Research on Financial Early Warning Based on Combination Forecasting Model

Abstract

Since entering the 21st century, “economic globalization” has become a hot topic. Under the impact of “economic globalization”, the competition of the Chinese domestic market continues to intensify, and Chinese enterprises are facing enormous pressure for survival and development. Among them, there are many cases of poor business operation caused by financial crisis which have directly put these companies in trouble, even causing them to go bankrupt. Therefore, it is very practical to establish a scientific data model to analyze and predict the financial data of enterprises. It can not only monitor the financial status of the enterprise in real time, but also play an effective financial early warning role. This research focuses on using the combined forecasting method to establish a more comprehensive financial early warning model to solve the related financial crisis forecasting problem. Specifically, two different forecasting methods are first adopted in this study to conduct financial early warning research. The first is time series forecasting. It is a dynamic data processing statistical method, which is often used in forecasting research in the business field. The second is the BP neural network algorithm (referred to as BP), which is an error back-propagation learning algorithm, which is often used in the field of artificial intelligence. Then, the prediction error values of the two methods are compared and they are applied to the combined prediction method. Finally, a new error prediction formula is obtained. The result shows that the BP method provides the best performance over others, while the combinational forecasting method offers better performance than any single method.

1. Introduction

With the vigorous development of the capital market, the capital market has become an important place for companies to raise funds, and investors can also obtain higher returns through the operation of the capital market. Therefore, the quality of a company’s financial situation is often the focus of corporate management, investor and creditors. However, market competition is very cruel, and the development of enterprises may also fall into financial crisis. Financial crisis does not happen suddenly; it needs a gradual process to develop. Precursors can be seen before financial crisis, and risk is also predictable [1]. Predicting the financial crisis of an enterprise precisely has great practical significance for protecting the interests of investors and creditors, preventing financial crisis for operators and monitoring the quality of listed companies and securities market risks by government departments.

From the perspective of the essence of the company’s financial situation, it is a dynamic process, and has a certain persistent and cumulative effect. The company’s financial crisis also evolves over time. It is obviously unreasonable to analyze the company’s financial situation from static data alone [2]. Therefore, it is necessary to establish a scientific data model to analyze the company’s financial time series numbers, and to monitor the company’s financial status, so that we can predict the company’s financial crisis accurately, and, thus, have an effective result of financial early warning. There are three contributions to the financial early warning literature in this paper. Firstly, the financial early warning literature is advanced by identifying different financial early warning forecasting studies and integrating the theoretical knowledge and forecasting models of financial early warning. Secondly, the result of the time series forecasting method and the BP neural network algorithm are compared in the paper; thus, the applicable characteristics of the two are obtained. Third, a new method of constructing financial early warning models based on the combined forecasting method is proposed, which expands the research field of financial crisis forecasting.

This article is divided into the following parts. After the introduction, the definition of financial crisis in the theoretical background is discussed in the second part, and different forecasting models of financial early warning research are integrated. The research method and data preprocessing of this paper are introduced in the third part. The fourth part focuses on the construction of data models, data analysis and interpretation. At last, the research conclusions and recommendations of this paper, such as contributions, significance of management and direction of future research, are presented in the fifth part.

Furthermore, this study has more practical implications. Firstly, it helps to improve the awareness and ability of enterprises to prevent crises. Corporate managers conduct real-time calculations on corporate financial data through the financial early warning model formula, identify financial crisis signals in time, and find the cause of the crisis, so that effective measures can be taken in time to respond to the crisis, thereby improving the sensitivity of listed companies on financial early warning and perception. Secondly, it provides investors with a rational and scientific financial decision-making basis. Through the early warning of financial crisis, investors can grasp the operation status of enterprises in time, choosing enterprises with good operation and reputation in which to invest. Third, financial crisis early warning can provide an important reference for government departments and industry associations, which is conducive to optimizing the allocation of market resources and formulating efficient macro policies.

2. Literature Review

Since the 1930s, some scholars have put forward the concept of “financial crisis” for the first time and have carried out relevant exploration and research on this enterprise phenomenon. In 1932, Fitzpatrick first proposed to predict the phenomenon of financial crisis in companies. He selected 19 companies as sample objects, compared the financial ratios of these companies one by one, and constructed a univariate early warning model [3]. Subsequently, William Beaver again proposed to use a single ratio model to conduct early warning research, and used profile analysis, classification inspection and likelihood analysis to conduct prediction experiments, respectively [4]. The results of the study show that the use of multiple comparison methods to identify the financial status of a company is more comprehensive and convincing.

American scholar Edward I. Altman, based on the research results of univariate analysis, took the lead in proposing that the multivariate approach can be used in the field of financial risk prediction, and proposed the famous classic financial early warning model—the Z-score model [3]. In the 1980s, Dutta and Shekhar took the lead in predicting the risk level of listed companies in the process of issuing bonds based on neural network theory. The formal application of neural network theory in financial early warning research was conducted by Odom and Sharda [5]. For the first time, they used neural network algorithm to predict financial crisis. The experimental results show that the accuracy of prediction research using neural network algorithm is as high as 81.81%, while the accuracy of the multivariate discriminant analysis method is 74.28%. The prediction accuracy of the former is significantly higher than that of the latter.

With the wide application of the neural network algorithm, some scholars have carried out financial crisis prediction research from the professional perspective of auditing based on the theoretical basis of the algorithm [6]. In this experiment, 282 companies were selected as sample companies, which were judged by professional auditors. Among them, 188 companies had a high frequency of abnormal financial phenomena in the past 20 years, so they were called “Special Treatment companies”, and the rest were normal companies. According to the criteria for selecting variables of the Z-score model, the researchers screened out the relevant financial ratios in the past three years, then predicted the sorted sample data by the neural network algorithm and the Z-score model, respectively. The study mainly draws two conclusions: firstly, compared with normal companies, financial ratios of abnormal companies changed more greatly during the same period, especially before the announcement of financial crisis, and changes of the ratio showed a significant deterioration. Secondly, although the financial status of the company can present intuitively by the Z-score model, the prediction accuracy of the neural network algorithm is more convincing in terms of predicting performance.

In 1994, Altman and other scholars selected 176 Italian listed companies as samples for the purpose of comparing the differences between neural network algorithms and the linear discriminant method in forecasting research, and then carried out forecasting research, respectively [7]. The research results show that the difference in the prediction effect between the two is not obvious. Although some samples have high accuracy in the operation of the neural network algorithm, some samples are overtrained due to the black box of the algorithm, and the error is relatively large, so the researchers believe that, from the perspective of the overall prediction performance, the linear discriminant method has the advantage of early warning.

The operation process of the entire neural network algorithm can be roughly divided into input layer, hidden layer and output layer. According to the complexity of the prediction problems and the specific characteristics of the sample data, researchers can freely decide the number of hidden layers. The more hidden layers, the more complicated the operation steps are. The single-hidden-layer neural network algorithm is adopted in the above-mentioned studies. On this theoretical basis, Lee et al. boldly selected the financial data of 86 Korean listed companies for bankruptcy prediction of the multi-layer neural network algorithm [8]. They also used the same sample data to conduct a prediction study of the multivariate linear discriminant method. By comparing the results of the studies, they concluded that the predictions made by the neural network algorithm performed better.

Subsequently, many scholars have compared the neural network algorithm with other prediction methods, and most of them believe that the prediction performance of the algorithm is better, and the accuracy is relatively high. Jain and Nag applied the same sample data to two different models of neural network algorithm and multiple logistic regression [9]. The comparison results showed that the former has a higher prediction accuracy rate than the latter in judging whether the financial situation is good or not. Based on the principle of traditional neural network algorithm, Luther combined the genetic algorithm to construct a new financial early warning model for forecasting research, then compared it with the research results obtained by forecasting through the multiple logistic regression model, and it proved again that the neural network algorithm has high prediction accuracy [10].

Although scholars continue to improve and innovate the research methods of financial early warning, the research on the Z-score model in this field has not ended. La Fleur proposed that the Z-score model as a management tool can be applied to the prediction research of enterprise distress [11]. Based on the scoring standard of the financial state of the company, the score of the sample company (Z-value) is calculated. When the Z-value is in the bankruptcy range, it proves that the company has fallen into a crisis state, and managers need to take timely countermeasures to reduce the crisis until the Z-value is in the normal value range, which means that the company’s crisis is relieved [12].

In recent years, some scholars have begun to apply data mining methods in the field of financial early warning. In 2003, Bishop and Mar Molinero proposed that a multi-dimensional scale forecasting model could be constructed to conduct systematic research on financial early warning. This model belongs to a clustering method in the data mining method. The selected research variables can be either quantitative or qualitative. The principle of its application is to research the whole process of an enterprise’s financial crisis as a case study.

According to the influence of time-dependent variables and independent variables on the estimation of model parameters, Marc J. Leclere conducted research on the influencing factors between the two, examined their role in financial distress prediction [13]. The results of the experiment show that the assumptions about time-dependent variables are reasonable, and the prediction performance is better.

By reading the relevant literature, it can be known that scholars have carried out much research on financial early warning, and there are more than 10 methods that can be used to create financial early warning models. Among them, many scholars adopted traditional linear combination forecasting models, such as the time series forecasting method, multiple regression model and logistic model. With the introduction of the concept of “artificial intelligence”, some scholars have combined artificial intelligence technology with forecasting theory to construct several nonlinear combined forecasting models, such as BP, support vector machines and machine learning algorithms.

To sum up, most of the existing research on financial early warning adopted the single forecasting model, and the level of forecasting error varies. Therefore, this study combines traditional forecasting methods with artificial intelligence algorithms, which can not only improve the accuracy of forecasting, but also reduce the risk of forecasting research. Finally, a new financial early warning model is constructed by combining the time series with the forecast results of BP through the combined forecasting method, which improves the forecasting accuracy yet again.

3. Research Design

After comparison with the experience of foreign related research and the domestic research status, it is obvious that the research on financial early warning is not mature enough in China [14]. In view of the different economic systems of Eastern and Western countries, the financial early warning model that has been successfully practiced abroad is not necessarily applicable to domestic listed companies [15]. Therefore, traditional forecasting theories and methods and forecasting methods in the field of big data are combined to create a scientific financial early warning model in this research.

Specifically, the financial variables that have been screened and mathematically counted are forecasted by the traditional time series forecasting method and the cross-domain BP neural network algorithm (back propagation, BP), respectively, then the characteristics of the two methods are compared and analyzed, obtaining the existing error size. Then, the combined forecasting method is used to integrate the two methods to obtain a scientific financial early warning system.

3.1. Methods

3.1.1. Literature Research Method

By reading a large number of domestic and foreign literature articles, the foreign research results were organized and analyzed to clarify the topic, determine the research method and research focus, then draw out the research framework of this study. The significance of using the literature research method is as follows: Firstly, the research status in the field of financial early warning can be understood from relevant domestic and foreign literature, and it can be used as the research background and theoretical basis of the thesis [16]; secondly, the research objects and research scope can be determined according to different measurement standards proposed by different scholars; finally, based on the existing research results, the advantages and disadvantages of their research methods can be compared, and the methods and models suitable for the research can be selected [17].

3.1.2. Qualitative Research Method

By organizing the relevant literature results, the research variables and their relationships were analyzed and discussed theoretically, based on which a research model was constructed and hypotheses put forward. Specifically, the methods of induction and deduction, analysis and synthesis, abstraction and generalization were adopted to summarize the acquired data [18]. The qualitative research typically applied deductive methods as a form of analysis of existing data to explain social phenomena or predictive theories, and then collected data and evidence to evaluate or validate models, hypotheses or theories envisioned before the research [19]. The study is based on the theoretical basis of domestic and foreign experts and scholars who conducted research according to the financial information disclosed by enterprises. It is conjectured that the financial early warning model can be constructed by financial predicting indicators.

3.1.3. Quantitative Research Methods

Quantitative analysis usually refers to the operation process of performing mathematical statistics on a specific research object [20]. Based on theoretical basis and standardized data, the research results are presented through logical induction and data quantification. Before the beginning of quantitative research, it needs to have clear research hypotheses and questions, and the researcher conducts the study under experimental conditions to exclude effects other than the research objective [21]. In this study, the researchers adopted the following three research tools to complete the quantitative analysis.

• Time series forecasting method. Time series is a collection of continuous observations formed with time as the coordinate axis [22]. Time series forecasting is a method of dynamic data analysis and processing; the core idea is to combine random process theory and mathematical statistics method [23]. Through the research on the statistical laws followed by random data sequences, the researchers are able to predict future values and solve practical problems. The components of the time series are the time to which the phenomenon belongs, and the index value that reflects the development level of the phenomenon [24,25,26,27].
  Foreign scholars have divided the time series models in more detail. The traditional time series analysis models include: autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA), exponential smoothing (ES), seasonal coefficient (SC), S-V model [28].
• BP neural network algorithm. The BP (back propagation) neural network algorithm is an error back-propagation learning algorithm [29]. In 1986, a group of scientists led by Rumelhart and MeCelland gave a comprehensive explanation of the error back-propagation process of neural networks in the book “Parallel Distributed Processing”. At the same time, Minsky also proposed and verified the hypothesis about multi-layer networks [30,31,32].
• Because of its strong nonlinear approximation capability and generalization capability, it could be widely applied, and may be applied to research in various industries in the future [33,34,35,36]. Therefore, the application of BP neural network algorithm in financial early warning is not only a research innovation in this field, but also lays a theoretical foundation for subsequent research, which has a high reference value [37,38,39].
  Combination forecasting method. The combination forecasting method is a combination of two or more different forecasting methods adopted for the same research object. The core idea is: in accordance with the size of the error value of each single prediction method, through formula operation, give a weight to the prediction value, respectively, and finally obtain a new combined prediction model. Granger C. W. J. and Bates first proposed the concept of combination forecasting [28]. They believe that in order to obtain a highly accurate prediction model, it is necessary to make full use of all the existing information. Therefore, when building a prediction model, it is necessary to combine various prediction methods for the same problem as much as possible. Regardless of whether the forecasting accuracy of these forecasting methods is consistent, as long as they have independent computing systems, they can be included in the combined forecasting. Even if there are some prediction methods with large errors, combining it with some more accurate forecasting methods can still construct a reliable combined forecasting model, and the accuracy and reliability will not be affected too much. The general expression of the combined prediction method is:

$${\hat{\mathrm{y}}}_t={\displaystyle \sum _{i=1}^n{w}_i{f}_{it}}$$

(1)

In the expression, i represents each prediction method, there are a total of n types, and w_i is the weight coefficient of the i-th prediction method, y_t represents the actual value of each method (t = 1, 2…n), fit is the predicted value of the i-th method. This formula is to obtain the predicted value of the combined model through the weighted average method [40,41,42].

It is well known that in this type of forecasting:

(i) Accuracy is a key point.

(ii) The adaptability of the data to the quantitative model is another key point.

In this study, the time series forecasting method, BP and combined forecasting method are adopted. Based on the time-series characteristics of financial ratios, the cumulative changes of these data over time can be used to evolve the process of financial crisis outbreaks, and the harbingers of business crisis can be found dynamically and instantly. Therefore, the use of the time series forecasting model for forecasting research can reflect the dynamic information of the financial crisis in stages. On the other hand, the BP neural network algorithm is a back-propagation algorithm, which is currently the most mature and widely used learning algorithm in the feedforward neural network. Applying this method to financial early warning can undoubtedly increase the accuracy and sensitivity of forecasting.

Based on these two different dynamic early warning models, under different input conditions, the output forms, their respective adaptation conditions, advantages and disadvantages are different. We should comprehensively consider the influencing factors of various aspects, so the combined forecasting method is adopted to integrate the two forecasting methods to establish a more scientific financial early warning model.

3.2. Selection of Sample Data

Big data processing technology is applied in this study to predict the financial crisis early warning problem of Chinese listed companies, and it is necessary to screen out a large amount of effective financial data for modeling. Therefore, financial indicators of listed companies on the Shanghai Stock Exchange for ten consecutive years from 2010 to 2019 from the China Center for Economic Research (CCER) database are initially selected, a total of 1746 companies. These companies are involved in more than a dozen different industries such as industry, agriculture, fishery, transportation and catering.

The main purpose of this research is to build a financial early warning model, so the financial data involved must have continuity. In the view of the number of listed companies in the Shanghai A-share market in the past ten years, it is not difficult to find that some companies have gone bankrupt in the middle, and some companies have grown for less than ten years. Due to the above situation, it is first important to screen out 816 listed companies that existed continuously from 2010 to 2019, then filter the financial indicators. Among them, 739 normal companies are in good financial position; the remaining 77 companies are in poor financial status, which is “ Special Treatment companies” (abbr. ST companies).

3.3. Data Preprocessing

After selecting the sample companies, specific predictors also need to be filtered. Based on the limitations of various factors in the real world, the data initially collected by the researchers often cannot be directly analyzed, because there will be some missing data or abnormality of a few individuals, and it cannot be explained by theoretical basis. Therefore, before conducting data analysis, researchers use data cleaning to remove duplicate, erroneous and incomplete data. Then, the researchers performed data transformation based on Z-score financial early warning model theory; that is, transforming the format and interval of the data to make them more suitable for the operational characteristics of the model. The selection of variables in this study is based on the Z-score financial early warning model theory proposed by the American scholar Altman [3]. In the Z-score model, Altman proposed a formula for calculating financial crisis:

$$Z=1.2X_1+1.4X_2+3.3X_3+0.6X_4+0.999X_5$$

(2)

$$X_1=(\mathrm{Current} \mathrm{Assets}-\mathrm{Current} \mathrm{Liabilities})/\mathrm{Total} \mathrm{Assets}$$

(3)

$$X_2=\mathrm{Retained} \mathrm{Earnings}/\mathrm{Total} \mathrm{Assets}$$

(4)

$$X_3=(\mathrm{Interest}+\mathrm{Earnings} \mathrm{Before} \mathrm{Taxes})/\mathrm{Total} \mathrm{Assets}=\mathrm{Earnings} \mathrm{Before} \mathrm{Interest} \mathrm{and} \mathrm{Taxes}/\mathrm{Total} \mathrm{Assets}$$

(5)

$$X_4=\mathrm{Shareholders}’ \mathrm{Equity}/\mathrm{Total} \mathrm{Liabilities}$$

(6)

$$X_5=\mathrm{Net} \mathrm{Sales}/\mathrm{Total} \mathrm{Assets}$$

(7)

The value obtained by the calculation formula of the Z-score model is called the Z-value. Professor Altman believes that the possibility of a company’s financial crisis has an inverse correlation with the Z-value. When Z < 1.81, the company is likely to be in bankruptcy; when 1.81 ≤ Z ≤ 2.65, the company is in a “grey area”, and it is difficult to determine whether the company will go bankrupt, but risk management can be implemented to prevent it; when Z > 2.65, the financial situation of the enterprise is in a healthy state, and the possibility of bankruptcy is very small, but it is still necessary to keep an eye on the financial dynamics [43].

The financial data of 816 listed companies for ten consecutive years from 2009 to 2018 are selected in this study. Based on the guidance of the Z-model theory, Excel statistical software is used to calculate the Z-value of 816 listed companies for ten consecutive years. The results show that the overall distribution of the sample is relatively stable. The number of companies with a Z-value less than 1.81 is approximately 10%; the number of companies with a Z-value over 2.65 accounts are around 55–65%; and 25–35% of the companies have a Z-value between the range of 1.81–2.65. This is basically consistent with the actual financial status of the sample companies, which proves the applicability and high accuracy of the Z-score model in the research field of financial early warning. Not only is the operation simple, but also saves the time cost of data processing; it also lays the foundation for subsequent data modeling [44,45,46].

4. Data Analysis

4.1. Time Series Forecasting

In this study, the classical time series model-ARIMA model and exponential smoothing method will be used to jointly predict the sample data.

4.1.1. Construction of ARIMA Predictive Model

The ARIMA (p, d, q) model is also known as the autoregressive integrated moving average model. Specifically, it consists of two parts: the AR model (autoregressive model) and the MA model (moving average model). P, d and q are three very important model parameters, the prediction results obtained by different parameter combinations are different. Therefore, it is very important to accurately estimate the model parameters before making formal predictions, which will directly affect the prediction results and model accuracy; p is the number of autoregressive, q is the number of moving average and d is the number of difference (set to maintain the stationarity of the time series).

In the expression of the ARIMA model, the Y value is the future forecast value obtained through the study, and Z is the forecast error. The prediction object Y_t, with the influence of its own changes, has the following rules:

$$Y_{\mathrm{t}}={\beta }_1{Y}_{\mathrm{t}-1}+{\beta }_2{Y}_{\mathrm{t}-2}+\dots +{\beta }_{\mathrm{p}}{Y}_{\mathrm{t}-\mathrm{p}}+Z_{\mathrm{t}}$$

(8)

Z is the error value, which has a different correlation in each period. The sample data are imported into the ARIMA model, and it is concluded that the error value interval between the predicted value of Z-value and the actual value of all sample companies in 2018 is [−1.56, 1.87], and the absolute value of the prediction error of the overall sample is 0.467, which is it shows that the relative error value level of the overall data of the sample is 0.4–0.5, which is in the range of the relative error value, so the prediction performance of the model is in line with the expected effect of the study.

4.1.2. Construction of Exponential Smoothing Prediction Model

The exponential smoothing method (ES) is proposed by the famous forecasting expert Professor Robert G. Brown. Its core idea is evolved from the weighted moving average method, that is, the existing statistical data and forecast data are weighted to obtain the future forecast value. The basic formula of exponential smoothing is as follows:

$$S_{\mathrm{t}}=\mathrm{a}\cdot {\mathrm{y}}_{\mathrm{t}}+\left(1-\mathrm{a}\right)S_{\mathrm{t}-1}$$

(9)

Among them, S_t is the smooth value of time t;

y_t is the actual value of time t;

S_t−1 is the smoothed value of time t−1;

a is a smoothing constant, the range of value is [0, 1].

After the forecast operation of the exponential smoothing method, it is concluded that the absolute value of the forecast error of all sample companies is 0.432, and the error value interval between the Z-value forecast value and the actual value in 2018 is [−1.03, 1.71]. It means that the relative error value level of the overall data of the sample is between 0.40 and 0.45, and the prediction performance of the model is also in line with the expected effect of the study.

4.2. BP Neural Network Prediction

In this study, a total of 816 listed companies’ financial data were selected, of which 80% of the sample data was intercepted for the training phase, that is, the financial data of 653 listed companies were randomly selected to train the neural network.

Figure 1 shows that more than half of the data have error values in the range of −0.33 to 0.49 and are distributed on both sides of the zero error. Within the margin of error, this comparison is in line with the expected effect of this study, and the entire neural network construction is suitable for the sample data of this study.

The results show that when the number of neurons is set to 9, the BP neural network algorithm is backpropagated to the sixth time, the neural network obtains a perfect error value, that is, after training 653 sets of data, a suitable algorithm is obtained. After that, the rules obtained in the training phase are used to test the remaining 163 sets of data, and a new set of Z-value data are obtained, the interval of which is [−9.57, 9.19], and compared with the data interval of Z-model statistics [−9.89, 9.58], the error value interval of the two is [−0.31, 0.39], and the average absolute error is 0.306.

Compared with the time series forecasting method, its error interval is much smaller than the ARIMA model and exponential smoothing method, and the mean absolute error is also relatively small. In summary, this experiment proves that the use of Matlab software to load BP neural network algorithm can be used to predict the financial data of listed companies so as to achieve the effect of financial early warning, and that it has good predictability and high accuracy.

4.3. Combined Forecast

The time series forecasting method and the BP neural network algorithm are compared and analyzed in this study. The results show that the forecasting using the BP neural network algorithm obtained forecast error of 0.306; the ARIMA model and exponential smoothing method constructed based on time series forecasting method have forecast errors of 0.467 and 0.432, respectively. Obviously, the prediction accuracy of the BP neural network algorithm is higher than that of the time series prediction method. However, due to the black box of the BP neural network algorithm, the entire operation process cannot be presented intuitively. From the theoretical basis of interpretation, time series forecasting is more convincing. In view of this situation, this study combines the above three single forecasting models based on the combined forecasting method to establish a new financial early warning model of combined forecasting.

By comparing the time series forecasting method and the BP neural network algorithm, three single-item forecasting model error values were generated. According to the average absolute error value of the above single prediction method, the average absolute error of the combined prediction method can also be simply calculated. The table of error value are as follows:

Table 1. Table of error values.

Forecasting Error	Forecasting Model	Error Value
E{i}	E{1}	0.467
	E{2}	0.432
	E{3}	0.306
	E{1, 2}	0.450
	E{1, 3}	0.387
	E{2, 3}	0.369
	E{1, 2, 3}	0.402

shows the error values of the single forecasting method and the combined forecasting method; E{1} is the mean absolute error value obtained by the ARIMA model; E{2} is the mean absolute error value obtained by the exponential smoothing method; E{3} is the mean absolute error value of the BP neural network algorithm. According to the error values of the first three columns, the average absolute error value of the combined forecasting of the last four columns can be calculated separately, for example: E{1, 2} = (E{1} + E{2})/2, that is, the mean absolute error of the combined forecasting of the ARIMA model and the exponential smoothing method. In the same way, the mean absolute error values of other combined forecasts can be calculated.

Since the forecast errors of the three are different, the combined forecast errors they should share cannot be equal. Therefore, in this experiment, the Shapley value of each single forecast method will be calculated to determine the combined forecast error amount that should be shared by each of them. On this basis, the respective weight coefficients will be calculated.

The Shapley value refers to the sum of the marginal contributions of the participants to the alliance divided by the various possible alliance combinations under various possible alliance orders. Its general expression is:

$$\phi \_i(v)={\displaystyle {\sum }_{S\in N}\frac{[(\left|S\right|-1)!(n-\left|S\right|)!]}{n!}}\times \left[v(S)-v(S\backslash \left.\left\{i\right.\right\})\right]$$

(10)

Among them, i represents the members participating in the alliance, S represents the type of alliance, |S| represents the number of members included in the alliance S, and there are a total of n members. When member i participates in the S alliance, there are (|S|−1)! arrangements in total, and the remaining (n-|S|) members have (n-|S|)! arrangements. Calculated by using the Shapley value method, the error amounts E1, E2 and E3 that should be apportioned by the three single forecasting methods are obtained. Among them, the forecast error (E1) that the ARIMA model should share is 0.183, the forecast error (E2) that the exponential smoothing method should share is 0.157, and the forecast error (E3) that the BP neural network algorithm should share is 0.062.

According to the above three summation results, E1 + E2 + E3 = 0.402, which is equal to the value of E{1, 2, 3}, which means that the sum of the apportioned errors of the three single forecasting methods is related to their total average absolute error. That is, the Shapley value of each single forecasting method is calculated correctly. Then, according to the weight coefficient calculation formula of the combined center method:

$$W_{\mathrm{i}}=\frac{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{S}_{\mathrm{i}}}-S_{\mathrm{i}}}{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}{S}_{\mathrm{i}}}}\cdot \frac{1}{\mathrm{n}-1}$$

(11)

S_i represents the quadratic root of the squared mean of the deviation between the forecasting result of the i-th model and the mean of the forecasting results of various models; n represents the number of forecasting models. The final weight coefficient is obtained by operation, that is, the weight coefficient W1 of the ARIMA model, the weight coefficient W2 of the exponential smoothing method, and the weight coefficient W3 of the BP neural network algorithm.

$$W_1=\frac{1}{3-1}\times \frac{0.402-0.183}{0.402}=0.272$$

(12)

$$W_2=\frac{1}{3-1}\times \frac{0.402-0.157}{0.402}=0.305$$

(13)

$$W_3=\frac{1}{3-1}\times \frac{0.402-0.062}{0.402}=0.423$$

(14)

Thereby, a new combined forecasting model is obtained, namely Y = 0.272Y₁ + 0.305Y₂ + 0.423Y₃. Among them, Y is the forecasting value obtained by the combined forecasting model, Y₁ is the forecasting value obtained by the ARIMA model, Y₂ is the forecasting value obtained by the exponential smoothing method, and Y₃ is the forecasting value obtained by the BP neural network algorithm.

The forecasting results obtained by these three single forecasting methods can be brought into the combined forecasting model for operation, and then the forecasting value Y of the combined forecasting model can be obtained. Then it can be compared with the corresponding actual value, and a new error value will be generated. The mean absolute error value E of the combined forecasting model can be obtained by averaging the error values of all sample companies.

According to the above operation steps, the mean absolute error value E of this combined forecasting model is 0.237, and the mean absolute error value of three single forecasting methods are: E{1} = 0.467, E{2} = 0.432, E{3} = 0.306. The error value is relatively small, and the accuracy is relatively high.

It shows that the combined forecasting model constructed in this experiment is suitable for studying financial crisis forecasting and can reduce the forecasting error of the single forecasting method, which meets the requirements of establishing a financial early warning model. At the same time, it also proves that the combination forecasting method is feasible in the combination of single financial crisis forecasting models, and even the accuracy is higher than the ordinary single financial early warning model, and it is a method that can be widely used.

5. Results

Not only the traditional time series forecasting method, but also the artificial intelligence forecasting model (i.e., BP neural network algorithm) was adopted for forecasting in this study to carry out comparative forecasting, and the results are as follows: the forecasting research using BP neural network algorithm produces a forecasting error of 0.306. The ARIMA model and exponential smoothing method based on the time series forecasting method produce forecasting errors of 0.467 and 0.432, respectively. Obviously, the forecasting accuracy of the BP neural network algorithm is higher than that of the time series forecasting method. However, due to the black box of the BP neural network algorithm, the entire operation process cannot be presented intuitively. From the theoretical basis of interpretation, the time series forecasting method is more convincing.

Obviously, the results of the above two prediction experiments are in the normal range, which is enough to prove that both methods are suitable for financial early warning research. Based on the above experimental results, a new method of constructing financial early warning model based on combined forecasting method is proposed, which expands the research angle of financial crisis forecasting. Based on the theoretical basis of the combined forecasting method, in this research, a combined forecasting model is constructed that combines the traditional forecasting method and the artificial intelligence method. According to the results of the research, the forecasting error value of this combined forecasting model is 0.237. Obviously, the forecasting accuracy is higher than that of the above-mentioned single forecasting method. The idea is correct and has strong feasibility, and it is worthy of being widely used.

6. Research Limitations

The study adopted multi-field research methods to predict the financial crisis of listed companies, so as to achieve the effect of financial early warning, and conducted related research on the establishment of financial early warning models. However, due to the limitations of some objective factors, this study has the following limitations and shortcomings:

6.1. Limitation on the Selection of Number of Sample Companies

In this study, big data processing technology is adopted to predict the financial crisis early warning problem of listed companies in China, and it is necessary to screen out a large number of effective financial data for modeling. Among the sample companies selected by the researchers, most of them are normal companies, and only a few, not exceeding 10%, are ST companies. Therefore, researchers can only make predictions by putting together the financial data of the two types of companies.

6.2. Limitations of Selecting Non-Financial Variables

According to the Z-score model proposed by the famous Professor Altman, the researchers selected 9 representative financial indicators from 30 financial indicators and obtained five variables through operations. Most of these five variables reflect financial information, and a few are related to corporate governance. Combining the research background of a large number of domestic and foreign literature articles and the real-time information reports of many listed companies, it can be seen that there are many reasons for the financial crisis of enterprises, and there are many factors that affect the company’s financial distress, and they come from various aspects, not only limited to the problems of the company’s financial situation. Based on the existence of the above problems, this study ignores some factors that affect the financial crisis of enterprises from other aspects, so the selected influencing variables are not comprehensive enough, and it is worthy of further discussion.

6.3. Limitation of the Selection of Forecasting Method

Based on the traditional forecasting method theory, in this research, artificial intelligence technology is added to jointly conduct financial early warning research. Specifically, the time series forecasting method and the BP neural network algorithm are selected, and three single forecasting models (namely the ARIMA model, exponential smoothing method and BP neural network) are created, then the combined forecasting method is used to combine these three single forecasting models, and finally a new financial early warning combined model is constructed.

From the above research status, it can be seen that there are more than ten single forecast models that can be used to create financial early warning models, including traditional financial early warning models and the currently popular artificial intelligence models. Due to the constraints of manpower, material resources, time and other reasons, in this study, only some methods are selected to establish a financial early warning model. In follow-up research, scholars can also add other prediction methods for comparison, which is worth further discussion.

7. Discussion

The researchers only selected 816 companies listed on the Shanghai Stock Exchange for ten consecutive years from 2010 to 2019 when conditions allowed. In the follow-up research, the sample size can be appropriately expanded; that is, the selection range of the sample can be expanded, and the reference value of the research results can be improved. For example, the A-share listed companies of the Shenzhen Evidence Exchange can be included in the research scope, and even extended to all listed companies. In addition, based on the research of forecasting the overall sample, healthy companies and crisis companies can be forecast separately, so as to establish financial early warning models with different mechanisms, and even analyze whether there is a linear or non-linear relationship between the two.

Combining with a large number of domestic and foreign literature articles, it can be seen that there are many reasons for the financial crisis of enterprises, and there are also many factors that affect the company’s financial distress, not only limited to the company’s financial problems. In this study, based on the Z-score model, more representative financial indicators were selected for prediction experiments. As we all know, the introduction of the Z-score model has laid a solid foundation for the research field of financial early warning, but it is limited to the overall judgment of the financial situation of enterprises. It is obviously not comprehensive enough to predict financial crisis from this aspect alone. Therefore, in the follow-up research, it is suggested to select variables from two perspectives: internal factors and external environmental factors. The internal factors of the enterprise can be considered: corporate governance indicators, operation management mode, corporate culture direction, etc. External environmental factors can be considered: RMB exchange rate, national economic-related policies, etc. Of course, some of these newly introduced variables can be directly quantitative statistics; some are qualitative indicators, which need to be converted into quantifiable indicators through some new technologies (such as Python), and then carry out later research. If the above-mentioned new variables are introduced into the existing financial early warning model, not only the accuracy of the early warning model can be further improved, but also the reasons for the formation of financial crisis can be more accurately explained [47].

This study mainly conducts forecasting research from two perspectives, traditional forecasting methods and artificial intelligence. Through repeated prediction and verification of sample data, this study proves that these methods are suitable for financial crisis early warning research and have high accuracy. However, with the continuous advancement of scientific standards and the continuous evolution of the economic and market systems in various countries, only by constantly learning and updating financial early warning research methods can we deal with complex financial crisis problems. According to the research status of domestic and foreign financial early warning, it can be seen that some scholars have begun to use artificial intelligence methods to conduct related research on financial early warning models; some scholars have used two or more forecasting methods (including artificial intelligence methods) to carry out financial early warning model comparison studies. Since the research and application of artificial intelligence methods in financial early warning is not mature enough, the artificial intelligence models chosen by most scholars are relatively simple. For follow-up research, the support vector machine method can be used, which is one of the more advanced artificial intelligence models at present.

8. Conclusions

Regarding financial crisis, in essence, it is the product of the accumulation of a crisis, and there is a long incubation period before the outbreak [48]. Its outbreak is often accompanied by some obvious features, such as a decline in market share, a continuous increase in operating expenses, a decline in cash inflow, etc. Therefore, in the process of crisis early warning, it is necessary to deeply analyze the causes and laws of the formation of the crisis, so as to establish a scientific, efficient financial early warning model. In this study, considering the characteristics of the sample data, the above three prediction models were selected for joint research, which can not only carry out more comprehensive research on the financial early warning problem, but also make theoretical innovations in the research method of this problem [49].

This study starts from the perspective of enterprise financial crisis forecasting and aims to build a financial early warning model. Based on the theory of time series forecasting, BP neural network algorithm and combination forecasting method, relevant research and innovation are carried out [50]. From the theoretical point of view, by reading a large number of domestic and foreign literature articles, the concept of corporate financial crisis is redefined, the existing forecasting research is also organized, and the forecasting methods that can be used to build financial early warning models are carried out. From the perspective of method, the time series forecasting method, BP neural network algorithm and combined forecasting method are selected for comparative analysis in this study, their respective scope of application found out, and individual forecasting research conducted according to their respective characteristics. From the perspective of application, the researchers first created three single forecast models (ie: the ARIMA model, exponential smoothing method and BP neural network algorithm) to establish a scientific financial early warning combination forecasting model in the research.

This study has certain reference value for future related research and practical application. From the perspective of theoretical contribution, the researchers tentatively expound the theoretical basis of variable selection in financial early warning research, as well as the theoretical framework of the overall research. In the study, the researchers comprehensively used the knowledge of finance, economics, information management and other disciplines to sort out the internal relationship between the above theories and financial crisis from different research perspectives, analyze the formation mechanism of financial crisis, and tentatively build a variable framework for financial crisis early warning, to provide a more explanatory research direction for the further expansion of empirical research. In addition, this study innovated the financial early warning method. Based on the time series model and BP neural network as the frontier theory of financial early warning, the researchers build a model based on the significant variables of financial crisis early warning of China’s A-share listed companies in consecutive years, and then conduct robustness tests on the sample data. Therefore, a combined forecasting model based on the time series forecasting method and the BP neural network algorithm is proposed, which creatively improves the accuracy of the early warning model.

From the perspective of practical contribution, it helps to improve the awareness and ability of enterprises to prevent crises. With the increasing downward pressure on China’s economic development, various industries have exposed a series of problems, such as overcapacity, technology of low-added value, unsalable products and low corporate profit margins. This requires the financial early warning model to identify financial crisis signals in time and issue early warning signals, so as to find the cause of the crisis, so that effective measures can be taken in time to deal with the crisis, so as to improve the sensitivity and perception of financial early warning of listed companies. Secondly, it is beneficial for creditors and shareholders to realize the appreciation of assets. Through financial crisis early warning, the creditor can grasp the business operation status of the enterprise in time and select the enterprise with good operation and reputation in which to invest, so as to ensure the effective circulation of capital and realize the preservation and appreciation of assets. Thirdly, it provides investors with a rational and scientific financial decision-making basis. To a certain extent, financial variable selection and variable screening research can systematically provide investors with investment decision-making information, which will provide investors with positive decision-making data support and feedback. Fourthly, it can provide reference for policy-making departments and regulatory departments to evaluate enterprises and reallocate market resources. Financial crisis early warning can provide an important reference for government departments and industry associations, which is conducive to optimizing the allocation of market resources and formulating high-efficiency macroeconomic policies to ensure orderly economic development.