Comprehensive signal indicators of financial distress prediction.
Abstract
This chapter aims to dynamically improve the method of predicting financial distress based on Kalman filtering. Financial distress prediction (FDP) is an important study area of corporate finance. The widely used discriminant models currently for financial distress prediction have deficiencies in dynamics. Based on the statespace method, we establish two models that are used to describe the dynamic process and discriminant rules of financial distress, respectively, that is, a process model and a discriminant model. These two models collectively are called dynamic prediction models for financial distress. The operation of the dynamic prediction is achieved by Kalman filtering algorithm, and further, a general nstepahead prediction algorithm based on Kalman filtering is derived for prospective prediction. We also conduct an empirical study for China’s manufacturing industry, and the results have proved the accuracy and advance of predicting financial distress in such case.
Keywords
 financial distress prediction
 pattern recognition
 state space model
 stochastic process
 optimal estimation
1. Introduction
Research on financial distress prediction (FDP) is an important area of corporate finance. Early prediction methods are univariate analysis (UA), multiple discriminant analysis (MDA), logistic model, probit model, and so on [1, 2, 3, 4, 5]. With the development of computer technology, some new methods based on artificial intelligence technology with distributed computing capabilities that can deal with problems of nonlinear systems are widely introduced into the field of financial distress prediction. These methods include neural network (NN), genetic algorithm (GA), rough set theory (RST), casebased reasoning (CBR) and support vector machine (SVM), and so on [6, 7, 8, 9, 10, 11, 12, 13, 14]. Each model established for financial distress prediction, whether based on statistical methods or artificial intelligence methods, has advantages and disadvantages under different conditions. Let us take the most widely used multiple discriminant analysis (MDA) and backpropagation neural network (BPNN) for example. MDA has the advantage of simplicity and good interpretation, but the deficiency in its application is limited by strict assumptions that sometimes cannot be satisfied. Besides, MDA is a static discriminant model [2, 3, 6, 15, 20]. For the application of BPNN, it does not need any probability distribution assumption. BPNN is considered as an effective tool of pattern recognition for nonlinear systems. Therefore, many researchers have tried to apply triple BPNN in financial distress prediction, using the nonlinear pattern recognition capability of BPNN for classification of different financial state [7, 8, 15].
The prediction often achieved through a crosssectional analysis at different time points. That is, the sample data of period
Actually, corporate financial distress is a gradual and cumulative process, which is developed from a healthy state. The mutation is often the result at which the gradual change and cumulation have reached the critical condition. It is neither reasonable nor logical if only the crosssectional data at the time point prior to the occurrence of financial distress are used to make a determination for the corporate future state. It should take into account two aspects at least when conducting the research on financial distress prediction: firstly, the alternative data for prediction should contain all the historical information; secondly, the prediction method is dynamic designed for financial distress characterized by cumulative variation [21, 22, 23]. However, the current discriminant models have some deficiencies in dynamic prediction. Also, there is a problem of massive data processing. This chapter attempts to make a dynamic improvement on prediction methods for financial distress based on Kalman filtering algorithm in order to solve the above problems.
The main contribution of the paper is that it constructs a statespace model of corporate financial distress from the perspective of the cumulative effect of historical information on current state and improves Kalman filtering algorithm for dynamic prediction. A whole process of dynamic prediction for corporate financial distress is developed from a long period of time, and timeseries data of highfrequency are collected for optimal estimation of financial state, which is seen as a stochastic process. The advantage of the model is proved by an empirical research, and the result shows that it can give relatively accurate warning before the occurrence of financial distress.
The rest of this chapter is organized as follows. Dynamic prediction models consisting of a process model and a discriminant model based on Kalman filtering algorithm are described in Section 2. Then, a whole process of dynamic prediction for corporate financial distress is elaborated in Section 3. Section 4 presents empirical analysis for China’s manufacturing industry. Section 5 draws conclusions and discusses future research.
2. Dynamic prediction models based on Kalman filtering algorithm
Based on the statespace method, we establish two models, being used to describe the dynamic process and discriminant rules of financial distress, respectively, that is, a process model and a discriminant model. These two models collectively are called dynamic prediction models for financial distress. We see the evolution of financial distress for a company as a stochastic process and establish a process model, which is used to describe the dynamic process of development of the financial state. We define the financial state as a set of vectors, which summarizes all the information necessary about the past behavior of the company except for the external effects of the inputs, so that it can uniquely describe the behavior of the company in the near future [24]. The financial state of a company often cannot be observed directly, but only some signal indicators associated with the financial state can be observed. Therefore, we establish a discriminant model, which is used to describe the correlation between the financial state and the signal indicators. The discriminant model can be a recursive form of any statistical model or artificial intelligence model, theoretically. At first, we take the linear models, which are simple and intuitive as an example and establish dynamic prediction models for financial distress, as
where
Assume that the process noise and the observation noise are Gaussian white noises, which are mutually independent and normally distributed, i.e.
where,
The above equations can be solved by Kalman filtering algorithm. The Kalman filter is named after Rudolph E. Kalman, who in 1960 published his famous paper describing a recursive solution to the discretedata linear filtering problem. The Kalman filter is essentially a set of mathematical equations that implement a predictor–corrector type estimator that is optimal in the sense that it minimizes the estimated error covariance, when some presumed conditions are met [25, 26]. Kalman filter is widely used for its relative simplicity and robust nature. Rarely do the conditions necessary for optimality actually exist, and yet, the filter apparently works well for many applications in spite of this situation. Application of Kalman filter in dynamic prediction for corporate financial state consists of five steps [27, 28]:
The first step is to compute the onestep prediction of the financial state
The second step is to compute the error covariance matrix
The third step is to compute the Kalman gain
The fourth step is to correct the onestep predicted financial state
The fifth step is to compute the error covariance matrix
These are the basic equations of Kalman filtering for a stochastic linear discrete financial system. The actual filtering process is an ongoing “predictingcorrecting” process of a recursive nature. Figure 1 below offers a complete picture of the operation of the Kalman filter in dynamic prediction for corporate financial state.
The Kalman filter does not require storing large amount of data in solving the problem. Once new data are observed, new filtering value can be calculated at any time. Therefore, this method facilitates realtime processing and is easy to implement on the computer.
3. A whole process of dynamic prediction for corporate financial distress
As previously described, corporate financial distress is a gradual and cumulative process, which is developed from a healthy state, and so the prediction should be longterm and continuous and the continuously updated timeseries data should be collected for the dynamic prediction, which could be the fresh input into the Kalman filter in order to obtain the optimal estimation closer to the actual state. The whole process of dynamic prediction for corporate financial distress is described as follows.
From
Figure 2
, we can see that if we want to predict the corporate financial state at time
Further, if we want to predict the corporate financial state
The general
The
Assume that the system parameters
Based on the Eqs. (9)–(12), we could use data at shorter time interval to predict
In the dynamic prediction models for financial distress established in Section 2, we suppose that the financial state
where,
If
This additional estimation equation is used every year, no matter if 1 year is divided into
4. Empirical analysis
4.1. Data description and experiment design
Manufacturing industry is a major industry in China. “Made in China” has an important impact on the global economy. Therefore, prediction of corporate financial distress for China’s manufacturing industry is of great significance. Generally, the manufacturing companies have complete production processes, equilibrious production cycle, as well as a more stable trend of development of the financial state. The characteristics of these companies can be well described using the existing financial indicators, and the dynamic prediction method described above can be put into practice for these manufacturing companies.
In this research, the data for our experiment are collected from the Shanghai Stock Exchange and Shenzhen Stock Exchange databases in China. ST (special treatment) companies because of financial problems are selected as distress samples; meanwhile, companies of similar asset size that have never been special treated are selected as healthy samples. The ST time is treated as period
According to the above principles, the data of 152 listed companies are collected, and the time span is year 2002 to year 2009, year 2003 to year 2010, year 2004 to year 2011, respectively. A total of 60 ST companies and 60 paired companies of the first half of year 2010 and 2011 are treated as training set, which is used to derive the model. A total of 16 ST companies and 16 paired companies of the first half of year 2012 are treated as testing set, which is used to test the effect of the model.
From the holistic perspective, we select 29 financial indicators covering four aspects of profitability, solvency, management efficiency, and market reaction as alternative signal indicators. The effect of the corporate financial problems may be amplified or reduced in information transmission mechanism of the market, and the problems may be exposed to the open market in advance or with a delay. If the problems are exposed in advance, the indicators can be used as a pilot signal of financial distress prediction; if delayed exposure, it can also be served as comprehensive evaluation of financial distress or the signal for the trend of development in the future. These are indicators of market reaction. The 29 signal indicators are listed in Table 1 .
Type  Code  Signal indicators 

Profitability 

Operating profit margin 

Net profit margin  

Return on assets  

Return on equity  

Operating profit margin growth  

Operating revenue growth  

Total assets growth  
Solvency 

Current ratio 

Quick ratio  

Cash debt ratio  

Debt coverage ratio  

Interest coverage ratio  

Liabilities to assets ratio  

Liabilities to equity ratio  
Management efficiency 

Total assets turnover 

Fixed asset turnover  

Current assets turnover  

Inventory turnover  

Accounts receivable turnover  

Cash ratio of main business  

Cash return on assets  
Market reaction 

Earnings per share 

Net assets per share  

Operating revenue per share  

Capital reserve per share  

Retained earnings per share  

Price to book ratio  

Equity to invested capital ratio  

Net cash flow per share 
A threedimensional database is established consisting of 16 periods’ timeseries data of the above 152 sample enterprises, the financial state of which is represented by 27 signal indicators each (As operating profit margin growth (
From Figures 3 – 6 , we can see most indicators show a certain trend, which is the foundation of dynamic prediction.
Then, we use nonparametric test of MannWhitney
4.2. Experiment results and analysis
We use principal component analysis to eliminate the effect of multicollinearity on the original variables. We extract first 10 principal components, and the accumulative contribution rate is above 92% each for 152 companies. These principal components are linear combinations of the original signal indicators, which can be served as part of discriminant models for each company.
The parameters of process model are estimated from the data of training set and also using the data of training set, the judgment for the threshold of financial distress is set as an interval, which has lower and upper confidence limit.
The results show that the lower confidence limit is −0.796 and the upper confidence limit is 0.205. When the predictive value of a company’s financial state is lower than −0.796, the company may fall into severe financial distress; when the predictive value is higher than 0.205, the company is well operated; and when the predictive value is between −0.796 and 0.205, it is possible that the company is getting into financial distress.
Then, we test the effect of the dynamic prediction models using the data of testing set. Subject to space restrictions, we just list dynamic prediction figures for six companies, among which first three are ST companies, while the other three are nonST companies. Names and stock codes of the companies are Sichuan Chemical Company Limited (000155), MCC Meili Paper Industry Co., Ltd. (000815), Guangzhou Guangri Stock Co., Ltd. (600894), Xinxiang Chemical Fiber Co., Ltd. (000949), Nantong Jiangshan Agrochemical & Chemicals Co., Ltd. (600389), Nanzhi Co., Ltd., and Fujian (600163), in turn. Dynamic prediction figures for these six companies are shown in Figure 7 .
The testing results show that almost all the curves of predictive value fits the ones of real value for 32 testing samples.
Of 16 distress testing samples, 15 companies give mild alarm in period
For healthy testing samples, none is lower than the severe alarm limit. But sometimes, the predictive values appear slightly below the mild alarm limit, showing that there have been cases of temporary deviation from healthy state for healthy testing samples. The dynamic model conducts a track and thereafter modifies. This shows that the model can objectively track and effectively predict the overall financial state of a company from a long run.
5. Conclusions and future work
In this chapter, we focus on the dynamic nature of corporate financial distress and establish dynamic prediction models consisting of a process model and a discriminant model, which are used to describe the dynamic process and discriminant rules of financial distress, respectively. The operation of the dynamic prediction is achieved by Kalman filtering algorithm, and a general
In this research, we suppose the dynamic process of financial distress is linear. The Kalman filtering algorithm will be applied to a nonlinear dynamic model in the future research, and it will offer a wider range of applications.
Acknowledgments
This research is supported by National Natural Science Foundation of China (Grant no. 71602188) and National Social Science Foundation of China (Grant no. 15ZDB167).
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