A generalized autoregressive integrated moving average (ARIMA) model for use in predictive analytics of time series is based upon creating all possible ARIMA models (by knowing a priori the largest possible values of the p, d and q parameters forming the model), and utilizing the results of at least two different performance measures to ultimately choose the ARIMA(p,d,q) model that is most appropriate for the time series under study. The method of the present invention allows each parameter to range over all possible values, and then evaluates the complete universe of all possible ARIMA models based on these combinations of p, d and q to find the specific p, d and q parameters that yield the “best” (i.e., lowest value) performance measure results. This generalized ARIMA model is particularly useful in predicting future operating hours of power plants and scheduling maintenance events on the gas turbines at these plants.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method of scheduling events for industrial equipment using an autoregressive integrated moving average (ARIMA) model for predicting future operating hours based on a times series of past operating hours of the industrial equipment, comprising defining a maximum possible value for each parameter p, d, q of an ARIMA(p,d,q) model, p defining a number of autoregressive terms to include in the ARIMA model, d defining a number of differencing operations to perform in the ARIMA model, and q defining a number of moving average terms to include in the ARIMA model, the maximum possible values identified as pr, dr, and qr; for all possible combinations of p from 0 to pr, d from 0 to dr, and q from 0 to qr, performing the following steps: determining a set of ARIMA coefficients associated with a training interval of the time series; predicting a set of N future hours based on the determined coefficients; computing at least one performance measure of the predicted set of N future operating hours with respect to actual time series data; and ranking all possible combinations of ARIMA(p,d,q) based on the computed performance measures; selecting a preferred set of (p, d, q) parameters based on the ranking; generating a predicted future time series of industrial operating hours using the selected ARIMA(p,d,q) model; and scheduling events based on the predicted future operating hours. 2. The method of claim 1, wherein the at least one performance measure is selected from the group consisting of: MAPE, SMAPE, MAE, and SSE. 3. The method of claim 1, wherein at least two different performance measures are computed for each possible ARIMA model. 4. The method of claim 1, wherein the ranking step creates a listing of all possible ARIMA models from the smallest value to the largest value of performance measure, for each computed performance measure. 5. The method of claim 1, wherein the ARIMA(p,d,q) model used in the analysis is the wavelet-ARIMA(p,d,q) model. 6. The method of claim 5, wherein the wavelet-ARIMA(p,d,q) module used in the analysis is the Daubechies wavelet transform. 7. A computer program product comprising a non-transitory computer readable recording medium having recorded thereon a computer program comprising instructions for, when executed on a computer, instructing said computer to perform a method for scheduling events associated with industrial equipment, using an autoregressive integrated moving average (ARIMA) model for predicting future operating hours based on past operating hours of the industrial equipment, comprising defining a maximum possible value for each parameter p, d, q of an ARIMA(p,d,q) model, p defining a number of autoregressive terms to include in the ARIMA model, d defining a number of differencing operations to perform in the ARIMA model, and q defining a number of moving average terms to include in the ARIMA model, the maximum possible values identified as pr, dr, and qr; for all possible combinations of p from 0 to pr, d from 0 to dr, and q from 0 to qr, performing the following steps: determining a set of ARIMA coefficients associated with a training interval of the time series; predicting a set of N future hours based on the determined coefficients; computing at least one performance measure of the predicted set of N future operating hours with respect to actual time series data; and ranking all possible combinations of ARIMA(p,d,q) based on the computed performance measures; selecting a preferred set of (p, d, q) parameters based on the ranking; generating a predicted future time series of industrial operating hours using the selected ARIMA(p,d,q) model; and scheduling events based on the predicted future operating hours. 8. The computer program product of claim 7, wherein the at least one performance measure is selected from the group consisting of: MAPE, SMAPE, MAE, and SSE. 9. The computer program product of claim 7, wherein at least two different performance measures are computed for each possible ARIMA model. 10. The computer program product of claim 7, wherein the ranking step creates a listing of all possible ARIMA models from the smallest value to the largest value of performance measure, for each computed performance measure. 11. The computer program product of claim 7, wherein the ARIMA(p,d,q) model used in the analysis is the wavelet-ARIMA(p,d,q) model. 12. The computer program product of claim 11, wherein the wavelet-ARIMA(p,d,q) module used in the analysis is the Daubechies wavelet transform. 13. A method of scheduling gas turbine maintenance events using an autoregressive integrated moving average (ARIMA) model for predicting future gas turbine operating hours based on a times series of past operating hours of the gas turbine, comprising defining a maximum possible value for each parameter p, d, q of an ARIMA(p,d,q) model, p defining a number of autoregressive terms to include in the ARIMA model, d defining a number of differencing operations to perform in the ARIMA model, and q defining a number of moving average terms to include in the ARIMA model, the maximum possible values identified as pr, dr, and qr; for all possible combinations of p from 0 to pr, d from 0 to dr, and q from 0 to qr, performing the following steps: determining a set of ARIMA coefficients associated with a training interval of the time series; predicting a set of N future operating hours based on the determined coefficients; computing at least one performance measure of the predicted set of N future operating hours with respect to actual time series data; and ranking all possible combinations of ARIMA(p,d,q) based on the computed performance measures; selecting a preferred set of (p, d, q) parameters based on the ranking; generating a predicted future time series of gas turbine operating hours using the selected ARIMA(p,d,q) model; and scheduling gas turbine maintenance events based on the predicted future time series of gas turbine operating hours. 14. The method as defined in claim 13 wherein the scheduled maintenance inventions comprises a set of disassembly maintenance events, each disassembly maintenance event to be scheduled after a predetermined number of operating hours. 15. The method as defined in claim 14 where the set of disassembly maintenance events includes a combustion inspection, hot gas path inspection and a major inspection. 16. The method as defined in claim 15 wherein the combustion inspection is scheduled more frequently than the hot gas path inspection, which is scheduled more frequently than the major inspection. 17. The method as defined in claim 16 wherein the combustion inspection is scheduled about every 8000 operating hours of the gas turbine, the hot gas path inspection is scheduled ever 16,000 operating hours, and the major inspection is scheduled every 32,000 operating hours. 18. The method of claim 13, wherein the at least one performance measure is selected from the group consisting of: MAPE, SMAPE, MAE, and SSE. 19. The method of claim 13, wherein at least two different performance measures are computed for each possible ARIMA model. 20. The method of claim 13, wherein the ARIMA(p,d,q) model used in the analysis is the wavelet-ARIMA(p,d,q) model. 21. The method of claim 20, wherein the wavelet-ARIMA(p,d,q) module used in the analysis is the Daubechies wavelet transform.