CN117522562A - Credit scale prediction model based on kernel density estimation - Google Patents

Abstract

The invention discloses a credit scale prediction model based on nuclear density estimation, which predicts the influence of factor fluctuation on credit scale variation by using microscopic detail loan data of past years, and comprises the following steps: s1, determining a future loan distribution function; s2, predicting the number of loan clients in the future; s3, carrying out random simulation by using a sampling method; the loan is classified into personal loan, enterprise loan, inter-bank loan, foreign administrative office and central bank loan. The credit scale prediction model based on the kernel density estimation realizes that the change trend of future credit data is accurately captured by utilizing microscopic detail loan data of the past year, and is displayed in a function fluctuation mode, so that the problem of low prediction precision caused by large macroscopic prediction granularity is avoided, and the random simulation method can ensure that the simulation result fully approaches to the real result under the condition of enough simulation times.

Description

Credit scale prediction model based on kernel density estimation

Technical Field

The invention relates to the technical field of credit prediction, in particular to a credit scale prediction model based on nuclear density estimation.

Background

Credit business, also called as credit property or loan business, is the most important property business of commercial banks, and benefits are obtained by paying and withdrawing principal and interest and deducting costs, so credit is the main profit-making means of commercial banks. In recent years, each large commercial bank is developing loan business, and the scale of credit is expanding. However, once the credit is oversized, the bank capital adequacy is reduced, thereby affecting the liquidity of the bank funds. It is therefore necessary to predict and understand the trend of credit size changes, which is beneficial to help banks formulate relevant loan policies and prepare abundant funds to deal with the funds squeeze brought by credit.

At present, the analysis method of loan scale trend mainly comprises trend analysis, period analysis, regression analysis, gray system analysis and the like, which are all based on macroscopic data for analysis, and the problem of low calculation precision exists.

Disclosure of Invention

The invention aims to solve the problems and provide a credit scale prediction model based on kernel density estimation.

A credit scale prediction model based on kernel density estimation, which predicts the influence of factor fluctuation on credit scale variation by using microscopic detail loan data over the years, comprising the steps of:

s1: determining a future loan distribution function;

s2: predicting the number of loan clients in the future;

s3: performing random simulation by using a sampling method;

the loan is divided into personal loan x ⁽¹⁾ Enterprise loan x ⁽²⁾ Loan x between banks ⁽³⁾ Loan x to foreign administration and central bank ⁽⁴⁾ 。

Further, a credit scale prediction model based on kernel density estimation, said step S1 comprises the sub-steps of:

s11: simulating probability distribution on detail data of each classified loan in the past year by a nuclear density estimation method;

s12: observing probability distribution of credit cost of each category in different years, and analyzing the changed track and trend;

s13: and creating a loan scale variation distribution function of the future year according to the track and the trend.

Further, a credit scale prediction model based on kernel density estimation, step S11 comprises the sub-steps of:

s111: is provided withFor sample data of previous person loan amount of the t-th year, the core density estimation formula of the loan cost is:

wherein the method comprises the steps ofRepresents the overall density function +.>Is a kernel estimate of (1);

wherein t represents year;

where k (x) represents the kernel function, n represents the number of samples, _i representing the variables in the sum-of-terms formula, i=1, 2 … … n;

wherein h is _n Represents bandwidth, h _n >0 is a parameter related to n;

s112: and verifying the parameter with highest precision on the set in the selection of the bandwidth by using a network searching method in machine learning, and obtaining the optimal probability distribution.

Further, a credit scale prediction model based on kernel density estimation, said step S2 comprises the sub-steps of:

s21: classifying loan clients according to a kernel density estimation method;

s22: establishing the number of loan clients by using a gray prediction model;

s23: and analyzing the law of the residual error of the gray prediction model, and correcting the variation value of the residual error to improve the precision of the gray prediction model.

Further, a credit scale prediction model based on kernel density estimation, said step S22 comprises the sub-steps of:

s221: the number of people loan clients in the previous s years is calculated, and the formula is as follows:

wherein N is ⁽¹⁾ Representing the number of loan clients for the previous s years, s representing the time of the last year;

s222: for N ⁽¹⁾ Accumulating to weaken the volatility and randomness of the random sequence, and generating new data, wherein the formula is as follows:

wherein M is ⁽¹⁾ The loan client number sequence of the previous s years after correction;

wherein the method comprises the steps ofRepresents the kth element in the sequence of post-loan client numbers, k representing the past year time;

s223: by M ⁽¹⁾ Generating a neighbor average value equal weight sequence, wherein the formula is as follows:

wherein Z is ⁽¹⁾ Represents the neighbor average value equal weight sequence,represents the kth element in the neighbor mean value equal weight series;

s224: setting M ⁽¹⁾ Ash of (2)The derivative, the formula:

wherein d (k) represents M ⁽¹⁾ Is a gray derivative of (2);

s225: according to the grey theory pair M ⁽¹⁾ A gray differential model GM (1, 1) is built for k, the formula:

wherein a and u represent undetermined parameters;

s226: setting a whitening equation, wherein the formula is as follows:

s227: obtaining undetermined parameters a and u by using a least square method according to initial conditionsAcquiring an event response sequence of a gray differential equation, wherein the formula is as follows:

wherein the method comprises the steps ofAn event response sequence representing a gray differential equation;

s228: the event response sequence of the gray differential equation is subtracted to obtain a reduction predicted value, and the formula is as follows:

wherein the method comprises the steps ofIs a reduction predicted value;

s229: replacing k with future year time, obtaining future prediction of the number of individual loan clients, and obtaining future prediction of the number of enterprise loan clients in the same wayInter-bank loan client number prediction ∈>Loan of foreign government and central bank>

Further, a credit scale prediction model based on kernel density estimation, the step S3 substep includes:

s31: prediction of personal credit customer number based on future year tProduction of->Random number subject to distribution->Simulating future t-th loan data, and obtaining the sum of the once simulated personal credit fees, wherein the formula is as follows:

wherein the method comprises the steps ofRepresenting the sum of individual credit fees for a simulation, j representing the variable in the sum-term formula,/>

S32: performing multiple simulation to obtainThe total amount of the personal credit cost is predicted for m times, the final total amount of the personal credit cost prediction in the t th year is obtained, and the formula is as follows:

wherein the method comprises the steps ofRepresenting the total amount of personal credit cost prediction, and m represents the number of predictions;

s33: obtaining an enterprise credit fee prediction total in the same mannerInter-bank credit fee predictive total +.>Loan fee forecast total amount of foreign government and central bank>Obtaining a final t-th credit cost prediction total;

the formula is:

wherein the method comprises the steps ofRepresenting the sum of the t-th credit cost predictions, l represents the variables in the sum-term formula and l=1, 2, 3, 4.

The invention has the beneficial effects that: the credit scale prediction model based on the kernel density estimation realizes that the change trend of future credit data is accurately captured by utilizing microscopic detail loan data of the past year, and is displayed in a function fluctuation mode, so that the problem of low prediction precision caused by large macroscopic prediction granularity is avoided, and the random simulation method can ensure that the simulation result fully approaches to the real result under the condition of enough simulation times.

Drawings

Fig. 1 is a flow chart of the present invention.

Detailed Description

For a clearer understanding of technical features, objects, and effects of the present invention, a specific embodiment of the present invention will be described with reference to the accompanying drawings.

As shown in FIG. 1, there is a large difference in the corresponding loan sizes considering the difference in the credit objects, and thus the loans are divided into individual loans x ⁽¹⁾ Enterprise loan x ⁽²⁾ Loan x between banks ⁽³⁾ Loan x to foreign administration and central bank ⁽⁴⁾ 。

First, a future loan distribution function is determined, the probability distribution of each classified loan over the years is simulated by a kernel density estimation method (KDE), if usedSample data representing the previous person's loan amount at the t-th year, the estimated formula for the loan cost core density may be noted as:

wherein the method comprises the steps ofCalled overall densityDegree function->Is represented by k (x), h _n >0 denotes a parameter related to the number of samples n, called bandwidth. Generally, k (x) uses a standard normal distribution function, the highest-precision parameter on a verification set is found by using a GridSearchCV method in machine learning with respect to bandwidth selection, so that optimal probability distribution is obtained, and the variation track and trend of each category of credit cost in different years are analyzed by observing the probability distribution of each category of credit cost in different years, so that a loan scale variation distribution function in future years is obtained.

And a second step of: predicting the future number of loan clients, and classifying the loan clients according to the first step method in order to be consistent with the caliber of the loan distribution determination method. Since the change of the number of loan subscribers is influenced by economic and market factors, the characteristics of uncertainty of gray prediction model (GM) information and small data volume requirement are satisfied. Meanwhile, if the precision of the prediction model is not ideal enough, the residual rule can be analyzed, the residual rule can be found, and the change value of the residual is corrected to improve the precision of the model. Taking the example of a personal loan client number prediction, assume thatRepresenting the number of loan clients for the previous s years, for N ⁽¹⁾ Accumulating to attenuate possible volatility and randomness of random sequence, generating new data +.>Wherein:

then utilize M ⁽¹⁾ Generating a neighbor mean equal weight sequenceWherein:

definition M ⁽¹⁾ The gray derivatives of (2) are:

according to the grey theory pair M ⁽¹⁾ A gray differential model for k, GM (1, 1) model, is built:

the corresponding whitening equation is:

obtaining undetermined parameters a and u by using a least square method according to initial conditionsThe event response sequence of the gray differential equation is:

and obtaining a reduction predicted value through accumulation and subtraction:

replacing k with the future year time, so that the future prediction of the number of individual loan clients can be obtained;

and a third step of: and (5) random simulation. Considering the idea that the average value of the sample approaches to the overall average value in the probability theory, and carrying out random modulus by using a sampling methodCredit cost distribution function fitting, i.e. at the known future t-th yearOn the premise of the future t-th personal credit client number prediction +.>Production of->Random number obeying this distribution->For modeling future annual loan data, the sum of the individual credit costs for one simulation is:

can be obtained after multiple simulationsThe sum of personal credit cost prediction for m times is equal, the simulated sample mean value approaches to the total mean value, namely the final predicted loan scale sum, on the premise of sufficiently large simulation according to the law of large numbers>The total is predicted as the final personal credit cost for the t-th year. Loans for other categories are available in accordance with the procedure described above>Final t-th credit fee predictive total ∈>

The credit scale prediction model based on the kernel density estimation realizes that the change trend of future credit data is accurately captured by utilizing microscopic detail loan data of the past year, and is displayed in a function fluctuation mode, so that the problem of low prediction precision caused by large macroscopic prediction granularity is avoided, and the random simulation method can ensure that the simulation result fully approaches to the real result under the condition of enough simulation times.

The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (6)

1. A credit scale prediction model based on kernel density estimation, characterized in that the influence of fluctuation of prediction factors on credit scale variation is utilized by microscopic detail loan data of past years, comprising the following steps:

s1, determining a future loan distribution function;

s2, predicting the number of loan clients in the future;

s3, carrying out random simulation by using a sampling method;

the loan is divided into personal loan x ⁽¹⁾ Enterprise loan x ⁽²⁾ Loan x between banks ⁽³⁾ Loan x to foreign administration and central bank ⁽⁴⁾ 。

2. The credit scale prediction model based on nuclear density estimation according to claim 1, wherein said step S1 comprises the sub-steps of:

s11: simulating probability distribution on detail data of each classified loan in the past year by a nuclear density estimation method;

s12: observing probability distribution of credit cost of each category in different years, and analyzing the changed track and trend;

s13: and creating a loan scale variation distribution function of the future year according to the track and the trend.

3. The credit scale prediction model based on nuclear density estimation according to claim 2, characterized in that step S11 comprises the sub-steps of:

s111: is provided withFor sample data of previous person loan amount of the t-th year, the core density estimation formula of the loan cost is:

wherein the method comprises the steps ofRepresents the overall density function +.>Is a kernel estimate of (1);

wherein t represents year;

where k (x) represents a kernel function, n represents the number of samples, i represents a variable in the sum-of-terms formula, i=1, 2 … … n;

wherein h is _n Represents bandwidth, h _n > 0 is a parameter related to n;

s112: and verifying the parameter with highest precision on the set in the selection of the bandwidth by using a network searching method in machine learning, and obtaining the optimal probability distribution.

4. The credit scale prediction model based on nuclear density estimation according to claim 1, characterized in that said step S2 comprises the sub-steps of:

s21: classifying loan clients according to a kernel density estimation method;

s22: establishing the number of loan clients by using a gray prediction model;

s23: and analyzing the law of the residual error of the gray prediction model, and correcting the variation value of the residual error to improve the precision of the gray prediction model.

5. The credit scale prediction model based on nuclear density estimation according to claim 4, wherein said step S22 comprises the sub-steps of:

s221: the number of people loan clients in the previous s years is calculated, and the formula is as follows:

wherein N is ⁽¹⁾ Representing the number of loan clients for the previous s years, s representing the time of the last year;

s222: for N ⁽¹⁾ Accumulating to weaken the volatility and randomness of the random sequence, and generating new data, wherein the formula is as follows:

wherein M is ⁽¹⁾ The loan client number sequence of the previous s years after correction;

wherein the method comprises the steps ofRepresents the kth element in the sequence of post-loan client numbers, k representing the past year time;

s223: by M ⁽¹⁾ Generating a neighbor average value equal weight sequence, wherein the formula is as follows:

wherein Z is ⁽¹⁾ Represents the neighbor average value equal weight sequence,represents the kth element in the neighbor mean value equal weight series;

s224: setting M ⁽¹⁾ Is calculated by the formula:

wherein d (k) represents M ⁽¹⁾ Is a gray derivative of (2);

s225: according to the grey theory pair M ⁽¹⁾ A gray differential model GM (1, 1) is built for k, the formula:

wherein a and u represent undetermined parameters;

s226: setting a whitening equation, wherein the formula is as follows:

s227: obtaining undetermined parameters a and u by using a least square method according to initial conditionsAcquiring an event response sequence of a gray differential equation, wherein the formula is as follows:

wherein the method comprises the steps ofAn event response sequence representing a gray differential equation;

s228, subtracting the event response sequence of the gray differential equation to obtain a reduction predicted value, wherein the formula is as follows:

wherein the method comprises the steps ofIs a reduction predicted value;

s229: replacing k with future year time, obtaining future prediction of the number of individual loan clients, and obtaining future prediction of the number of enterprise loan clients in the same wayInter-bank loan client number prediction ∈>Loan of foreign government and central bank>

6. The credit scale prediction model based on nuclear density estimation according to claim 1, wherein said step S3 substep comprises:

s31: prediction of personal credit customer number based on future year tProduction of->Random number subject to distribution->Simulating future t-th loan data, and obtaining the sum of the once simulated personal credit fees, wherein the formula is as follows:

wherein the method comprises the steps ofRepresenting the sum of individual credit fees for a simulation, j representing the variable in the sum-term formula,/>

S32: performing multiple simulation to obtainThe total amount of secondary personal credit cost is predicted, the final total amount of personal credit cost prediction in the t th year is obtained, and the formula is as follows:

wherein the method comprises the steps ofRepresenting the total amount of personal credit cost prediction, and m represents the number of predictions;

s33: by the same squareObtaining a predicted total amount of credit fees for an enterpriseInter-bank credit fee predictive total +.>Loan fee forecast total amount of foreign government and central bank>Obtaining a final t-th credit cost prediction total;

the formula is:

wherein the method comprises the steps ofRepresenting the sum of the t-th credit cost predictions, l represents the variables in the sum-term formula and l=1, 2, 3, 4.