Computer-implemented systems and methods for processing time series data

• US 7,716,022 B1
• Filed: 05/09/2006
• Issued: 05/11/2010
• Est. Priority Date: 05/09/2005
• Status: Active Grant

• Current Assignee: SAS Institute Incorporated
• Original Assignee: SAS Institute Incorporated
• Inventors: Park, Youngjin, Chang, Ming-Chun, Selukar, Rajesh S., Leonard, Michael J.
• Primary Examiner(s): FREJD, RUSSELL WARREN
• Application Number:
  US11/431,116
• Time in Patent Office: 1,463 Days
• Field of Search: 703/2, 703/22, 702/181, 702/189
• US Class Current: 703/2
• CPC Class Codes: G06F 17/18 for evaluating statistical data , e.g. average values, frequency distributions, probability functions, regression analysis forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04
• CPC Class Codes: G06Q 10/10 Office automation; Time management
• CPC Class Codes: G06Q 30/0201 Market modelling; Market analysis; Collecting market data
• CPC Class Codes: G06Q 30/0202 Market predictions or forecasting for commercial activities

Abstract

Computer-implemented systems and methods for providing a forecast using time series data that is indicative of a data generation activity occurring over a period of time. Candidate models and candidate input variables are received. For each candidate model, transfer functions are determined for the candidate input variables in order to relate a variable to be forecasted to the time series data. For each candidate model there is a selection of which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions. A model is selected from the candidate models to forecast the time series data using the selected input variables of the selected model.

Claims

1. A computer-implemented method to provide one or more model specifications using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

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

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data, wherein determining transfer functions includes determining delay for each regressor;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

2. The method of claim 1, wherein selecting a model to forecast the time series data includes:

determining families of ARIMA and UCM models; and

choosing a reference model from ARIMA and UCM models.

3. The method of claim 2, further comprising:

for ARIMA models, determining a functional transformation and stationary transformation for a variable to be forecasted to the time series data; and

determining regular and seasonal autoregressive and moving average polynomials.

4. The method of claim 2, further comprising:

for UCM models, determining a functional transformation for a variable to be forecasted to the time series data; and

determining level, slope, and seasonal components.

5. The method of claim 1, wherein the plurality of candidate models includes an ARIMA reference model, and wherein determining transfer functions from an ARIMA reference model includes:

determining a functional transformation and stationary transformation for

each regressor;

determining delay for each transformed regressor; and

determining simple numerator and denominator polynomial orders for each transformed regressor.

6. The method of claim 1, wherein the plurality of candidate models includes a white noise reference model, and wherein determining transfer functions from a white noise reference model includes:

determining a functional transformation and stationary transformation for each regressor;

determining delay for each transformed regressor;

determining simple numerator and denominator polynomial orders for each transformed regressor; and

determining the disturbance ARMA polynomials.

7. The method of claim 1, wherein the plurality of candidate models include a UCM reference model, and wherein determining transfer functions from a UCM reference model includes:

determining a functional transformation for each regressor;

determining delay for each functional transformed regressor;

determining of the level, slope, seasonal, and cycle components.

8. The method of claim 1, wherein the determining of the transfer functions includes determining simple numerator and denominator polynomial orders for each regressor.

9. The method of claim 1, wherein the selection of the candidate input variables is based upon computing cross-correlations between a variable to be forecast and each of the candidate input variables, the method further comprising:

using the computed cross-correlations to determine a significant lag that is zero or larger for a candidate input variable; and

wherein if no delay lag is significant for a candidate input variable, then the candidate input variable is not included in the generated model.

10. The method of claim 9, wherein the selection of the candidate input variables is based upon computing cross-correlations between first residuals and second residuals;

wherein the first residuals are determined by estimating residuals resulting from determining a model for a candidate input variable; and

wherein the second residuals are determined by estimating residuals resulting from prewhitening the variable to be forecast using the model determined from the candidate input variable.

11. The method of claim 1, wherein the model determined for the candidate input variable is an ARIMA model.

12. The method of claim 1, wherein the selection of the candidate input variables is based upon computing cross-correlations between residuals resulting from fitting a model for a candidate input variable and from pre-whitening the variable to be forecast using the fitted model.

13. The method of claim 12, further comprising:

using the computed cross-correlations to determine a significant lag that is zero or larger for a candidate input variable;

wherein if no delay lag is significant for a candidate input variable, then the candidate input variable is not included in the generated model.

14. The method of claim 1, further comprising:

performing outlier detection with respect to each of the candidate models;

for a detected outlier, creating dummy regressors for use in forecasting the time series data.

15. The method of claim 14, wherein detected outliers are selected from the group consisting of additive outliers, level shift outliers and combinations thereof.

16. The method of claim 1, further comprising:

storing the selected model in a model repository.

17. The method of claim 1, wherein the candidate input variables comprise one or more events.

18. A computer-implemented system to provide a forecast using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

one or more processors;

a computer-readable storage medium containing instructions configured to cause the one or more processors to perform operations, the instructions including;

input software instructions to receive a plurality of candidate models and a plurality of candidate input variables;

software instructions to determine, for each candidate model, transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data, wherein determining transfer functions includes determining delay for each regressor;

variable selection software instructions to automatically select for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions; and

model selection software instructions to automatically select a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

19. Computer software stored on one or more computer-readable storage mediums, the computer software comprising program code for carrying out a method to provide a forecast using time series data that is indicative of a data generation activity occurring over a period of time, the method comprising:

receiving a plurality of candidate models;

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data, wherein determining transfer functions includes determining delay for each regressor;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

20. A computer-implemented method to provide one or more model specifications using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

receiving a plurality of candidate models;

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions, wherein the selection of the candidate input variables is based upon computing cross-correlations between residuals resulting from fitting a model for a candidate input variable and from pre-whitening the variable to be forecast using the fitted model; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

21. A computer-implemented system to provide a forecast using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

one or more processors;

a computer-readable storage medium containing instructions configured to cause the one or more processors to perform operations, the instructions including;

input software instructions to receive a plurality of candidate models and a plurality of candidate input variables;

software instructions to determine, for each candidate model, transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data;

variable selection software instructions to automatically select for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions, wherein the selection of the candidate input variables is based upon computing cross-correlations between residuals resulting from fitting a model for a candidate input variable and from pre-whitening the variable to be forecast using the fitted model; and

model selection software instructions to automatically select a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

22. Computer software stored on one or more computer-readable storage mediums, the computer software comprising program code for carrying out a method to provide a forecast using time series data that is indicative of a data generation activity occurring over a period of time, the method comprising:

receiving a plurality of candidate models;

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions, wherein the selection of the candidate input variables is based upon computing cross-correlations between residuals resulting from fitting a model for a candidate input variable and from pre-whitening the variable to be forecast using the fitted model; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

23. A computer-implemented method to provide one or more model specifications using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

receiving a plurality of candidate models;

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions;

performing outlier detection with respect to each of the candidate models;

for a detected outlier, creating dummy regressors for use in forecasting the time series data; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

24. A computer-implemented system to provide a forecast using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

one or more processors;

a computer-readable storage medium containing instructions configured to cause the one or more processors to perform operations, the instructions including;

input software instructions to receive a plurality of candidate models and a plurality of candidate input variables;

software instructions to determine, for each candidate model, transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data;

variable selection software instructions to automatically select for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions;

outlier detection software instructions to perform outlier detection with respect to each of the candidate models, wherein for each detected outlier, dummy regressors are created for use in forecasting the time series data; and

model selection software instructions to automatically select a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

25. Computer software stored on one or more computer-readable storage mediums, the computer software comprising program code for carrying out a method to provide a forecast using time series data that is indicative of a data generation activity occurring over a period of time, the method comprising:

receiving a plurality of candidate models;

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions;

performing outlier detection with respect to each of the candidate models;

for a detected outlier, creating dummy regressors for use in forecasting the time series data; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

26. A computer-implemented method to provide one or more model specifications using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

receiving a plurality of candidate models;

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data, wherein the plurality of candidate models includes an ARIMA reference model, and wherein determining transfer functions from an ARIMA reference model includes;

determining a functional transformation and stationary transformation for each regressor,

determining delay for each transformed regressor, and

determining simple numerator and denominator polynomial orders for each transformed regressor;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

27. A computer-implemented method to provide one or more model specifications using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

receiving a plurality of candidate models;

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data, wherein the plurality of candidate models include a white noise reference model, and wherein determining transfer functions from a white noise reference model includes;

determining a functional transformation and stationary transformation for each regressor,

determining delay for each transformed regressor, determining simple numerator and denominator polynomial orders for each transformed regressor, and

determining the disturbance ARMA polynomials;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.

28. A computer-implemented method to provide one or more model specifications using time series data that is indicative of a data generation activity occurring over a period of time, comprising:

receiving a plurality of candidate models;

receiving a plurality of candidate input variables;

for each candidate model, determining transfer functions for the candidate input variables in order to relate a variable to be forecasted to the time series data, wherein the plurality of candidate models include a UCM reference model, and wherein determining transfer functions from a UCM reference model includes;

determining a functional transformation for each regressor,

determining delay for each functional transformed regressor, and

determining of the level, slope, seasonal, and cycle components;

automatically selecting for each candidate model which of the candidate input variables to include in each of the candidate models based upon the determined transfer functions; and

automatically selecting a model from the candidate models to forecast the time series data using the selected candidate input variables of the selected model.