KR20200145347A - Method and apparatus for predicting stock price based on case-by-company event identification and multi-category emotional analysis - Google Patents

Abstract

The present invention relates to a method and a device for stock price prediction based on event identification by enterprise and multi-category sentiment analysis. The device includes a processor and a memory connected to the processor. Program commands that can be executed by the processor are stored in the memory such that an event identification reference for each enterprise is generated by calculating the number of news articles by enterprise collected for a preset past period, a sentiment score is calculated by performing multi-category sentiment analysis with reference to a pre-established sentiment dictionary on the news article pertaining to an event period in which news articles exceeding a first event identification reference of a first enterprise are present, a stock price prediction model is trained using the calculated sentiment score as an input variable and the excess return of the first enterprise for the event period as a result variable, and future stock price prediction is performed using the trained stock price prediction model in a case where the news articles of the first enterprise exceed the first event identification reference.

Description

Method and apparatus for predicting stock price based on case-by-company event identification and multi-category emotional analysis}

The present invention relates to a method and apparatus for predicting stock prices based on event identification and multi-category sentiment analysis for each company.

In general, a company's stock price prediction system using online unstructured data collects unstructured data generated from social media by checking only the association with the company targeted for stock price prediction, and then analyzing the emotions as positive or negative. Is being used to predict the company's stock price.

In the existing related technology, a method of simply collecting unstructured data from various sources related to a company and then analyzing the sentiment in a positive or negative dichotomy category is used to predict a company's stock price.

This is a practical use plan of unstructured data for stock price prediction, as major events occurring in the process of business activities have a relatively high impact on stock prices, and since the various events that can occur in business activities require more detailed analysis. It has a problem that it is overlooked.

KR registered patent 10-1531970

In order to solve the problems of the prior art, the present invention proposes a method and apparatus for predicting stock prices based on event identification and multi-category sentiment analysis, which can increase the accuracy of stock price prediction for each company.

In order to achieve the above object, according to an embodiment of the present invention, a stock price prediction apparatus based on event identification and multi-category sentiment analysis for each company, comprising: a processor; And a memory connected to the processor, wherein the memory generates an event identification criterion for each company by calculating the number of news articles for each company collected over a preset past period, and a first event identification criterion for the first company A news article during the event period in which there is a news article in excess of is calculated by analyzing a multi-category emotion with reference to a previously built emotion dictionary, and using the calculated emotion score as an input variable, during the event period A stock price prediction model is learned by using the excess return of the first company as an outcome variable, and when the current news article of the first company exceeds the first event identification criterion, the future stock price using the learned stock price prediction model In order to predict, there is provided a stock price prediction apparatus based on event identification and multi-category sentiment analysis for each company storing program instructions executable by the processor.

The multi-category emotion may include at least one emotional variable among hate, fear, anger, surprise, happiness, and sadness.

The hatred and sadness may have a higher weight than other emotional variables.

Among the news articles, sponsor-related articles and photo articles may be excluded.

The sentiment score may be determined using the number of news titles during the event period and the number of sentiment words belonging to individual sentiment categories included in the news title.

The stock price prediction model is a machine including at least one of a logistic regression model, a support vector machine, a Naive Beysian Classifier, and a random forest regression model. It can be built with a running algorithm.

The future stock price may be a stock price for a period of 15 to 20 days after a predetermined time point of the reference date of the current event.

The excess return may be an index indicating an increase or decrease in the stock price of an individual company in consideration of the increase in stock price in the market.

According to another aspect of the present invention, as a method of predicting a stock price based on event identification and multi-category sentiment analysis in a device including a processor and a memory, the number of news articles for each company collected during a preset past period is calculated. Generating an event identification criterion for each company; Calculating a sentiment score by analyzing a multi-category sentiment with reference to a preset sentiment dictionary for a news article during an event period in which a news article exceeding a first event identification criterion of the first company exists; Learning a stock price prediction model using the calculated emotion score as an input variable and the excess return rate of the first company during the event period as a result variable; And predicting a future stock price using the learned stock price prediction model when the current news article of the first company exceeds the first event identification criterion, event identification for each company and stock price based on multi-category sentiment analysis. A prediction method is provided.

According to another aspect of the present invention, there is provided a program stored in a recording medium performing the above method.

According to the present invention, the accuracy of the stock price prediction can be further improved by prioritizing the timing when the company's stock price fluctuations are likely to occur in the identification of a company's event, analysis of multi-category sentiment for it, and the generation of a stock price prediction model using this. have.

In addition, according to the present invention, it will be possible to check the size of a company's stock price fluctuations for each event, and use it for purposes such as monitoring business activities and managing reputation.

1 is a diagram illustrating a process of constructing a stock price prediction model according to the present embodiment.
2 is a diagram illustrating an actual stock price prediction process according to an embodiment of the present invention.
3 shows the accuracy of a stock price prediction model using only a technical index (technical statistical variable) as an input variable.
4 shows the accuracy of a stock price prediction model using only an emotion score as an input variable.
5 shows the accuracy of a stock price prediction model using emotion scores and technical indicators as input variables.
6 shows the accuracy of the descriptive statistical variable model, the emotion analysis model, and the mixed model according to the test period.
7 shows the accuracy of each algorithm in a stock price prediction model using only emotion scores as input variables.
8 shows the correlation between the stock price and the sentiment variable through regression analysis among sentiment variables.
9 is a diagram showing the configuration of a stock price prediction apparatus according to an embodiment of the present invention.

In the present invention, various modifications may be made and various embodiments may be provided, and specific embodiments will be illustrated in the drawings and described in detail.

However, this is not intended to limit the present invention to a specific embodiment, it is to be understood to include all changes, equivalents, and substitutes included in the spirit and scope of the present invention.

In the present invention, when a company-related event occurs, the stock price of an individual company is predicted by analyzing the multi-category sensitivity of a news article.

The stock price prediction process according to the present embodiment can be largely divided into a model building phase and a scoring phase.

1 is a diagram illustrating a process of constructing a stock price prediction model according to the present embodiment.

Referring to FIG. 1, first, a news article database is created by collecting news articles of each company for a past preset period through web crawling (step 100).

Step 100 may be a process of collecting news article titles of each company and establishing a news article title database.

Among the news collected in this example, articles related to corporate sports sponsorship activities such as baseball, soccer, volleyball, etc., which are judged to have very little impact on stock prices, and articles related to sponsored clubs and players belonging to the club may be excluded. Since most of the news (photo news) are simply gossip articles rather than corporate-related information that can affect the stock price, photo news (photo news) can also be excluded.

However, news articles related to advertising models such as advertisements and celebrities are judged as information that can affect the stock price as a marketing activity of a company and included in the analysis target.

Next, the number of news articles for each company is statistically calculated (step 102), and event identification criteria for each company are set (step 104).

Here, the event identification criterion for each company may be defined as a sum of a daily average and standard deviation calculated through the number of news articles for a predetermined period in the past.

In the present invention, the occurrence of an event may be defined as a case where the number of daily news articles of a specific company exceeds the event identification criterion.

For example, rather than judging all the articles as information related to the company, if the number of news increases more than usual, it is considered that an event related to the company has occurred.

An event identification criterion, which is a preset threshold, is set by statistically calculating the number of web-crawled news articles for N years, and an event occurs when the number of news articles on the current date t exceeds the event identification criterion.

According to the present embodiment, in order to exclude confounding effects between events, a short event window is set and clustered around the main contents of each event, or events are combined on an arbitrary basis to form one event. Discrete periods that do not set to and meet the statistical event criteria are considered as individual events.

Next, the event sentiment score is calculated by analyzing the multi-category sentiment of the news article during the event period in which the news article exceeding the event identification criterion of a specific company exists (step 106).

Step 106 may be performed with reference to a pre-built Sentiment Lexicon.

Emotional dictionary-based sentiment analysis has been widely used because of its practicality and accuracy, but for the accuracy of analysis, a high-quality emotional dictionary is essential. Therefore, in this embodiment, for the accuracy of analysis, a multi-category sensibility dictionary in a more advanced form from the existing Korean sensibility dictionary is applied.

In this embodiment, the emotions are categorized into'happiness','sad','fear','anger','hate','surprise','neutral', and six emotional variables, and do not exceed the threshold. Emotions whose classification is ambiguous are treated as neutrality. This classification has the advantage of being easy to understand because it is intuitive and similar to the form that people describe emotions in everyday life.

According to this embodiment, in order to calculate the emotional score during the event period of each company, the following formula is used.

Here,'Number of Sentiment Words' means the number of sentiment words in the title of a news article during the event period, and'Number of Event News Articles' means the news title during the event period.

According to this embodiment, since the degree of each emotion ('happiness','sad','fear','anger','hate','surprise') caused by the event is measured regardless of the size of the event,'Number Dividing'of Sentiment Words' by'Number of Event News Articles' to calculate the emotional score during the event.

Before analyzing the title of the news article during the event, a pre-processing process is performed for accurate sentiment analysis. Special symbols and stop words are removed so that only morphemes with meaning can be used from the collected news.

The sentiment analysis is performed with reference to the sentiment dictionary built in advance of the pre-processed text data, and the sentiment score according to the multi-category sentiment according to the present embodiment is calculated.

In conjunction with step 106, a technical indicator is calculated through analysis of stock price data of a specific company during the event period (step 108).

Technical analysis is one of the methods commonly used for stock price prediction, and the main technical indicators used for this are SMA (Simple Moving Average), MACD (Moving Average Convergence Divergence) oscillator, and Stochastic. oscillator, etc.

These technical indicators can be calculated based on the transaction price and volume in the stock market, and are used in a number of previous studies to analyze changes such as the rise or fall of stocks.

The technical indicators used in this embodiment are SMA (Simple Moving Average), EMA (Exponential Moving Average), MACD (Moving Average Convergence Divergence) oscillator, RSI (Relative Strength Index), Stochastic oscillator K%, Stochastic oscillator D%, Ultimate Oscillator (Larry William's R%), which is widely known to a person skilled in the art, and thus a detailed description thereof will be omitted.

According to an embodiment of the present invention, an emotion score may be a major input variable of a stock price prediction model, and a technical index may be selectively input.

This will be described in detail again in the process of comparison through experiments.

The sentiment score in step 106 and the technical index in step 108 serve as input variables for the stock price prediction model.

Next, the excess return of individual companies is calculated using the stock price data during the event period, and this is set as an outcome variable of the stock price prediction model (step 110).

Finally, by substituting the Event Sentiment Score and Event Technical Indicator of date t into the stock price prediction model, we learn the stock price prediction model by predicting the excess return rate from date t to t+α of individual companies ( Step 112).

Here, the excess return is an index indicating an increase or decrease in the stock price of an individual company in consideration of the increase in the stock price in the market.

The stock price prediction model according to the present embodiment is a model that is trained by an algorithm using past sentiment scores and/or technical indicators as input variables and excess returns as result variables.

In many previous studies, we measured the impact of unforeseen events on stocks by measuring the market model for each company and calculating abnormal returns. In other words, the abnormal rate of return is viewed as the result of the stock market's reaction to new information (events).

In order to find an abnormal return, you need to find the expected return for sample stock over an estimation period. For example, the Market-model-adjust return model may be selected among several models for the expected return rate and E(R _it ).

This is the most commonly used method in previous studies of various event studies (Bonnier and Bruner, 1989; Lummer and McConnell, 1989; Schipper and Thompson, 1983; Homan, 2006; Small et al., 2007). You can find the rate of return on the share price of Entity i at.

은 일별 회사 i의 주가에 대한 수익률(the rate of return on the share price of firm i on day t),

은 시장 포트폴리오의 주식 수익률(the rate of return on a market portfolio of stocks)로서 벤치마크 수익률이라고도 한다. 보통 대표적인 주가 지수를 사용한다. here,

Is the rate of return on the share price of firm i on day t,

Is the rate of return on a market portfolio of stocks, also known as the benchmark rate of return. Usually a representative stock price index is used.

는 절편(the intercept term),

는 주식 i의 구조적인 위험(the systematic risk of stock i)이다.

Is the intercept term,

Is the systematic risk of stock i.

과

는

의 측정 기간 동안의 회귀분석으로부터 얻을 수 있는 Ordinary Least Squares(OLS) parameter estimates이다.

and

Is

These are Ordinary Least Squares (OLS) parameter estimates that can be obtained from regression analysis over the measurement period of.

는 에러(the error term)을 의미한다.

Means the error term.

After finding the Expected Return, you can find the abnormal return (or excess return) for each individual stock. It is obtained through the difference between the actual return on date t during the event period and the expected return on individual stocks, as shown in the following formula.

2 is a diagram illustrating an actual stock price prediction process according to an embodiment of the present invention.

2 is a process of predicting a stock price after an event occurs using a learned stock price prediction model.

First, web crawling of news articles for each company of the new date t (step 200), and it is determined whether or not there is a company whose number of news articles of the date t exceeds a preset event identification criterion (step 202).

For companies exceeding the event identification criterion, a sentiment score is calculated by analyzing the multi-category sentiment of news article titles of the reference date t of the event occurrence (step 204).

Optionally, a descriptive index, which is a result of descriptive statistical analysis on the date t, of the past stock price data during the same event period is calculated (step 206).

Next, by substituting the input variable including the sentiment score into the stock price prediction model, the stock price at a future point in time is predicted from the reference date t of the occurrence of an event of an individual company (step 208).

Preferably, in step 208, the stock price may be predicted from the time point t+α has elapsed from the event occurrence reference date t, and more preferably, the stock price for a preset period from the event occurrence reference date t may be predicted.

The stock price prediction model according to the present embodiment targets the analysis of the news article title during the period when the event related to a specific company occurred, not the entire period, and also analyzes the emotions of individual companies in a multi-category, not polarity. It differs from previous models in that it is a model that tries to predict the stock price of a company by analyzing the analysis results through machine learning techniques.

According to the present embodiment, as an algorithm of a stock price prediction model, a logistic regression model, a support vector machine, a Naive Beysian Classifier, and a random forest regression analysis, which are machine learning techniques. Regression Model) can be used.

Since the algorithms have the characteristics of a classifier, the model according to the present embodiment calculates and inputs a sentiment score and a technical index when an event occurs, and classifies whether the future stock price will rise or fall. .

The accuracy of the algorithm is an indicator that intuitively indicates the performance of the model, and refers to the proportion of predictions with correct answers among all predictions.

The accuracy can be expressed in the following equation, and in this embodiment, True( means an increase in excess return, False means a decrease in excess return rate.

Here, True Positive (TP): The correct answer that predicts the true answer as true

False Positive (FP): Incorrect answer that predicts true false answer

False Negative (FN): Incorrect answer predicting that the correct answer that is true is false

True Negative (TN): This is the correct answer that predicts the true answer that is false as false.

As for the accuracy, the data in the test set are not usually evenly distributed, so there is a problem that it is impossible to be sure that the performance evaluation of the model is valid.

Therefore, in the present embodiment, the following complementary indicators are used to solve the bias of the data domain caused by the unbalanced data domain.

The specificity is the ratio of the actual false among those classified as false by the model and is expressed in the following equation. In the present embodiment, it refers to the ratio of the decline in the total excess return on which the stock price prediction model predicts the decline.

Sensitivity is the ratio of what the model predicts to be true among those that are actually true, and refers to the ratio of the stock price prediction model's prediction for the rise among the rise of the total excess return, and is as follows.

Sensitivity and specificity generally tend to decrease when one side increases. As such, since sensitivity and specificity tend to move in opposite directions, it is difficult to find a diagnostic method that increases both.

F1-Score is a harmonic average of precision and sensitivity, an index that helps to accurately evaluate the model's performance when the label of data has an unbalanced structure, and can be expressed through numbers.

The precision is the ratio of what is actually true among those classified as true by the model, and is expressed in the following equation. It is also called PPV (Positive Predictive Value).

Through the concept of the harmonic average, the bias caused by the large proportion of precision and sensitivity is largely resolved, and is expressed in the following equation.

AUC (Area Under Curve) is a metric for easily evaluating the discrimination power of a model numerically and shows the classification performance of the model in the entire range of possible cut-off values.

In ROC (Receiver Operating Characteristic) Curve, AUC (Area Under Curve) is the numerical value of the area under the graph. The maximum value is 1, and the better the model, the closer to 1 is calculated.

Here, ROC is the result of visualizing changes in recall and false positive rates based on several threshold values. The false positive rate, also called FPR (False Positive Rate), is the ratio of the actual false data that the model predicted to be true, and is expressed by the following equation.

In other words, the AUC is a model with good performance as a value closer to 1 comes out as the value of the recall rate increases compared to the false positive rate. AUC is a commonly accepted performance metric when evaluating the performance of a classification model in the area of data mining.

Hereinafter, an experiment process for evaluating the stock price prediction model according to the present embodiment will be described.

If an event exceeding the event identification criteria of a specific company occurs, the test period is 1day, 2days, 3days, 4days, 5days, 6days, 7days, 10days, from the day before, the day, the next day, two days, and three days after the event occurrence reference date. It is set as 15days, 20days, 25days, 30days.

A model with input variables as descriptive statistical variables (technical indicators) (descriptive statistics variable model), a model with sentiment analysis scores (sensibility analysis model), and a model with both descriptive statistical variables and sentiment analysis scores (mixed model) We have seen how the accuracy of is changed when variables and conditions are changed.

We looked at how the accuracy of each machine learning algorithm changes when the test period changes.

The test period was set as a variable variable, and the accuracy of each event occurrence reference date was set as a fixed variable by calculating the arithmetic mean value for the entire date.

3 shows the accuracy of a stock price prediction model using only a technical index (technical statistical variable) as an input variable.

3, in a stock price prediction model using only descriptive statistics as input variables, logistic regression model (LR), support vector machine (SVM), naive Bayesian classifier (NB) ) And Random Forest Regression Model (RF), the prediction accuracy increases with a relatively long test period rather than a short test period, and starts to increase significantly from 10 days to 15 days. And 20 days showed the highest prediction accuracy.

4 shows the accuracy of a stock price prediction model using only an emotion score as an input variable.

Referring to FIG. 4, even in the stock price prediction model using only the emotion score as an input variable, the accuracy of the prediction increased significantly after 10 days of the event occurrence reference date, and was most accurately predicted at 15 days and 20 days. In addition, during the test period, the model with the sentiment score as the input variable predicted the stock price more accurately than the model with the technical indicator as the input variable.

5 shows the accuracy of a stock price prediction model using emotion scores and technical indicators as input variables.

Referring to FIG. 5, the mixed model also showed a similar aspect to the above two models, but the accuracy was not higher than that of the descriptive statistical variable model and the sentiment analysis model, but rather, it can be found that it is inferior to the two models.

6 shows the accuracy of the descriptive statistical variable model, the sentiment analysis model, and the mixed model according to the test period.

Referring to FIG. 6, it can be seen that the emotional variable model has a higher accuracy than other models in 15 days and 20 days when viewed in a long test window (7 days to 30 days) relative to the short test window. .

7 shows the accuracy of each algorithm in a stock price prediction model using only emotion scores as input variables.

In FIG. 7, the reference date of event occurrence is a variable variable, but the test period variable is calculated as an arithmetic mean value and set as a fixed variable.

All algorithmic techniques show a trend of increasing prediction accuracy as the time increases after the event occurs. In particular, it can be seen that all algorithmic techniques predict the most accurately when 3 days after the event occurs (t=+3).

7 shows three selections of emotional variable models showing the highest prediction accuracy for each algorithm technique.

It can be seen that most of the models show the highest prediction accuracy when the event occurs 2 days (T=+2) or 3 days (T=+3), and 10, 15, and 20 days have elapsed from the reference date of the event. . It can be seen that most of the models show high sensitivity and tend to predict the rise of the stock price well.

As shown in FIG. 7, the model with the highest prediction accuracy predicts the stock price after 15 days from 3 days after the event occurs (T=+3) using a logistic regression model technique. It is a model.

Therefore, a regression analysis was performed between the fluctuation of the excess return 15 days after the event occurrence reference date and the sentiment variable according to the present embodiment to examine which sentiment showed a high correlation with the stock price. As shown in Figure 8, disgust and sadness showed significant F values of 0.007883 and 0.057358, respectively, indicating that they were statistically significant variables, and the excess return fluctuations were -2.18886 and -1.21878. By showing the coefficient, it can be confirmed that there is a negative correlation. The regression equation between the excess return fluctuation and the emotional variable is as follows, and the significant F value of the equation is 0.053723. Of the 2660 total observations, the degrees of freedom are 2653 and the residuals are 7.

9 is a diagram showing the configuration of a stock price prediction apparatus according to an embodiment of the present invention.

As shown in FIG. 9, the stock price prediction apparatus according to the present embodiment may include a processor 900 and a memory 902.

The processor 900 may include a central processing unit (CPU) capable of executing a computer program or a virtual machine.

The memory 902 may include a nonvolatile storage device such as a fixed hard drive or a removable storage device. The removable storage device may include a compact flash unit, a USB memory stick, or the like. The memory 902 may also include volatile memories such as various random access memories.

Program instructions executable by the processor 900 are stored in the memory 902.

The memory 902 according to the present embodiment generates an event identification criterion for each company by calculating the number of news articles for each company collected during a preset past period, and a news article that exceeds the first event identification criterion of the first company. Calculate the emotional score by analyzing the multi-category sentiment with reference to the sentiment dictionary built in advance for the news article during the event period in which there is, and the calculated sentiment score as an input variable, and the excess return of the first company during the event period. A stock price prediction model is trained as an outcome variable, and when the current news article of the first company exceeds the first event identification criterion, the learned stock price prediction model is used to predict the future stock price, and executed by the processor 902 Stores possible program instructions.

Here, the multi-category sensibility includes at least one emotional variable among hate, fear, anger, surprise, happiness, and sadness, and among them, hate and sadness may have a higher weight than other emotional variables.

Also, among news articles, sponsor-related articles and photo articles may be excluded.

The sentiment score according to the present embodiment may be determined using the number of news titles during the event period and the number of emotional words belonging to individual sentiment categories included in the news title.

The above-described embodiments of the present invention have been disclosed for the purpose of illustration, and those skilled in the art who have ordinary knowledge of the present invention will be able to make various modifications, changes, and additions within the spirit and scope of the present invention, and such modifications, changes and additions It should be seen as belonging to the following claims.

Claims (10)

As a stock price prediction device based on event identification and multi-category sentiment analysis by company,
Processor; And
Including a memory connected to the processor,
The memory,
By calculating the number of news articles for each company collected over a preset past period, an event identification criterion for each company is created,
Calculate a sentiment score by analyzing a multi-category sentiment by referring to a pre-built sentiment dictionary for news articles during an event in which news articles exceeding the first event identification criteria of the first company exist,
Using the calculated emotional score as an input variable, and using the excess return of the first company during the event period as a result variable, a stock price prediction model is learned,
When the current news article of the first company exceeds the first event identification criterion, to predict a future stock price using the learned stock price prediction model,
A stock price prediction device based on enterprise-specific event identification and multi-category sentiment analysis that stores program instructions executable by the processor. The method of claim 1,
The multi-category sensibility is,
Stock price prediction device based on enterprise-specific event identification and multi-category sentiment analysis including at least one emotional variable among hate, fear, anger, surprise, happiness, and sadness. The method of claim 2,
A stock price prediction device based on event identification and multi-category sentiment analysis in which the hate and sadness have a higher weight than other emotional variables. The method of claim 1,
A device for predicting stock prices based on event identification and multi-category sentiment analysis for each company that excludes sponsor-related articles and photo articles among the above news articles. The method of claim 2,
The sentiment score is determined by using the number of news titles during the event period and the number of sentiment words belonging to individual sentiment categories included in the news title. The method of claim 1,
The stock price prediction model,
A company built with machine learning algorithms including at least one of Logistic Regression Model, Support Vector Machine, Naive Beysian Classifier, and Random Forest Regression Model. Stock price prediction device based on event identification and multi-category sentiment analysis. The method of claim 1,
The future stock price is a stock price prediction device based on event identification and multi-category sentiment analysis, which is a stock price for a period of 15 to 20 days after a predetermined point of a reference date of a current event. The method of claim 1,
The excess return is,
A stock price forecasting device based on company-specific event identification and multi-category sentiment analysis, which is an index indicating the rise or fall of the stock price of an individual company in consideration of the share price increase in the market. As a method of predicting stock prices based on event identification and multi-category sentiment analysis in a device including a processor and memory,
Generating an event identification criterion for each company by calculating the number of news articles for each company collected during a preset past period;
Calculating a sentiment score by analyzing a multi-category sentiment with reference to a preset sentiment dictionary for a news article during an event period in which a news article exceeding a first event identification criterion of the first company exists;
Learning a stock price prediction model using the calculated emotion score as an input variable and the excess return rate of the first company during the event period as a result variable; And
When the current news article of the first company exceeds the first event identification criterion, event identification and multi-category sentiment analysis-based stock price prediction for each company including predicting future stock prices using the learned stock price prediction model Way. A program stored on a recording medium performing the method according to claim 9.

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