Computer implemented method for estimating age-period-cohort models on account-level data
A computer-implemented method and invention for calculating a loan-level model with the age, period, and cohort functions found in the structure of an Age-Period-Cohort models. The invention uses one observation per account per time period, processed with a uniquely structured set of basis functions, so that the model may be estimated with either Generalized Linear Models (GLM) or Generalized Linear Mixed Models (GLMM). The model created by the invention may be used for account-level forecasting or stress testing of the defined performance variable if the historic extrapolation of the period function is detrended, the age and cohort functions are re-estimated appropriately, and a suitable scenario for the future of the period function. Scores may also be created by combining traditional scoring inputs with an account-level offset computed as the sum of the age and period functions at each time point.
1. A machine for estimating the future behavior of accounts, in which the machine incorporates an offset that improves the robustness and stability out of sample and results in a system that is better able to predict the probability of events for longer periods of time than known systems, the machine comprising:
a computer system for receiving and processing account data for a plurality of individual accounts, which includes at least two of the three values of the account origination date (cohort), observation date that said accounts were observed for each account (period) and the age of each of said accounts (age);
an engine for receiving and processing said account data and providing estimates of one or more of three parametric functions of age, period and cohort:
wherein said computer system is configured to use said parametric functions to predict the behavior of said accounts using parametric functions of age and period to compute account-level offsets and creating scores of account specific behavior using the account-level offsets in order to predict the account behavior with increased stability for longer periods of time and enabling the system to be used for a broader range of applications, and
wherein said engine is configured to utilize orthonormal basis functions for estimating any of said parametric functions, wherein only one of said basis functions includes a constant term and only two of the basis functions include linear terms.
2. The machine as recited in claim 1 , wherein said engine utilizes orthonormal basis functions for estimating said functions, wherein said basis functions include constant and linear terms.
3. The machine as recited in claim 1 , wherein said engine utilizes spline basis functions for estimating said functions, wherein said spline functions have a total of one constant term and two linear terms.
4. The machine as recited in claim 1 , wherein said engine utilizes non-parametric functions for estimating said functions of age, period and cohort, wherein said non-parametric functions have a total of one constant term and two linear terms.
5. The machine as recited in claim 1 , wherein said engine takes into consideration a random effects term on the account number.
6. The machine as recited in claim 2 , wherein said engine takes into consideration a random effects term on the account number.
7. The machine as recited in claim 3 , wherein said engine takes into consideration a random effects term on the account number.
8. The machine as recited in claim 1 , wherein said future behavior includes account response to stress testing.
9. The machine as recited in claim 1 , wherein said engine is configured to compute an account-level offset for creating scores as a function of age and period functions.
10. The machine as recited in claim 1 , wherein said engine is configured to stabilize the estimation of the period function and adjust the age and cohort functions to compensate based upon additional economic data.
11. The machine as recited in claim 1 wherein said engine is configured to create scores for each account based upon said account specific behavior.
12. The machine as recited in claim 1 , wherein said engine utilizes parametric functions for estimating said functions of age, period and cohort.
13. The machine as recited in claim 1 , wherein said engine is configured to forecast future behavior of said accounts using the parametric functions and historical macroeconomic data and wherein the engine is configured to use additional historical macroeconomic data to stabilize the estimation of the period function and adjust the age and cohort functions to compensate.