Prediction of corporate financial distress based on digital signal processing and multiple regression analysis

In the study of financial distress forecasting, domestic and foreign scholars have adopted a variety of methods and techniques, it is mainly divided into two categories: one is the discriminant classification method based on statistical model, such as linear discriminant analysis, Logistic regression, Probit regression, etc.; The second is artificial intelligence methods, such as decision trees, artificial neural networks, support vector machines, evolutionary computing, etc. In order to examine the role of the textual quantitative indicators constructed by the authors in predicting financial distress, in order to ensure the robustness of the research conclusions, the authors chose the above two types of methods, the most widely used and most representative logistic regression and support vector machines are used for empirical analysis [8].

Logistic regression model

(1) Among the traditional statistical methods of credit risk early warning, logistic regression is the most commonly used multivariate statistical method for modeling binary dependent variables, which can solve the problem of nonlinear classification, there are no specific requirements for the distribution of variables, and the accuracy of the judgment is relatively high. The general form is as follows: (1) ln(pi1−pi)=α+∑i=1nβiXi \ln \left({{{{p_i}} \over {1 - {p_i}}}} \right) = \alpha + \sum\limits_{i = 1}^n {{\beta_i}{X_i}}

Where p_i represents the probability of an event occurring, and X_i represents the explanatory variable.

(2) Support vector machine

Support vector machine is a classification method based on statistical learning theory, it has many advantages in solving small sample, nonlinear and high-dimensional pattern recognition, its purpose is to construct a hyperplane, maximize the margins between the two classes in the high-dimensional feature space, its advantage is to use the kernel function to provide a classification model with high accuracy, and to avoid the over-adaptation of the model with the help of regular terms, while avoiding the influence of local optima and multiple collinearity [9]. The optimization problem solved by the support vector machine is as follows: (2) min12wTw+C∑i=1Mξis.t.yi[wTϕ(x)+b]≥1−ξi \matrix{{\min {1 \over 2}{w^T}w + C\sum\limits_{i = 1}^M {{\xi_i}}} \hfill \cr {s.t.{y_i}\left[{{w^T}\phi \left(x \right) + b} \right] \ge 1 - {\xi_i}} \hfill \cr}

Where i=1, 2,., M, ξ_i ≥ 0 represents the error limit determined by the penalty factor C, y_i represents the categories in the training set, ϕ(x) represents the nonlinear transformation from the input layer to the feature layer, w and b represent weight and threshold, respectively. Support vector machine through quadratic programming, the above optimization problem is solved by replacing the dot product ϕ(x_i)^T · ϕ(x_j) of the optimal classification plane with the kernel function K(x) = K(x_i, x_j), there are many forms of kernel function, such as linear kernel function, multinomial kernel function, Gaussian kernel function, etc. The author selects the Gaussian kernel function for modeling here [10].

Financial ratios are the basic variables for predicting the financial distress of listed companies, on the basis of combining existing literature and considering the availability of data, the author selects 32 financial ratios from the perspectives of solvency, operating ability, profitability, development ability, per share index, risk level, etc, including fixed asset ratio (FIX), current ratio (CURRENT), quick ratio (ACID), working capital (WC), interest coverage ratio (INTEREST), net cash flow from operating activities/current liabilities (CASH), cash flow interest coverage multiple (CINTEREST), asset-liability ratio (LEV), tangible asset-liability ratio (TLEV), equity multiplier (EM), equity Ratio (EQUITY) Equity/Liability (ED), Total Assets Growth Rate (AGROWTH), Equity Growth Rate (EGROWTH), Financial Leverage (FL), Operating Leverage (OL), Comprehensive Leverage (CL), operating cycle (0C), total asset turnover (TAT), earnings per share (EPS), operating income per share (OIPS), operating profit per share (OPPS), net assets per share (BPS), retained earnings per share (REPS), net cash flow from operating activities per share (CPS), net cash flow per share (NCPS), return on invested capital (RIA), return on assets (ROA), net interest rate on assets (JROA), return on Equity (ROE), Operating Profit Margin (OPM) and Total Operating Cost Ratio (OCR) [11].

(1) Extraction method of feature words

Due to the company's operating and financial conditions, the wording and style of its disclosure text will be affected, the author uses the R language open source segmentation tool JiebaR to perform word segmentation, and then uses the chi-square test method to select feature words that can distinguish financial distressed companies from normal companies. N represents the total number of documents in the training corpus, and A represents the frequency of documents belonging to the C_j class and containing the feature word t_i, let B represent the frequency of documents that do not belong to the C_j category but contain the feature word t_i, and let C represent the frequency of documents that belong to the C_j category but do not contain the feature word t_i, (3) χ2(ti,Cj)=N×(A×D−C×B)2(A+C)×(B×D)×(A×B)×(C×D) {\chi^2}\left({{t_i},{C_j}} \right) = {{N \times {{\left({A \times D - C \times B} \right)}^2}} \over {\left({A + C} \right) \times \left({B \times D} \right) \times \left({A \times B} \right) \times \left({C \times D} \right)}}

According to the critical value of one degree of freedom of the chi-square distribution, it can be determined whether the feature word t_i can significantly distinguish the financially distressed company from the normal company, from this, we can construct the feature word list of financially distressed companies and normal companies.

(2) Weight setting of feature words

Considering the relative importance of feature words in classification, the weights are set by extending the term frequency inverse document frequency (TFHDF, Term Frequency Inverse Document Frequency). The weight w_i of the feature word t_i can be expressed as: (4) wi=∑jtfijk×ln(Nl+1nl+1)×ln(nk),k,l∈{1,2},k≠l {w_i} = \sum\limits_j {t{f_{ijk}} \times \ln \left({{{{N_l} + 1} \over {{n_l} + 1}}} \right) \times \ln \left({{n_k}} \right),k,\,l \in \left\{{1,\,2} \right\},k \ne l}

Where j represents documents, k and l represent categories, tf_ijk represents the word frequency of the feature word i in the h class j document, N represents the total number of documents, and n represents the total number of k-type documents containing the feature word i [12].

(3) Construction of Default Propensity Index Based on Text Analysis

By selecting feature words and setting their weights, the feature words contained in each information disclosure text can be counted, from this, the Tendency toward Default (TTD, Tendency toward Default) indicator based on text analysis can be constructed: (5) TTDj=∑itfiD×wiD∑itfiND×wiND TT{D_j} = {{\sum\limits_i {tf_i^D \times w_i^D}} \over {\sum\limits_i {tf_i^{ND} \times w_i^{ND}}}}

Where TTD_j is the default propensity index of company j, tfiD tf_i^D represents the word frequency of the financial distressed company feature word t_i in the information disclosure text of company j, wiD w_i^D represents the weight of the feature word t_i to the financially distressed company, tfiND tf_i^{ND} represents the word frequency of the normal company feature word t_i in the information disclosure text of company j, wiND w_i^{ND} represents the weight of the feature word t_i to the normal company. The higher the TTD value, the more negative words the author uses.

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When using Logistic regression analysis, the author applies stepwise regression method to eliminate insignificant variables, firstly, the Tendency to Default Index (TTD) is not considered, and then this index is added to compare and analyze the fitting degree and predictive ability of the mode, at the same time, according to whether the propensity to default indicator (TTD) will be eliminated in the process of gradual regression, we can judge its role in the construction of financial distress model.

Table 1, Figure 1 shows the out-of-sample prediction results of the logistic stepwise regression. It can be seen from Table 1 that when the ratio of ST company to normal company is 1:1, the addition of the Tendency to Default Index (TTD) has improved the AUC and overall accuracy to a certain extent, both the first and second types of errors have been reduced, and the reduction of the first type of errors is more obvious; After increasing the matching ratio and increasing the number of normal companies, the improvement of the prediction effect by the addition of the propensity to default indicator (TTD) decreased, but it can also improve the overall accuracy and AUC, reduce the first type of error and the second type of error, again, the reduction in Type 1 error is more pronounced. It can be seen that when using the logistic regression method, the propensity to default indicator (TTD) reflected in the text content, it can indeed improve the out-of-sample prediction accuracy of the financial distress prediction model, and it is consistent with the in-sample test, this is mainly reflected in the reduction of the first type of error, that is, the probability of misjudging a financial distressed company as a normal company.

Figure 1

When using support vector machine modeling and analysis, in order to judge the relative importance of the propensity to default indicator (TTD) and financial ratio variables to model financial distress forecasts, the author introduces sensitivity analysis method to calculate the relative importance of each variable before and after adding TTD, and conducts in-sample test, then, the out-of-sample prediction ability of SVM before and after adding TTD is compared and analyzed.

(1)

In-sample test

Table 2, Figure 2 presents the results of the SVM within-sample test. As can be seen from Table 2, when the sample ratio is small, the overall accuracy of the support vector machine is higher, mainly because the probability of the first type of error is relatively much lower, after the sample ratio is enlarged, the probability of Type 1 error is significantly improved; After adding the propensity to default indicator (TTD), regardless of the proportion, the probabilities of both the first type of error and the second type of error have been reduced, and the reduction of the first type of error will be relatively more significant, at the same time, the overall accuracy and AUC also have a certain degree of improvement. From the results of the sensitivity analysis, the change of the proportion of the ratio has little effect on the relative importance of the financial ratio variable when using support vector machine modeling, the propensity to default indicator (TTD) entered the top ten important variables in both proportions, and when the ratio is 1:2, it ranks fourth in all indicators, and the importance increases significantly. It can be seen that when the support vector machine is used to build a financial distress prediction model, the propensity to default indicator (TTD) has played an important role.

Table 2

In-sample test results of support vector machines

	1:1 ratio		1:2 ratio
	Do not join TTD	Join TTD	Do not join TTD	Join TTD
AUC	95.73%	96.82%	94.70%	96. 32%
Type I error	6.02%	4.51%	16.07%	14.56%
Type II error	9.03%	8.53%	8.28%	7.53%
Accuracy	92.45%	93.46%	89.10%	90.11%

Figure 2

(2)

Out-of-sample prediction

Table 3, Figure 3 presents the results of SVM out-of-sample prediction. As can be seen from Table 3, also, when the sample proportion is small, the overall accuracy of the support vector machine is higher, and after the sample proportion is enlarged, the probabilities of both types of errors are significantly improved; From the impact of the addition of propensity to default (TTD), when the ratio is 1:1, significantly reduces the probability of type 2 errors, AUC has also been significantly improved, and the overall accuracy has been greatly improved, however, after the proportion is enlarged, its impact is reduced, and the impact on Type II errors is small, it just reduces the probability of type 1 error. Overall, in the case of using the support vector machine method, add the Tendency to Default Index (TTD) reflected by the text information, it can also improve the accuracy of financial distress prediction models.

Table 3

Out-of-sample prediction results of support vector machines

	1:1 ratio		1:2 ratio
	Do not join TTD	Join TTD	Do not join TTD	Join TTD
AUC	92.96%	99.82%	92.11%	92.14%
Type I error	3.32%	3.32%	16.65%	15.01%
Type II error	12.51%	3.32%	12.51%	12.51%
Accuracy	90, 82%	96.66%	86.10%	86.65%

Figure 3