rainfall.

19. The method of claim 2, wherein the weighted average is a forecasted future value for calendar years, fiscal years, quarters of years, months, weeks, days, hours, minutes, or seconds.

20. A system for generating a weighted average forecast model, comprising:

one or more processors;

one or more non-transitory computer-readable storage mediums containing instructions configured to cause the one or more processors to perform operations including;

receiving a plurality of forecasting models;

receiving time series data;

optimizing one or more parameters for each of the received forecasting models, wherein

optimizing a parameter includes using the received time series data;

determining an information criteria value for each of the optimized forecasting models, wherein the information criteria value indicates fit quality and complexity;

determining a lowest calculated information criteria value;

determining an information criteria delta value for each of the optimized forecasting models, wherein a delta value indicates a difference between an information criteria value for an optimized forecasting model and the lowest calculated information criteria value;

determining raw weights for each of the optimized forecasting models using the information criteria delta values;

determining normalized weighting factors for each of the optimized forecasting models using the raw weights;

generating a weighted average forecast model using the optimized forecasting models and the normalized weighting factors; and

generating a forecast using the weighted average forecast model.

22. The system of claim 20, further comprising instructions configured to cause the one or more processors to perform operations including:

generating a forecasted output for each of the optimized forecasting models; and

generating a weighted average of the forecasted outputs using the normalized weighting factors.

23. The system of claim 22, further comprising instructions configured to cause the one or more processors to perform operations including:

receiving updated time series data;

generating an updated forecasted output for each of the optimized forecasting models utilizing the updated time series data; and

generating an updated weighted average of the updated forecasted outputs using the normalized weighting factors.

24. The system of claim 20, further comprising instructions configured to cause the one or more processors to perform operations including:

using an Akaike Information Criterion for the information criteria value.

25. The system of claim 24, further comprising instructions configured to cause the one or more processors to perform operations including:

calculating the Akaike Information Criterion (AIC) according to;

AIC=−

2 ln(L)+2·

P,

wherein L is a likelihood value corresponding to the optimized forecasting model; and

wherein P is a number of fitted parameters in the optimized forecasting model.

26. The system of claim 24, further comprising instructions configured to cause the one or more processors to perform operations including:

calculating the Akaike Information Criterion (AIC) according to;

AIC=n·

ln(mse)+2·

P,

wherein mse is a mean squared error;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

27. The system of claim 20, wherein the information criteria value is an adjusted Akaike Information Criterion (AICc), the method further comprising instructions configured to cause the one or more processors to perform operations including:

calculating the adjusted Akaike Information Criterion (AICc) according to;

AICc=AIC+(2·

P·

(P+1))/(n−

P−

1),

wherein AIC is an Akaike Information Criterion for the optimized forecasting model;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

28. The system of claim 20, wherein the information criteria value is a Bayesian Information Criterion (BIC), the method further comprising instructions configured to cause the one or more processors to perform operations including:

calculating the Bayesian Information Criterion (BIC) according to;

BIC=−

2·

ln(L)+ln(n)·

P,

wherein L is a likelihood value corresponding to the optimized forecasting model;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

29. The system of claim 20, further comprising instructions configured to cause the one or more processors to perform operations including:

computing the raw weights (wraw) according to;

wraw=exp(−

Δ

/2),

wherein Δ

is the information criteria delta value.

30. The system of claim 20, further comprising instructions configured to cause the one or more processors to perform operations including:

computing the raw weights (wraw) according to;

wraw=exp(λ

·

−

Δ

/2),

wherein Δ

is the information criteria delta value; and

wherein λ

is an adjustment factor.

21. A non-transitory computer program product for generating a weighted average forecast model, tangibly embodied in a machine-readable non-transitory storage medium, including instructions configured to cause a data processing system to:

receive a plurality of forecasting models;

receive time series data;

optimize one or more parameters for each of the received forecasting models, wherein optimizing a parameter includes using the received time series data;

determine an information criteria value for each of the optimized forecasting models, wherein the information criteria value indicates fit quality and complexity;

determine a lowest calculated information criteria value;

determine an information criteria delta value for each of the optimized forecasting models, wherein a delta value indicates a difference between an information criteria value for an optimized forecasting model and the lowest calculated information criteria value;

determine raw weights for each of the optimized forecasting models using the information criteria delta values;

determine normalized weighting factors for each of the optimized forecasting models using the raw weights;

generate a weighted average forecast model using the optimized forecasting models and the normalized weighting factors; and

generating a forecast using the weighted average forecast model.

31. The computer program product of claim 21, further comprising instructions configured to cause the data processing system to:

generate a forecasted output for each of the optimized forecasting models; and

generate a weighted average of the forecasted outputs using the normalized weighting factors.

32. The computer program product of claim 31, further comprising instructions configured to cause the data processing system to:

receive updated time series data;

generate an updated forecasted output for each of the optimized forecasting models utilizing the updated time series data; and

generate an updated weighted average of the updated forecasted outputs using the normalized weighting factors.

33. The computer program product of claim 21, further comprising instructions configured to cause the data processing system to:

use an Akaike Information Criterion for the information criteria value.

34. The computer program product of claim 33, further comprising instructions configured to cause the data processing system to:

calculate the Akaike Information Criterion (AIC) according to;

AIC=−

2ln(L)+2·

P,

wherein L is a likelihood value corresponding to the optimized forecasting model; and

wherein P is a number of fitted parameters in the optimized forecasting model.

35. The computer program product of claim 33, further comprising instructions configured to cause the data processing system to:

calculate the Akaike Information Criterion (AIC) according to;

AIC=n·

ln(mse)+2·

P,

wherein mse is a mean squared error;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

36. The computer program product of claim 21, wherein the information criteria value is an adjusted Akaike Information Criterion (AICc), the method further comprising instructions configured to cause the data processing system to:

calculate the adjusted Akaike Information Criterion (AICc) according to;

AICc=AIC+(2·

P·

(P+1))/(n−

P−

1),

wherein AIC is an Akaike Information Criterion for the optimized forecasting model;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

37. The computer program product of claim 21, wherein the information criteria value is a Bayesian Information Criterion (BIC), the method further comprising instructions configured to cause the data processing system to:

calculate the Bayesian Information Criterion (BIC) according to;

BIC=−

2·

ln(L)+ln(n)·

P,

wherein L is a likelihood value corresponding to the optimized forecasting model;

wherein n is a number of data points for which the optimized forecasting model is calibrated; and

wherein P is a number of fitted parameters in the optimized forecasting model.

38. The computer program product of claim 21, further comprising instructions configured to cause the data processing system to:

compute the raw weights (wraw) according to;

wraw=exp(−

Δ

/2),

wherein Δ

is the information criteria delta value.

39. The computer program product of claim 21, further comprising instructions configured to cause the data processing system to:

compute the raw weights (wraw) according to;

wraw=exp(λ

·

−

Δ

/2),

wherein Δ

is the information criteria delta value; and

wherein λ

is an adjustment factor.