TWI399699B - Forecasting taifex based on particle swarm optimization - Google Patents

Description

Taiwan stock index futures forecasting method based on particle swarm optimization algorithm

The invention relates to a method for predicting Taiwan stock index futures, in particular to a Taiwan stock index futures forecasting method based on particle swarm optimization algorithm and fuzzy time series.

In order to solve the human needs for various specific problems and economic activity predictions, researchers have tried to propose various prediction methods and models in recent years. In the early stage, the traditional regression analysis method was adopted for the forecast of the securities and futures index. However, the regression analysis is mainly applicable to the prediction of phenomena with less variation, linearity and low complexity. For the securities futures market full of uncertainty, the regression analysis is There are quite some limitations. The main reason is that the securities and futures trading activities are random phenomena, and the overall time series data is generally nonstationary. If the direct regression analysis will produce spurious regression, An estimate that caused a serious error. The traditional time series analysis mode is a quantitative forecasting method. Its prediction mode generally has the following shortcomings: 1. Determine the accuracy of the prediction mode based on the change of historical data; 2. If the data is insufficient or the collected data has errors, the traditional prediction The mode will have a high error; 3. If there is an unexpected situation that is sufficient to affect the next real value, the prediction of the traditional time series. In order to overcome the shortcomings of traditional statistical prediction methods, such as poor prediction results and low accuracy, many new prediction methods and models have been developed in recent years. With the continuous improvement and improvement of prediction methods, scholars have found that to construct specific problems. The specific purpose activity prediction method is more accurate than the general purpose prediction method.

The predictive concept of time-fuzzy sequence is the theoretical application of fuzzy theory added to the time series model, which plays an important role in various research fields, such as traffic load estimation, stock market stock price forecast, medical blood pressure. Forecast and so on. In 1993, scholar Song et al first merged fuzzy logic concepts into time series prediction, and proposed a fuzzy time series prediction architecture, which uses fuzzy logic reasoning to effectively deal with semantic data in fuzzy and uncertain environments; through fuzzy time series theory, Song et al. proposed two predictive models (ie, time-varying predictive models and non-time-varying predictive models) and predicted the number of students at the University of Alabama. In 1996, scholar Chen improved the previous prediction method and established a relatively simple prediction model, which has the advantages of reducing the number of calculations and simplifying the calculation method, which is a prediction method commonly used in the field of later prediction research. Later, Chen proposed a prediction method using High-Order Fuzzy Time Series. The scholar Yu et al. adjusted the time interval of the fuzzy time series to obtain a more accurate prediction rate. The scholar Liu built a new prediction model based on the trapezoidal fuzzy numbers. In the research of Taiwan stock index forecasting, scholars Yu and Huarng et al. established a bivariate fuzzy time series forecasting model for Taiwan stock index forecasting. Later, Professor Wang Lihui and Professor Chen Ximing used fuzzy time series theory and genetic algorithm ( Genetic Algorithm), and Simulated Annealing algorithm, establish different fuzzy prediction models to predict temperature and Taiwan stock index. Through the evolution of the application of fuzzy time series theory, we can know that "lengths of intervals" and "content of forecast rules" are the two major factors affecting the accuracy of prediction. The predictive models are known to use empirical rules or evolutionary rules to adjust these two factors, but their effects are still unsatisfactory.

In view of this, a high-accuracy Taiwan stock index futures forecasting method is necessary.

In view of the above-mentioned lack of prior art, the present invention proposes a method based on Particle Swarm Optimization and fuzzy time series for predicting futures index of Taiwan stock index, which combines particle swarm optimization algorithm with fuzzy time series theory. A high-precision Taiwan stock index futures forecasting model is proposed. The theory of Particle Swarm Optimization was first proposed by Kennedy and Eberhart in 1995. The inspiration was mainly derived from the clustering behavior of birds and fish. Therefore, the spirit of this algorithm is mainly to use the concept of clustering and moving to find the best solution in our search space. In each optimization operation, each particle (particle, meaning bird or fish) is responsible for a part of the region-optimized parameter search. During this search, each particle records the most current one. Local best, so that there is a moving target in the search process. In addition to the best solution that we have found so far, each particle will move to the best solution of all current particles (Global best), which will enable us to find solutions that are globally optimized. effect.

One object of the present invention is to use the particle swarm optimization algorithm to adjust the "lengths of intervals" and the "content of forecast rules" to the optimal value, thereby effectively improving the forecast of the Taiwan stock index futures. The accuracy rate. The invention utilizes a particle swarm optimization algorithm to establish fuzzy rules based on all training data; when all fuzzy prediction rules are trained to be established, the fuzzy rules can be used to predict new test data, that is, the Taiwan stock market is calculated. The forecast value of the stock index futures.

Another object of the present invention is to provide a method for judging trends in a Taiwan stock index futures market to evaluate market transactions.

A further object of the present invention is to provide a method for predicting future market trends in the Taiwan stock index futures market to evaluate market transactions to increase profitability and reduce investment risk.

The above-described objects, features and advantages will be apparent from the following detailed description of the preferred embodiments.

The preferred embodiments of the present invention will be described in detail with reference to the appended drawings. In the drawings, the same or similar elements are represented by the same reference numerals even if they are drawn in different drawings. In the following description, the detailed description of the known functions and structures incorporated herein is omitted when it may obscure the subject matter of the present invention.

As shown in the first figure, it is a flow chart of a conventional fuzzy time series prediction method, and the steps are as follows:

1. In step 11, segment and blur the historical data 10, define the length of the interval, the upper and lower bounds of the domain, and the number of intervals: Let D _min and D _max be the minimum and maximum values in the historical data, respectively. The two values are respectively subtracted and added with an appropriate adjustment value so that the domain is [D _min - U _min , D _max + U _max ], the number of set intervals is n, and the domain is divided into groups by a constant group. I ₁ , I ₂ , I ₃ , I ₄ ,..., I _n .

2. In step 12, define a fuzzy set and a fuzzy relationship, and establish a fuzzy relationship group: rewrite the interval data in which the historical data falls into the data represented by the text, and obtain the fuzzy set relationship. Fuzzy relationships, the inferred fuzzy logical relationships are grouped into the same group; all groups can be divided into trained data groups and untrained data groups.

3. In step 13, according to the fuzzy relationship, establish a fuzzy prediction rule: establish a fuzzy prediction rule by using the above-mentioned fuzzy logical relationship group; including a matching part and a corresponding forecasted value; The conforming portion includes a current state of the group, and the corresponding predicted values are calculated by an estimating based on next state scheme (EBN) and a mater voting (MV) scheme, respectively.

4. In step 14, predict the training and test data according to the aforementioned fuzzy prediction rule.

As shown in the second figure, it shows a flow chart of the method for predicting the Taiwan stock futures index according to the present invention; the present invention is based on the fuzzy time series prediction method, and combines the particle swarm optimization algorithm to adjust the number of intervals (lengths Of intervals) and "content of forecast rules" to improve the accuracy of the Taiwan stock futures index. In the embodiment of the present invention, first, in step 201, the historical data 10 is defined as Y(t), and the number of intervals is defined as n, and the upper and lower bounds of the domain are d ₀ and d _n , respectively. a time series of historical data; with a vector having n - 1 elements (ie, d ₁ , d ₂ , ..., d _i , ..., d _{n -2} and d _{n -1} , where And d _{i -1} < d _i ) as one of the particle group optimization algorithms; in step 202, according to the n -1 elements, the n interval is defined as I ₁ =( d ₀ , d ₁ ], I ₂ =( d ₁ , d ₂ ],..., Ii =( d _{i -1} ,d _i ],..., I _{n -1} =( d _{n -2} , d _{n -1} ] and I _n = ( d _{n -1} , d _n ], that is, fuzzy according to the fuzzy time series theory; in step 203, further define a fuzzy set and a fuzzy relationship of each particle to establish a fuzzy relationship group; in step 204 For the trained fuzzy prediction rule, calculated by the secondary state based estimation scheme (EBN); in step 205, for the untrained fuzzy prediction rule, calculated by the mother voting (MV) scheme. According to the results of steps 204 and 205 , establish a fuzzy prediction rule for each particle, as shown in step 206.

In a training phase, as shown in step 207, the mean square error (MSE) value is used to represent the prediction accuracy of a particle. The lower the mean squared difference, the higher the accuracy.

In a specific embodiment, the mean square error is expressed as follows:

Where, N _forecasted represents the predicted data quantity, FD _i represents the i th prediction data, and TD _i represents the corresponding historical training data about FD _i .

Depending on the result of step 207, when the result satisfies a predefined stop condition, such as: obtaining the best solution or reaching the maximum moving step, as shown in step 208, the training of the prediction rule is completed, and the optimal solution of all particles is selected. The fuzzy prediction rule constructed by the best one is the final result, as shown in step 211.

As shown in step 209, if the result of step 207 fails to satisfy the stop condition, then in step 210, each particle is moved to a new position, and the element corresponding to the new vector is first adjusted to Make sure each element d _i ( ) is tied to an ascending order.

One embodiment of the present invention moves all particles to other locations during the training phase. The movement of a particle is expressed as follows:

V _id = ω × V _id + C ₁ × Rand () × ( P _id - X _id ) + C ₂ × Rand () × ( P _gbest - X _id ) (2)

X _id = X _id + V _id (3)

Where V _id is the rate of a particle id, the rate is limited to the pre-custom range of [- V _MAX , V _MAX ]; ω is the inertial weight coefficient; C ₁ and C ₂ respectively represent self-confidence Self confidence coefficient and social confidence coefficient.

In the particle swarm optimization algorithm, in the whole operation program, the ω value is linearly decreasing, C ₁ and C ₂ are constant, and Rand () is a Random Number Generator, which is normally distributed. Below, a random real number is generated between 0 and 1. P and _X-id id _id lines represent the optimal solution of the present position data range of a _particle; P gebst line represents the optimal solution in all of the particles within the full range of information.

In a training phase, an embodiment of the present invention constructs an independent group of fuzzy prediction rules by using fuzzy time series theory in the training stage, and uses it to predict all historical training data of each particle.

In an embodiment of the present invention, all particles are moved to a new position in the training phase, and the basis of the motion is expressed by equations (2) and (3), and all the particles are evaluated according to equation (1). The accuracy is predicted, and steps 203 through 207 are cycled until a predefined stop condition is met, such as: obtaining an optimal solution or reaching a maximum moving step. If the stop condition is satisfied, as shown in step 208, the fuzzy prediction rule constructed by the best one of the best solutions of all particles is selected as the final result. If the stop condition is not satisfied, then steps 203 through 207 are cycled until the predefined stop condition is met, and the fuzzy prediction rule trained by the best one of the best solutions of all particles is selected as the final result.

One embodiment of the present invention, in the test phase, as shown in step 212, uses the fuzzy prediction rules constructed by the best of the best solutions for all particles to predict new test data. First, if the corresponding part of the new test data conforms to an already trained fuzzy prediction rule, the predicted value is calculated according to the fuzzy prediction rule.

If the corresponding part of the new test data meets an untrained fuzzy prediction rule, the new test data is predicted by the mother voting (MV) scheme; if not, the prediction system of the new test data is It is carried out in accordance with the fuzzy prediction rules. The mother voting (MV) scheme calculates its predicted value according to the following equation:

Where W _h represents the user's preset maximum number of votes, λ refers to the fuzzy relationship series, m _t1 and m _tk ( ) indicates the current past text representation value in the current state and the point in the corresponding interval of other past text representation values.

In order to facilitate the explanation of the present invention, a specific embodiment of the present invention is exemplified by the situation of the Taiwan stock index futures market from August 3 to August 31, 1998. First of all, for the convenience of explanation, the case of the transaction history data of the Taiwan stock index futures market from August 3 to August 31, 1998 assumes that the number of particles is 5, and each particle is defined as an independent group with 7 intervals. Group, ie I ₁ =( b ₀ , b ₁ ], I ₂ =( b ₁ , b ₂ ], I ₃ =( b ₂ , b ₃ ], I ₄ =( b ₃ , b ₄ ], I ₅ =( b ₄ , b ₅ ], I ₆ =( b ₅ , b ₆ ], I ₇ =( b ₆ , b ₇ ]; the data shown is merely illustrative of the invention, not enumerated; The data Y ( t ) is as follows:

The maximum and minimum values of the data are D _{m in} =6566 and D _max =7560, respectively. The adjusted Y ( t ) domain is represented by Y ( t )=(6500,7600].

In order to facilitate the description of the present invention, the fuzzy rules for constructing the particles 1 are exemplified, and the fuzzy rules for the other particles are established by those skilled in the art and are specifically embodied by the specific embodiments disclosed herein. In this embodiment, it is assumed that seven intervals of the particles 1 of the five particles are I ₁ = (6500, 6657], I ₂ = (6657, 6814), I ₃ = (6814, 6971), I ₄ = (6971, 7128), I ₅ = (7128, 7285), I ₆ = (7285, 7442), and I ₇ = (7442, 7600), but it should be noted that the data shown in this embodiment is only a brief description. The examples of the invention are not listed, but are not limited thereto.

Also, the domain of Y ( t ) in the particle is divided into seven intervals, respectively, A ₁ = "worst", A ₂ = "bad", A ₃ = "a little bad", A ₄ = "average", A ₅ = "good", A ₆ = "very good", and A ₇ = "excellent" text representation values, and are represented as a fuzzy set by equation (5) below, respectively.

A _i = I ₁ / u ₁ + I ₂ / u ₂ + I ₃ / u ₃ + I ₄ / u ₄ + I ₅ / u ₅ + I ₆ / u ₆ + I ₇ / u ₇ (5)

Where u _j ( ) is a real number between 1 and 0.

The fuzzy set and the interval comparison are expressed as follows:

Accordingly, the results of the obscuring of historical data are shown in the following table:

Secondly, the present embodiment establishes a lambda -level fuzzy relation, and ( F ( t - λ ), F ( t - λ +1), ..., F ( t -2), F ( t -1)) represents the current state. (current state)", F ( t ) means "next state", and its fuzzy relation is ( F ( t - λ ), F ( t - λ +1),..., F ( t -2), F ( t -1)) → F ( t ) is a representation; for convenience of explaining the present invention, this embodiment sets λ = 3 in the λ -level fuzzy relation, but the data shown is merely an illustration of the present invention, not enumerated For example, the fuzzy relationship ( A ₇ , A ₇ , A ₇ ) → A _{7 is} ( F (8/3/1998), F (8/4/1998), F (8/5/1998)) → F (8/6/1998).

Here, the fuzzy relationship is shown in the following table:

Where ( A ₂ , A ₂ , A ₁ )→# refers to ( F (8/28/1998), F (8/29/1998), F (8/31/1998))→ F (9/1/ 1998), while F (9/1/1998) is not listed, so it is marked with #. Moreover, in the foregoing list, each group contains more than one fuzzy relationship; in this embodiment, a fuzzy prediction rule is established according to the fuzzy relationship of the foregoing list. The fuzzy prediction rule is composed of a matching part and a corresponding forecasted value. The former is composed of the current state of the group; the latter calculation distinguishes the trained and untrained parts, and the trained part is Calculated by the estimating based on next state scheme (EBN), the untrained part is calculated by the mater voting (MV) scheme. For the follow-up state basis estimation scheme (EBN), each corresponding interval is further divided into three equal intervals, and a predicted value is obtained according to the following equation (6):

Where n represents the total number of next states in the same group, mid _k ( ) Represents the number of states times on the corresponding section among the k point (midpoint), submid _k represents k times the number of states corresponding to the midpoint of the interval of three sub-interval by one. For example, the above table group 4 is only one state A ₆ , and the inter-partition I ₆ (ie (7285, 7442)) such as the state-based estimation scheme (EBN) is three sub-intervals, respectively SR _6,1 = (7285, 7337.3), SR ₆ , ₂ = (7337.3, 7389.6) and SR _{6, 3} = (7389.6, 7442). According to the aforementioned group 2 is taken from the fuzzy relationship ( F (8/6/1998), F ( 8/7/1998), F (8/10/1998))→ F (8/11/1998); the order-based estimation scheme (EBN) knows that F (8/11/1998) corresponds to the actual data Y ( 8/11/1998) (ie 7360) is in the sub-interval SR _6,2 , and the submid ₆ is 7363.45 (ie 7337.3+(7389.6-7337.3)/2) in this interval; accordingly, SR _6,2 among point interval I _{6 6} average mid midpoint of, and in accordance with the equation that calculates the value of the group 2 7363.475 prediction.

For the untrained part, the mater voting (MV) scheme is used to predict the calculation; the above table group 14 is taken as an example, and is calculated according to the equation (4), setting W _h = 2, and the latest past text indicates the highest vote of the value A ₁ The number is 2, and the remaining words indicate that the votes of the values A ₂ and A _{2 are} each 1, and the predicted values of the group 14 of the above table are calculated as follows:

According to the results of the previous table, the relevant fuzzy prediction rules can be obtained. Among them, a fuzzy prediction rule includes a matching part and a prediction part; the current state of the part-group fuzzy relationship is met. The prediction part is the prediction value part. The fuzzy prediction rule obtained in this embodiment is shown in the following table:

Accordingly, the historical data of the Taiwan Stock Index Futures Market from August 3 to August 31, 1998 in this example, the predicted values are as follows:

The above is a specific embodiment of the present invention, and the particle 1 of the assumed five particles is taken as an example to construct the fuzzy rule of the particle 1; accordingly, the establishment of other particle fuzzy rules is generally known to those skilled in the art. It is embodied by the specific embodiments of the above disclosed embodiments of the present invention.

According to the results of the above list, in the above equations (2) and (3), X _{id is} limited to (6500, 7600), V _{id is} limited to [-50, 50], C ₁ and C ₂ are 2, and ω is 1.4, and calculate the mean square error of each particle according to equation (1); then the random starting position and mean square error of each of the five particles are as shown in the following table:

The random starting rates of the five particles are shown in the following table:

Based on the foregoing assumptions for the seven segments of each particle, the present embodiment is predicted by the fuzzy prediction rules listed above; however, it should be known to those skilled in the art that if there are different definitions for particles, The choice of fuzzy prediction rules is not limited to the data in the above table.

Accordingly, for example, the mean square error (MSE) value of the particle 1 can be calculated according to equations (1), (2), and (3), and is calculated as follows:

Among them, the forecasted data quantity N _forecasted is 20, FD _i ( ) indicates the predicted value of Y (8/5/1998+ i ); TD _i represents the corresponding historical training material for FD _i (ie Y (8/5/1998+ i )). It should be noted that FD ₂₁ represents the predicted value of the new test data (i.e., Y (9/1/1998)) and thus is not used in this illustration to calculate the mean square error (MSE) value of particle 1.

According to the calculation of the pre-opening, each particle of the embodiment can obtain the mean square error, and obtain the current optimal position of each particle according to the following table;

According to the above table, the current optimal solution of all five particles in the present embodiment in the entire data range (ie, P _{gebst of} equation (1)) is particle 4 (since the mean squared difference is the smallest) . Thereafter, all the particles are adjusted to the second position according to equations (1) and (2), and the mean square difference of the relevant position is obtained according to equation (3); the historical data exemplified in the embodiment is calculated, and the second The location and its mean squared difference table are as follows:

As shown in the above table, the current best solution of all particles in this example in the entire data range (i.e., P _{gebst of} equation (1)) is still particle 4. Here, in the embodiment, according to the foregoing steps, all the particles are adjusted to the third position by the equations (1) and (2), and the mean square error of the relevant position is obtained according to the equation (3), and the cycle is calculated according to the upper step. Until the stop condition is met. When the stop condition is satisfied, it means that the prediction rule has been completed, and the test data is predicted by the prediction rule of the completed training.

According to an embodiment of the present invention, the accuracy of the prediction of the Taiwan stock index futures is effectively improved by the fuzzy time series theory and the particle swarm optimization algorithm. In comparison with the prediction results of other prior art embodiments of the present invention, the present invention has a higher accuracy rate for the prediction of the Taiwan stock index futures, wherein the present invention is a three-level fuzzy relationship of 16 intervals, and the prediction results are as follows: Show:

Among them, the previous technologies listed in the above table are: Linear model : y =-27.348 x +7509 Polynomial model of degree 2: y =1.2779 x ² -75.907x+7824.6 Polynomial model of degree 3: y =0.1247x ³ - 5.8308x ² +33.592x+7454.9 Moving average model : period = 3 It can be seen that the present invention has a higher accuracy rate than the conventional stock index futures forecast.

From the above, it will be appreciated by those skilled in the art that the present invention is described herein for the purpose of illustration only. However, a person skilled in the art can make a number of modifications without departing from the spirit and scope of the invention. Accordingly, the invention is not limited except in the scope of the appended claims.

10. . . Historical data

201. . . Define the number of particles program

202. . . Set particle interval and blur program

203. . . Fuzzy relationship group establishment procedure

204. . . Secondary state basic estimation scheme calculation program

205. . . Parent voting scheme calculation program

206. . . Particle fuzzy prediction rule establishment program

207. . . Mean variance calculation program

208. . . Stop condition reached

209. . . Stop condition not reached

210. . . Particle position shift program

211. . . Prediction rule completion training

212. . . Test data prediction program

The preferred embodiment of the present invention will be further described in the following description and the accompanying drawings, in which:

The first diagram is a flow chart of a prior art conventional fuzzy time series prediction method.

The second figure is a flow chart of the prediction method according to the present invention.

10. . . Historical data

201. . . Define the number of particles program

202. . . Set particle interval and blur program

203. . . Fuzzy relationship group establishment procedure

204. . . Secondary state basic estimation scheme calculation program

205. . . Parent voting scheme calculation program

206. . . Particle fuzzy prediction rule establishment program

207. . . Mean variance calculation program

208. . . Stop condition reached

209. . . Stop condition not reached

210. . . Particle position shift program

211. . . Prediction rule completion training

212. . . Test data prediction program

Claims (6)

A prediction method of Taiwan stock index futures based on particle swarm optimization algorithm, which includes: based on historical training data, using particle swarm optimization algorithm to train fuzzy prediction rules, including: using each particle The interval generates an independent group of fuzzy prediction rules for predicting all training data; each particle is moved to another position according to the first equation and the second equation, wherein the first equation is V _id = ω × V _id + C ₁ × Rand () × ( P _id - X _id ) + C ₂ × Rand () × ( P _gbest - X _id ), where the second equation is X _id = X _id + V _id , where V _id represents one The rate of particle id , ω represents the inertial weight coefficient, C ₁ represents the self confidence coefficient, C ₂ represents the social confidence coefficient, and Rand () is a random number. The Random Number Generator, which has a normal distribution, produces a random real number between 0 and 1, X _id represents the current position of the particle id , P _id represents the best solution of the particle id , and P _gebst represents all One of the best solutions of the optimal solution of the particle; subtracting and adding an adjustment value to the minimum and maximum values in the historical data to define the domain of the historical data; dividing the historical data into n intervals, defining the The interval is I ₁ =( d ₀ , d ₁ ], I ₂ =( d ₁ , d ₂ ],..., I _i =( d _{i -1} , d _i ],..., I _{n -1} = ( d _{n -2} , d _{n -1} ] and I _n =( d _{n -1} , d _n ]; expressed as a fuzzy set according to a third-party program, wherein the third-party program is A _i = I ₁ / u ₁ + I ₂ / u ₂ + I ₃ / u ₃ + I ₄ / u ₄ + I ₅ / u ₅ + I ₆ / u ₆ + I ₇ / u ₇ ; establish a lambda -level fuzzy relation to ( F ( t - λ ), F ( t - λ +1),..., F ( t -2), F ( t -1)) means "current state", F ( t ) means "secondary state" (next state)", the fuzzy relation is ( F ( t - λ ), F ( t - λ +1),..., F ( t -2), F ( t -1)) → F ( t ) To represent; and to establish a fuzzy prediction rule according to the λ -level fuzzy relationship; and to predict the test data by using the completed fuzzy prediction rule after the training of the fuzzy prediction rule is completed, the method includes: for the trained fuzzy prediction rule The four equations calculate the predicted value, and the untrained fuzzy prediction rule calculates the predicted value by the fifth equation; wherein the fourth equation is Where, Forecasted Value represents the predicted value, and n represents the total number of next states in the same group, mid _k (1 k n ) indicates that the secondary state number k corresponds to the midpoint of the interval, and submid _k indicates that the secondary state number k corresponds to the midpoint of one of the three secondary intervals in the interval. For example, the method for forecasting the index of Taiwan stock index in item 1 of the scope of patent application, wherein the fifth equation is Among them, Forecasted Value represents the predicted value, W _h represents the preset maximum number of votes, λ refers to the fuzzy relationship series, m _t1 and m _tk (2 k λ ) indicates that the latest past text representation value and other past text representation values correspond to the midpoint of the interval in the current state. For example, the method for predicting the futures index of the Taiwan stock index according to item 1 of the patent application, wherein the step of using the particle swarm optimization to train the fuzzy prediction rule based on the training data further comprises: expressing the mean squared deviation according to the sixth equation The prediction accuracy of a particle, where the sixth equation is MSE represents the mean square error, N _forecasted represents the predicted data quantity, FD _i represents the i th prediction data, and TD _i represents the corresponding training data about the FD _i . For example, the method for predicting the futures index of Taiwan stock index in the first paragraph of the patent application, which is based on the training data, the step of using the particle swarm optimization to train the fuzzy prediction rule includes: repeating the second and third items of the patent application scope The steps are described until a predetermined stop condition is met. For example, the method for forecasting the index of Taiwan stock index in item 4 of the patent application scope, The predetermined stopping condition includes that the movement of all of the particles reaches a maximum value or an optimal solution of the particles has been obtained. For example, in the method for predicting the futures index of the Taiwan stock index in the first application of the patent scope, the step of predicting the test data by using the fuzzy prediction rule of the completed training includes: when the corresponding part of the test data conforms to the trained fuzzy prediction rule, The predicted value of the test data is obtained according to the trained fuzzy prediction rule; and when the corresponding part corresponding to the test data conforms to the untrained fuzzy prediction rule, the predicted value of the test data is obtained by using the fifth equation.