Information Criterion-Based Systems And Methods For Constructing Combining Weights For Multimodel Forecasting And Prediction

• US 20090319310A1
• Filed: 06/20/2008
• Published: 12/24/2009
• Est. Priority Date: 06/20/2008
• Status: Active Grant

• Current Assignee: SAS Institute Incorporated
• Original Assignee: SAS Institute Incorporated
• Inventors: Little, Mark Roland
• Granted Patent: US 8,374,903 B2
• Time in Patent Office: Days
• US Class Current: 705/7
• 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 automatically generating a weighted average forecast model comprising:

receiving a plurality of forecasting models;

receiving time series data;

optimizing at least one parameter of each of the received forecasting models utilizing the received time series data;

generating a weighting factor 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

storing the generated weighting factors in a computer-readable medium.

2. The method of claim 1, further comprising:

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

outputting a weighted average of the forecasted output from each of the optimized forecasting models by weighting each of the forecasted outputs according to the generated weighting factor.

3. The method of claim 1, further comprising:

receiving updated time series data;

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

outputting a weighted average of the forecasted output from each of the optimized forecasting models by weighting each of the forecasted outputs according to the stored weighting factor.

4. The method of claim 3, wherein the receiving updated time series data, generating a forecasted output, and outputting a weighted average are repeated over a plurality of time periods.

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

6. The method of claim 2, wherein the method is repeated a plurality of times such that the automatic forecasting is executed for a plurality of stock keeping units.

7. The method of claim 1, wherein an information criterion type to be utilized is automatically selected.

8. The method of claim 1, wherein the time series data includes data representative of operating a physical system over a period of time.

9. The method of claim 8, wherein the physical system is a system selected from the group consisting of a manufacturing system, a grocery store chain, a retail store chain, and combinations thereof.

10. The method of claim 1, wherein the at least one parameter of each of the received forecasting models is optimized according to a least squares regression.

11. The method of claim 1, wherein the information criteria value utilized for each of the weighting factors is an Akaike Information Criterion.

12. The method of claim 11, wherein the Akaike Information Criterion (AIC) is calculated according to the formula:

AIC=−

2ln(L)+2·

P,

wherein ln(L) is a natural log of a likelihood of the optimized forecasting model; and

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

13. The method of claim 11, wherein the Akaike Information Criterion (AIC) is calculated according to the formula:

AIC=n·

ln(mse)+2·

P,

wherein ln(mse) is a natural log of mean squared error;

wherein n is a number of data points to 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, wherein the information criteria weight value utilized in generating the weighting factor for each of the optimized forecasting models is an adjusted Alkaike Information Criterion (AICc) calculated according to the formula:

AICc=AIC+(2·

P·

(P+1))/(n−

P−

1),

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

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

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

15. The method of claim 1, wherein the information criteria weight value utilized in generating the weighting factor for each of the optimized forecasting models is an Bayesian Information Criterion (BIC) calculated according to the formula:

BIC=−

2·

ln(L)+ln(n)·

P,

wherein ln(L) is a natural log of a likelihood of the optimized forecasting model;

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

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

16. The method of claim 1, wherein generating a weighting factor for each of the plurality of optimized forecasting models utilizing an information criteria value indicating fit quality of each of the optimized forecasting models further comprises:

calculating an information criteria delta value for each of the optimized forecasting models indicating a difference between the information criteria value for each optimized forecasting model and a lowest information criteria value calculated for the optimized forecasting models;

calculating raw weights for each of the optimized forecasting models based on the corresponding calculated information criteria delta value; and

calculating normalized weights for each of the optimized forecasting models based on the corresponding calculated raw weight.

17. The method of claim 16, wherein the raw weights (w_raw) are computed according to the formula:

w_raw=exp(−

Δ

/2),

wherein Δ

is the calculated information criteria delta for an optimized forecasting model.

18. The method of claim 16, wherein the raw weights (w_raw) are computed according to the formula

w_raw=exp(λ

·

−

Δ

/2)

wherein Δ

is the calculated information criteria delta for an optimized forecasting model; and

wherein λ

is an adjustment factor that adjusts the raw weights such that equal weights are assigned to all optimized forecast models as selected values for λ

approach zero;

a weight of one is assigned to the optimized forecasting model with a lowest calculated information criteria value with weights of zero for all other optimized forecasting models as values much greater than one are selected; and

weights exhibiting hybrid characteristics are assigned to the optimized forecasting models for values in between.

19. The method of claim 16, wherein the adjustment factor, λ

, is user selected.

20. The method of claim 1, wherein the information criteria value further indicates model complexity of each of the optimized forecasting models.

31. The method of claim 1, wherein the generated weighting factors are stored in a random access memory.

32. The method of claim 2, wherein the outputted weighted average is indicative of a forecasted future values for a business activity selected from the group consisting of:

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

33. The method of claim 2, wherein the outputted weighted average is indicative of a forecasted future value over a time period selected from the group consisting of:

calendar years, fiscal years, quarters of years, moths, weeks, days, hours, minutes, seconds, and combinations and multiples thereof.

21. An automatic forecasting system, comprising:

a plurality of forecasting models;

a file containing time series data indicative of transactional activity;

a model fitter configured to receive the plurality of forecasting models and the file of time series data and to optimize at least one parameter of each of the plurality of forecasting models based on the file of time series data; and

a model evaluator configured to receive the plurality of optimized forecasting models and to generate a weighting factor utilizing an information criteria for each of the optimized forecasting models indicating fit quality of each of the optimized forecasting models.

22. The automatic forecasting system of claim 21, further comprising:

a forecast calculator configured to receive the plurality of optimized forecasting models and to generate a forecasted output for each of the plurality of optimized forecasting models; and

a weighted average calculator configured to receive the forecasted outputs calculated for each of the plurality of optimized forecasting models and corresponding weighting factors and to compute and output a weighted average of the forecasted outputs by weighting each of the forecasted outputs according to the generated weighting factor.

23. The automatic forecasting system of claim 21, further comprising:

a data store configured to receive and store the generated weighting factors such that the forecast calculator is run with updated time series data to produce a plurality of forecast outputs;

wherein the plurality of forecast outputs are combined with the stored generated weighting factors to calculate a weighted average of the forecasted outputs.

24. The automatic forecasting system of claim 22, wherein the weighted average calculator is configured to output a weighted average indicating forecasted sales of a product.

25. The automatic forecasting system of claim 21, wherein the automatic forecasting system is configured to operate repeatedly such that forecasts for a plurality of stock keeping units are outputted.

26. The automatic forecasting system of claim 21, wherein the model evaluator is configured to receive user input for selecting the information criteria type to be utilized.

27. The automatic forecasting system of claim 21, wherein the file containing time series data includes data representative of operating a physical system over a period of time.

28. The automatic forecasting system of claim 27, wherein the physical system is a system selected from the group consisting of a manufacturing system, a grocery store chain, a retail store chain, and combinations thereof.

29. The automatic forecasting system of claim 21, wherein the information criteria calculated is a Akaike Information Criterion.

30. The automatic forecasting system of claim 21, wherein the information criteria for each of the optimized forecasting models further indicates model complexity.