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

Pubblicato online: 15 Jul 2022
Volume & Edizione: AHEAD OF PRINT
Pagine: -
Ricevuto: 06 Mar 2022
Accettato: 24 May 2022
Dettagli della rivista
License
Formato
Rivista
eISSN
2444-8656
Prima pubblicazione
01 Jan 2016
Frequenza di pubblicazione
2 volte all'anno
Lingue
Inglese
Introduction

Science and technology are the primary productive forces, and technological innovation is the driving force for enterprise development. The key to the development and growth of an enterprise lies in its core competitiveness, and the core support for an enterprise to adapt to the development and changes of the environment is technological innovation. High-tech enterprises are emerging enterprises with huge potential for technological innovation and development. Under the background of technological revolution and technological innovation on a global scale, high-tech enterprises should seize business opportunities and seek innovative development[1]. The unique characteristics of high-tech enterprises make them different from ordinary enterprises in terms of production, operation and growth, they are high in technology, knowledge-intensive, high-input, high-growth, high-risk, and high-income, the development of technological innovation has led to great changes in corporate performance [2]. Therefore, the author chooses high-tech enterprises as the research object, and then discusses how to enhance their core competitiveness and improve their performance through technological innovation. Digital signal processing technology has been widely used in various industries in recent years, mainly due to its ability to convert many analog information, such as sound or pictures, to digital information, it can meet the digital development requirements in the field of computer or other industrial machinery and equipment [3]. At the same time, after the emergence of DSP processor, the processed information can also be output in the form of analog information, which has strong practicability [4]. Therefore, it is of great significance to analyze the application and development of digital signal processing technology. In response to this research problem, Dewanthikumala, Jasruddin and others took pharmaceutical companies in listed companies as the research object, collected their patent application data, and concluded that the increase in the number of patent applications will lead to the continuous improvement of corporate profitability [5]; Kumar D G et al. used the annual number of patent applications to measure the impact of technological innovation on enterprise performance, and empirically found that the two are significantly positively correlated [6]; When Liu J et al. studied the impact of technological innovation of listed manufacturing companies on enterprise performance, they used invention patents, design patents and utility model patents to reflect technological innovation indicators, the results show that different types of patents have different effects on performance, and the impact of utility model patents on enterprise performance is weaker than that of the other two types of patents [7]. Based on the current research, the author proposes to use digital signal processing, and multiple regression analysis to study the financial distressed company forecasting system. Firstly, the research method is designed, Logistic regression model is the most commonly used multivariate statistical method when modeling binary dependent variables, it can solve the problem of nonlinear classification, there is no specific requirement for the distribution of variables, and the accuracy of judgment is high. The author selects 32 financial ratios from the perspectives of solvency, operating ability, profitability, development ability, per share index, and risk level. Taking special treatment (ST) due to abnormal financial status as a sign of financial distress in listed companies, when selecting samples, the matching principle is adopted to select non-ST companies as matching samples. Two methods of logistic regression and support vector machine are used for empirical testing, and both in-sample testing and out-of-sample prediction are performed.

Methods
Choice of empirical method

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: ln(pi1pi)=α+i=1nβiXi \ln \left({{{{p_i}} \over {1 - {p_i}}}} \right) = \alpha + \sum\limits_{i = 1}^n {{\beta_i}{X_i}}

Where pi represents the probability of an event occurring, and Xi 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: min12wTw+Ci=1Mξis.t.yi[wTϕ(x)+b]1ξi \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, ξi ≥ 0 represents the error limit determined by the penalty factor C, yi 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(xi)T · ϕ(xj) of the optimal classification plane with the kernel function K(x) = K(xi, xj), 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].

Selection of financial ratios

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].

Quantitative analysis of text content

(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 Cj class and containing the feature word ti, let B represent the frequency of documents that do not belong to the Cj category but contain the feature word ti, and let C represent the frequency of documents that belong to the Cj category but do not contain the feature word ti, χ2(ti,Cj)=N×(A×DC×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 ti 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 wi of the feature word ti can be expressed as: wi=jtfijk×ln(Nl+1nl+1)×ln(nk),k,l{1,2},kl {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, tfijk 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: TTDj=itfiD×wiDitfiND×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 TTDj is the default propensity index of company j, tfiD tf_i^D represents the word frequency of the financial distressed company feature word ti in the information disclosure text of company j, wiD w_i^D represents the weight of the feature word ti to the financially distressed company, tfiND tf_i^{ND} represents the word frequency of the normal company feature word ti in the information disclosure text of company j, wiND w_i^{ND} represents the weight of the feature word ti to the normal company. The higher the TTD value, the more negative words the author uses.

Data Signal Processing

In the fields of test instruments and measuring instruments, digital signal processing technology can also be used, which can improve the function of products. High-end single-chip microcomputer in traditional equipment, gradually replaced by this technology, the rapid development of digital signal processing technology, its internal resources are now very rich, which can not only simplify the hardware circuit on the instrument, but also further improve the reliability, precision and accuracy of instrument measurement. Programmable digital signal processing technology is widely used in the field of personal computers, which can combine Motion Picture Experts Group and high-speed communication technology, and can convert audio and video formats. The computers we usually use are based on digital signal processing technology, handles a variety of versatile, multi-modal digital signal processors. The application of this technology in the field of shortwave communication is mainly manifested in analyzing link quality, processing audio signals, detecting and scanning channels, and realizing channel digitization. The principle is that after processing the front-end RF signal, the digital signal module will analyze and process the intermediate frequency signal of the input digital signal, then output the audio signal, and ensure that the AGC control signal and the baseband signal are digitally quantized. The AGC control signal can reflect the digital baseband signal and the gain of the amplifier signal, providing a reference for the analysis of spectrum and waveform, and the terminal equipment can also make full use of the signal to achieve the goal of reducing the noise of the analog signal. The mode adopted in the design of hardware structure in the module mainly combines AD, PDC and DSP, after completing the amplification and filtering process, the intermediate frequency signal is input into the high-speed modulus to complete the quantization purpose, when the programmable inverter is used to filter and decelerate the signal, it will output a spectrum of a certain component, at this time, through the conversion of the signal, the analog signal for the end user will be output.

Samples and Data
Sample

The author takes special treatment (ST) due to abnormal financial status as a sign of financial distress in listed companies, and adopts the matching principle to select non-ST companies as matching samples when selecting samples. In order to ensure the robustness of the empirical results, the authors follow the same industry, based on the principle of similar asset size, non-ST companies are selected as matching samples, and the matching ratios are selected according to 1:1 and 1:2 respectively. Since the annual report of a listed company is prepared and released within 4 months of the end of the year, the release of the annual report of year t-1 occurs at the same time as whether it is specially treated in year t, to this end, the author uses the data of listed companies in t-2 years to build a model to predict whether they will have credit risk in year t. Based on the above conditions, the author selected 199 listed companies that were listed by ST from 2016 to 2021 as a sample of financially distressed companies, according to the principle of similar industries and similar scales, 398 non-ST companies were selected as matched normal company samples, the corresponding data period is from 2014 to 2020. Considering that enough samples should be considered for the selection of feature words, regardless of whether the ratio of financially distressed companies to normal companies in the empirical analysis is 1:1 or 1:2, the author selects feature words based on all samples. After preprocessing and word segmentation, when selecting feature words, since the chi-square test is difficult to exclude some words that cannot distinguish financially distressed companies from normal companies, such as “cash flow”, “operating activities”, “investors”, “management measures”, “suppliers”, “subsidiaries” and other common accounting or industry terms, therefore, the author screened the words that passed the chi-square test, finally, 93 characteristic words of financial distressed companies and 98 characteristic words of normal companies were selected, then calculate the weight of each feature word.

Data

The financial data in this article are all from the Guotai'an database, and the annual report is from the www.cninfo.com.cn, from which the text content of the management discussion and analysis is intercepted. As to whether the propensity to default indicator (TTD) and financial ratios reflect significant differences between financially distressed firms and healthy firms, a nonparametric Mann-Whitney test was performed on all variables, the results show that except for the operating cycle (OC) and net cash flow per share (NCPS) in the financial ratio variables, which are not significant, all other variables, including the propensity to default indicator (TTD), were significantly different and could be used to distinguish financially distressed firms from healthy firms. For the propensity to default indicator (TTD), the mean value of the normal company is 0.08898, the mean value of the financial distressed company is 0.23461, the Z value of the nonparametric test is −10.621, the significance level is 1%, indicate in the text of a financially distressed company that, in the text of its annual report, indeed, more negatively meaningful feature words related to financial distress were used.

Results Analysis

Regarding the role of default propensity index in predicting financial distress, the author uses two methods of logistic regression and support vector machine to conduct empirical test, and conducts in-sample test and out-of-sample prediction at the same time. First, the training set and the test set are not distinguished, and the in-sample test is carried out with all samples (in two ratios of 1:1 and 1:2), the models are modeled according to the two situations before and after adding the default propensity indicator (TTD); Then, 139 ST companies and paired samples from 2016 to 2021 were selected as the training set, and two methods were used for modeling, taking the samples of 60 ST companies and paired normal companies from 2016 to 2017 as the test set, the accuracy of the model in predicting financial distress is compared and analyzed. There are three main judgment criteria: First, whether the addition of TTD can improve the overall accuracy of classification (Accuracy); The second is whether the addition of TTD can reduce the probability of Type I error (Type I error, identifying ST company as a normal company) and Type II error (Type II error, identifying a normal company as ST company); The third is whether the addition of TTD can improve the AUC (Area Under Curve) of the receiver operating characteristic curve (ROC, Receiver Operating Characteristic Curve), AUC is calculated according to the probability that the sample is predicted to be ST based on the modeling result, and the value ranges from 0.5 to 1, the larger the value, the better the fitting effect of the in-sample model or the accuracy of the out-of-sample prediction.

Analysis Based on Logistic Regression

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.

Out-of-sample prediction results of Logistie regression

1:1 ratio 1:2 ratio

Do not join TTD Join TTD Do not join TTD Join TTD
AUC 91.80% 93.05% 90.01% 90.14%
Type I error 13.32% 6.66% 18.32% 13.32%
Type II error 18.32% 16.66% 15.82% 15.01%
Accuracy 84.16% 88.32% 83.32% 85.55%

Figure 1

Out-of-sample prediction plot of the Logistie regression

Analysis based on support vector machine

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.

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.

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

Plot of the in-sample test results for the SVM

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.

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

Out-of-sample prediction results plot for the SVM

Conclusion

The author proposes a study on the prediction of corporate financial distress by digital signal processing and multiple regression analysis, the authors used the chi-square test method, through a comparative analysis of the content of the management discussion and analysis texts of financial distressed companies and normal companies' annual reports, feature words reflecting financial distressed companies and normal companies are extracted, by extending the term frequency-inverse document frequency (TF-IDF), the feature word weights are set to construct the company manager's default tendency index (TTD), the default propensity indicator is then combined with financial variables, logistic regression and support vector machine methods were used, respectively, for empirically test whether the default propensity indicator can improve the accuracy of financial distress prediction, the results show, default propensity indicator reflected by text content, it can indeed improve the fit and prediction accuracy of the financial distress prediction model, reduce the Type 1 error rate and Type 2 error rate where false positives occur. However, the author's research is limited to listed companies, and it is difficult to apply to non-listed companies, but for these companies, it can be achieved by mining and analyzing the text content of news reports, social media and other channels, of course, since the text information of these channels comes from outside the enterprise, further research is needed on the selection of specific methods and technologies.

Figure 1

Out-of-sample prediction plot of the Logistie regression
Out-of-sample prediction plot of the Logistie regression

Figure 2

Plot of the in-sample test results for the SVM
Plot of the in-sample test results for the SVM

Figure 3

Out-of-sample prediction results plot for the SVM
Out-of-sample prediction results plot for the SVM

Out-of-sample prediction results of Logistie regression

1:1 ratio 1:2 ratio

Do not join TTD Join TTD Do not join TTD Join TTD
AUC 91.80% 93.05% 90.01% 90.14%
Type I error 13.32% 6.66% 18.32% 13.32%
Type II error 18.32% 16.66% 15.82% 15.01%
Accuracy 84.16% 88.32% 83.32% 85.55%

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%

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%

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