TW201039264A - Forecasting TAIFEX based on particle swarm optimization - Google Patents

Abstract

In the past decades, the TAIFEX (Taiwan Stock Index Futures) forecasting problem has attracted some researchers' attention. Several prior arts for the TAIFEX forecasting based on the statistic theorems have been proposed, but their results are not satisfied. To solve nonlinear problems, fuzzy time series models are believed to be more suitable; however, most of these studies were for one variable only. The lengths of intervals and the content of forecast rules are two main factors to impact the forecasted accuracy of the forecast models created based on the fuzzy time series. The present invention provides a new hybrid forecast method to solve the TAIFEX forecasting problem based on fuzzy time series and particle swarm optimization. By means of particle swarm optimization, the present invention would find the best main factors influencing forecasted accuracy. The present invention provides a more precise forecasted accuracy than those of existing forecast methods.

Description

201039264 VI. Description of the invention: [Technical field of invention] It is a method of the Taiwan stock index (IV) 'Special number futures ^ method group optimization algorithm and fuzzy time series of Taiwan stock index [previous technology] long, decisive human For a variety of specific problems and the prediction of economic activities ο period for scholars to try to put forward various prediction methods and models. Early,,,: The forecast of the vouchers futures index adopts the traditional regression analysis method. However, it is suitable for the Sit to be applied to the securities futures market with uncertainties, linearity and low complexity. Regression points! There are four phases of 'phases'. The main system is that securities (4) tongue = 1 is a random phenomenon, and its overall time series data is generally non-stationary:::_ry) 'If regression analysis directly produces false regression (spUn_ Regressi〇n) problem, causing serious errors ❹ Time series analysis mode is a quantitative forecasting method, its prediction mode, the ubiquitous history data changes determine the accuracy of the prediction mode, 2. The right data is insufficient or the collected material has When the error occurs, the transmission mode will have a south error; 3. If there is a sudden occurrence, the true time value, the prediction of the traditional time series. The effect of the ringing/monthly prediction is not ideal. The accuracy is too low. The near = Γ = continued development is established; as the forecasting party (4) * breaks the change, the scholars find that the specific purpose of the specific problem is predicted. The method is more accurate than the general purpose prediction method. 4 201039264 The concept of time fuzzy sequence prediction is the application of fuzzy theory in time series mode, which plays an important role in various research fields, such as traffic load estimation, stock market stock price forecast, medical Blood pressure predictions, etc. 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 the 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, to 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 201039264 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. There is a 4α here, and a Taiwan stock index futures forecasting method with a degree of accuracy is necessary. SUMMARY OF THE INVENTION In view of the above-mentioned shortcomings of the prior art, the present invention proposes a method for predicting the futures index of a stock index based on a particle swarm optimization algorithm (particle Swarm 〇ptimizati〇n) and a fuzzy inter-day sequence, which combines the most Based on the optimization algorithm and fuzzy time series theory, a high-accuracy Taiwan stock index futures forecasting model is proposed. The theory of Particle Swarm Optimization was first proposed by two scholars in 1995, and it was mainly inspired by the clustering behavior of birds and fish. Therefore, the spirit of this algorithm is mainly to use the concept of clustering to find the best solution in our search space. In each optimization operation, each particle (particle 'meaning bird or fish) is responsible for the parameter search of the partial optimization of the region - each particle will record the current self-find The best (Local best) is to have a moving target during the search. In addition to the best solution that we have found so far, each particle will move to the best solution of all current particles (this will allow 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 "established fuzzy rules (c〇ntent 6 201039264 〇ff〇recast rules)" to an optimum value. Improve the accuracy of the forecast of Taiwan stock index futures. The invention utilizes a particle swarm optimization algorithm, based on the full = training data to establish a fuzzy rule; when all the fuzzy prediction rules are trained to be established, it is possible to make a new rule based on the rules, that is, to calculate the Taiwan securities market. 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. Ο Ο The re-purpose of the present invention is to provide a method for predicting the future market to assess the market crossover in the Taiwan stock index futures market to improve profitability and reduce investment risk. The above described features and advantages of the present invention will be apparent from the following detailed description of the preferred embodiments. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings, in which the same or similar elements are represented by the same reference numerals. 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 the conventional fuzzy time series prediction method. The steps are as follows: 1. In step 11, the historical data 1〇 is segmented and blurred, the length of the meaning interval, the upper bound of the domain and Lower bound, and number of intervals: Let Dmin and Dmax be the minimum and maximum values in the historical data respectively, and subtract the two values and add an appropriate adjustment value to make the domain 201038264 [Dmin-i7 Yang Dmax+t/wa ;c]'The number of set intervals is η, and the domain is grouped into /丨, /2, /3, /4, ···, 4 by a constant group distance. 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 0 data groups and untrained data groups. 3. In step 13, based on the fuzzy relationship, establish a fuzzy prediction rule: through the above-mentioned fuzzy logical relationship group, establish a fuzzy prediction rule 1J; including a matching part and a corresponding forecasting value (corresponding forecasted value) The matching part includes the current state of the group, and the corresponding predicted value is calculated by an estimating based on next state scheme (EBN) and a mater voting (MV) scheme, respectively. In step 14, the training and test data are predicted according to the foregoing 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 implementation of the present invention 201039264 !!: 'First in step 2G1', the historical data 1G is defined as γ(1), and the number of intervals is η, and the upper and lower bounds of the domain are Α and 4, respectively, t is historical data. Time series; with "-1 elements (elem(10) - ° quantity (P meaning '4, 4-2 and 1, its towel 1S, S «-1 and ^ (6) as one of particle particle optimization algorithms) (panicie); in step 202, according to the "one element", the η interval is defined as L Ui], (1? 2]' ..., person «-1, A], 1 = (d«-2 , U and /« = «-1' ί/„], that is, fuzzy according to the fuzzy time series theory, in step 〇203, further define the fuzzy set and fuzzy relationship of each particle, and establish a fuzzy relationship group; In step 2〇4, the trained fuzzy prediction rule is calculated by the sub-state based estimation scheme (ΕΒΝ); in step 2〇5, the untrained fuzzy prediction rule is calculated by the mother voting (MV) scheme. Based on the results of steps 204 and 205, a fuzzy prediction rule for each particle is established, as shown in step 206.

In an embodiment of the present invention, in the training phase, as shown in step 2〇7, the mean square error (MSE) value is used to represent the prediction accuracy of a particle. The lower the mean square difference, the higher the accuracy. high. In a specific embodiment, the mean square error is expressed as follows: to forecasted £ (FD^TD^

MSE

Costed

Among them, w indicates the number of predicted data, FA· indicates ah forecast data, Π), and indicates the corresponding historical training data about households. According to the result of step 207, when the result satisfies the predefined stop condition, such as: obtaining the best solution or reaching the maximum moving step, as shown in step 2〇8 9 201039264, the training of the prediction rule is completed, and all the particles are selected. The fuzzy prediction rule constructed by the best one of the best solutions 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 that each element A (1 s / s «-1) is in the ascending 〇rder. One embodiment of the present invention moves all particles to other locations during the training phase. The motion pattern of a particle is expressed as follows: (2) (3) +Clx Random -^)+C2 x ^id = ^id + ^id where is the rate of a particle W, the rate of which is limited to the pre-custom range The calendar indicates the inertial weight coefficient; c丨 and q respectively represent the self confidence coefficient and the social confidence coefficient. In the particle swarm optimization algorithm, the logarithmic value is linearly decremented, C2 is constant, and "() is a Random Number Generator' under normal distribution. A random real number U 4 system is obtained to represent the optimal solution of the current position and the data range of the particle w; iW is the optimal solution for all particles in the entire data range. 201039264 In a specific embodiment, in the training phase, an independent group of fuzzy prediction rules is constructed using fuzzy time series theory using an interval of each particle representation and used to predict all historical training data for each particle. In the training phase, all particles are moved to a new position, and the basis of their motion is expressed by equations (?), (3) and the above-mentioned evaluation of all particle prediction quasi-breaking according to equation (1), and broadcast ring Steps 203 to 207 until a predefined stop condition is met, such as: obtaining an optimal solution or reaching a maximum moving step. If the stopping condition is sufficient, as shown in step 208 , that is, selecting the fuzzy prediction rule constructed by the best one of the best solutions of all particles as the final result. If the stop condition is not satisfied, loop steps 2〇3 to 2〇7 until the predefined stop is satisfied. Conditions, and select the best solution for all particles - the fuzzy prediction rule of the trained construction as the final result. One embodiment of the present invention in the test phase, as shown in step 212, uses the most particles The best prediction of the best solution is to construct a fuzzy prediction rule to predict the new test data. First, if the corresponding part of the new test data meets a trained fuzzy prediction rule, the prediction is calculated according to the fuzzy prediction rule. If the corresponding part of the new test data meets an untrained fuzzy rule, the cardinal vote (Mv) (4) predicts (4) the test data; if it is not the case, the new test data The prediction is performed in accordance with the fuzzy prediction rules. The mother voting (MV) scheme calculates its predicted value according to the following equation: 11 (4) 201039264

Forcasted Vnh^ = ) + mh+mh+A+ mti

Wh+(Al) where % indicates the user's default maximum number of votes, 』 refers to the fuzzy relationship series, Wtl and Wtk (2 s A sj ) are expressed in the current state... The latest past text representation value and other past text representations The value corresponds to the midpoint of the interval.便于 In order to facilitate the explanation of the present invention, one embodiment of the present invention is based on the situation of the Taiwan stock index futures market from August 3 to August 31 of the chest year, first of all, for the convenience of explanation, 羑August 3, 1998 &quot In the transaction history data of the 2nd Taiwan Stock Index Futures Market, the number of particles is assumed to be 5, and the parent particle is defined as one of 7 intervals, ie Λ = (6〇, Bu], /2 = (6〗 , 62], /3 u3], & group ' /5,, 65], /6 = (M6], /7 u7]; the number shown therein =], a brief description of the present invention, not enumerated ; This is shown as: 枓叩) The following period is actually ^ 8/3/1998 7552^~ 8/4/1998 ~ ~S---- 7560 8/5/1998 7 48^7~~~~ 8 /6/1998 —- 一___ 7462^ 8/7/1998 75lT^^ 8/10/1998 ~ '~ ^—----- 73 65^ 8/11/1998 73 ^ -- 〇12 201039264 8 /12/1998 73 3 0 8/13/1998 7291 8/14/1998 7320 8/15/1998 7300 8/17/1998 72 19 8/18/1998 7220 8/19/1998 7285 8/20/1998 7274 8/21/1998 7225 8/24/1998 6955 8/25/1998 6949 8/26/1998 6790 8/27/1998 683 5 8/28/1998 ----- 6695 8/29/1998 6728 8/ 31/1998 6566 where the information is the most The value and the minimum value are respectively and £) = 7560 'The adjusted field of y(1) is represented by y(7):^(65〇〇, 76〇〇). For the sake of convenience, the fuzzy rule of constructing particle 1 is For example, the fuzzy rules for other particles are established by those skilled in the art and are specifically implemented by the specific embodiments disclosed in the present invention. In this embodiment, 7 of the particles in 5 particles are assumed. Intervals, respectively L = (6500, 6657], /2 = (6657, 6814), /3 = (6814, 13 201039264 6971] > /4 = (6971,7128] '/5 = (7128, 7285] ^/6 = (7285, 7442) and ^ = (7442, 76 (^, however, it should be noted that the data shown in this embodiment is merely illustrative of the present invention, not enumerated, and is not limited thereto. In addition, the domain of Γ(ί) in the particle is divided into seven intervals, namely, mountain = ''w〇m', von=, bad', 禹=, alittlebad, mountain= average, 々 = ''good', 4 = "very good" ' and 禹 = "excellent" are textual representations and are represented as a fuzzy set by equation (5) below. A, = IJu, + I2/u2 + I3/u3 + I4/u4 + I5/u5 + I6/U6 + 1ηΙηη (5) where Wy (1 SJ < 7) is a real number between 1 and 0 . The fuzzy set and interval comparison are expressed as follows: Interval text indicates value fuzzy set /1 worst /2 Π bad ^ 2 ha little bad ^ 3 /4 average a4 /5 good ^ 5 u very good ^ 6 II excellent A 7 o The results of the fuzzification of historical data are shown in the following table: 14 201039264 The actual capital fuzzy set in the flood season 8/3/1998 7552 ^ 7 8/4/1998 7560 ^ 7 8/5/1998 7487 ^ 7 8/6/1998 7462 d 7 8/7/1998 75 15 ^ 7 8/10/1998 73 65 d 6 8/11/1998 7360 ^ 6 8/12/1998 73 30 / 6 8/13/1998 729 1 A 6 8/14 /1998 7320 A 6 8/15/1998 7300 d 6 8/17/1998 7219 8/18/1998 7220 8/19/1998 7285 A5 8/20/1998 7274 As 8/21/1998 7225 A5 8/24/ 1998 6955 a3 8/25/1998 6949 As 8/26/1998 6790 ^ 2 8/27/1998 683 5 A 3 8/28/1998 6695 / 2 8/29/1998 6728 2 8/31/1998 6566 Secondly, In this embodiment, a 2-level fuzzy relationship is established, and (F(i- 2 ), F(i- 15 201039264 2+1), ..., F〇-2), rush-1)) represents "current state (current office (8)", F (〇 indicates "next state"" and its fuzzy relationship is (F (division), corpse (Bu/2+1)' For the purpose of illustrating the present invention, this embodiment sets the level 2 fuzzy relationship 2 = only the data shown is merely illustrative of the invention, not enumerated; for example, the fuzzy relationship 〇 47, is, J7 )~^47 is (F(8/3/1998), corpse (8/4/1998) F(8/5/1998))-F(8/6/1998). Here, the fuzzy relationship is as follows: Shown as follows:

〇 ❹ 201039264

8 d 5,d 5, 9 d 5,d 3, A s~>A 2 10 j 3,d 3, A 2~>A 2 11 d 3,d 2, 3 —> ^ 2 12 j 2, / 3, A Λ 2 13 d 3,d 2, A 1 14 ^ 2 j ^2, A where 〇42, J2, 4)4# refers to (F(8/28/1998), corpse (8 /29/1998),

F(8/31/1998))-»F(9/1/1998), and the corpse (9/1/1998) is an unlisted material, so it is marked with #. Moreover, in the foregoing list, each group contains more than one fuzzy relationship; this embodiment establishes a fuzzy prediction rule based on the fuzzy relationship of the foregoing list. The fuzzy prediction rule consists of a matching part and a corresponding forecasted value. The former consists of the current state of the group; the latter calculates the trained and untrained parts. 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. 17 201039264 For the subsequent 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): ^submidk +midk

Forcasted Valuer —----- ( 6 ) where “represents the total number of next states in the same group, (1 SA: < w) represents the midpoint of the corresponding interval of the secondary state moxibustion, 〇ϊΜττπΆ indicates the midpoint of one of the three sub-intervals in the corresponding number of sub-states. The above table group 4 is taken as an example, and only one state, and the state-based estimation scheme (EBN) and other partitions/6 (ie, (7285, 7442)) are three sub-intervals, respectively = (7285, 7337.3), SR6f2 = (7337.3, 7389.6) and 3 = (7389.6, 7442). According to the aforementioned group 2 is taken from the fuzzy relationship 〇F (8/6/1998), F (8/7/1998), corpse (8/10 /1998)) —F(8/ll/1998); The continuation of the state based estimation scheme (EBN) is informed that the corpse (8/11/1998) corresponds to the actual data 8 (8/11/1998) (ie 7360) In the ® interval interval 6, 2, the middle point of the interval is 6 lectures ^ 6 series 7736.45 (ie 7337.3 + (7389.6 - 7337.3) / 2); accordingly, with M6, 2 midpoint and interval / 6 midpoint The average value 'and calculated according to the above equation' is that the predicted value of group 2 is 7363.875. Here, the predicted values calculated in this embodiment are as follows: Group marker fuzzy relationship prediction value - 1 A 7, Α Ί , 7459.72 18 201039264

Α η —> A, A 1,A Ί, d 7 6 2 j 7, meaning 7, A e~^>A ^ 7363.5 3 d 7,d 6, 73 3 7.3 3 4 j 6,/ 6, ^6, ^6, ^ 6~^ ^ 5 7304.625 5 j 6,d 6, 7206.5 6 ^ 6 5 ^5, ^ 5 5 7232.66 7 ^5, ^5, λ5-^λ5 ^5, ^5, Λ s~^> Λ 2, 7119.27 8 ^5, ^5, ^2,-^ A -i 6918.66 9 ^ 5 > ^3, A 3 —>A 2 6761.66 19 201039264 Ο Ο r 10 A3 , ^ 2~>A 2 6866.3 3 11 ^3, A2, ___^ 3 ~>A 2 6709.33 --- 12 A2, A3, AA 2 6735.5 ---~~-- 13 A3, A2, ^ 2~&gt ;A i 6578.5 6657 14 (The most tfj votes counted by the mother vote (mater ^2, A2, Ai-># voting, MV) scheme - 2) For the untrained part 'use the mother vote voting, My The scheme prediction calculation; the above table group 14 is taken as an example, calculated according to the equation (4), setting % = 2', the latest past text indicates that the highest vote number of the mountain is 2, and the remaining texts represent the voting values of the value 4 and 乂2. For each 1, the predicted value of the above table group 14 is calculated as follows: ijnidjXWh) + rnid1+mid^ _ (6578.5x2) + 6735.5 + 6735.5 ^Ηλ-\) = -=6657 According to the results of the previous list, available Out of phase The fuzzy prediction rule includes: a fuzzy prediction rule including a matching part and a prediction part; and a current state of the partial group fuzzy relationship, the predicted part prediction value part, this embodiment Obtained fuzzy prediction gauge 20 201039264

The following table shows: The rule number meets the partial prediction part 1 such as corpse (ί -3) is equal and F(i-2) is equal and corpse (ί-1) is equal to a7 then the predicted value Γ(ί) =7459.72 2 (ί-3) is equal to and the corpse (纟-2) is equal to and F(il) is equal to the predicted value Γ (〇=7363.5 3 if F(i-3) is equal to and -2) is equal and F(il) is equal to the prediction Value = 73 3 7.3 3 4 If F(i - 3) is equal and F(i-2) is equal and F(il) is equal to "6" then the predicted value 7(ί) = 7304.625 5 If F(i-3) is equal to F(i-2) is equal to and F(il) is equal to the predicted value Ζ(ί) =7206.5 6 If F(i-3) is equal and F(i-2) is equal and corpse (ί-l) is equal to the predicted value Γ(ί) =7232.66 7 If F(i-3) is equal to the predicted value Γ(ί) 21 201039264

And the corpse (ί-2) is equal to and F(il) is equal to =7119.27 8 If F(i-3) is equal to and FG-2) is equal and F(il) is equal to then the predicted value Γ(ί) =6918.66 9 such as F( I-3) is equal to 乂5 and F(i-2) is equal and F(il) is equal to the predicted value Mi) =6761.66 10 If F(i-3) is equal and F(i-2) is equal to and F(il) Equal to the predicted value F(i) =6866.33 11 If F(i-3) is equal and F(i-2) is equal and corpse (ί-l) is equal to the predicted value Γ(ί) =6709.33 12 如尸(ί- 3) equal and F(i-2) is equal and F(il) is equal to the predicted value Γ (〇=6735.5 13 if F(i-3) is equal and F(i-2) is equal and corpse (ί-l) is equal Then the predicted value Γ(ί) = 6578.5 14 If F(i-3) is equal and F(i-2) is equal and F(il) is equal to ^ then the predicted value Γ(ί) =6623.35 accordingly, this embodiment is 1998 From August 3rd to August 31st, the historical data of Taiwan 2010 201026264 stock index futures market, the predicted value is as shown in the following table: The actual data fuzzy set meets the rule number forecast value 8/3/1998 7552 ^ 7 Prediction 8/4/1998 75 60 A 7 Not forecast 8/5/1998 7487 ^ 7 Unpredicted 8/6/1998 7462 A 1 1 7459.72 8/7/1998 75 15 ^ 7 1 7459 .72 8/10/1998 73 65 ^ 6 1 7459.72 8/11/1998 73 60 d 6 2 7363.5 8/12/1998 73 3 0 3 73 3 7.3 3 8/13/1998 729 1 d 6 4 7304.625 8/ 14/1998 7320 j 6 4 7304.625 8/15/1998 7300 d 6 4 7304.625 8/17/1998 72 19 4 7304.625 8/18/1998 7220 ^ 5 5 7206.5 8/19/1998 7285 ^ 5 6 7232.66 8/20 /1998 7274 ^ 5 7 7119.27 8/21/1998 7225 ^ 5 7 7119.27 8/24/1998 6955 3 7 7119.27 8/25/1998 6949 ^ 3 8 6918.66 8/26/1998 6790 ^ 2 9 6761.66 8/27/ 1998 683 5 d 3 10 6866.33 23 201039264

8/28/1998 6695 α2 11 6709.33 8/29/1998 6728 ^ 2 12 --^~-- 6735.5 8/31/1998 6566 Α: 13 6578.5 9/1/1998 Ν/Α Ν/Α 14 6623.35 In one embodiment of the present invention, the particle 1 of the five particles is assumed to be an example, and the fuzzy rule of the particle 1 is constructed; accordingly, the establishment of other particle fuzzy rules in the technical field is generally understood by the present disclosure. The specific embodiments of the invention disclosed above are embodied. According to the results of the above list, in the above equations (2), (3),

Not limited to (6500, 7600), limited to [-50, 50], q and C2 are 2' and ω is 1.4' and the mean square error of each particle is calculated according to equation (1); then the randomization of each of the 5 particles The starting position and the mean square error are shown in the following table: ------ bl b2 b 3 b4 b 5 b6 MSE particles - 1 6 6 5 7 68 14 697 1 7 128 7285 7442 4497.87 Particles ----- 2 6590 6680 6790 6 8 95 7000 73 00 7091.33 Particles 3 66 10 6750 6900 7000 7 150 7400 5613.6 Particles -~ > 4 66 80 6800 6940 7 160 7320 7480 4494.03 Particles 5 — 6640 6 7 8 0 6925 7095 7280 75 10 5035.16 The random starting rates of the five particles are shown in the following table:

Vl v2 v3 v4 v5 v6 particles 1 12 14 19 30 25 16 particles 2 16 20 8 1 5 13 7 particles 3 19 23 13 25 8 30 24 201039264 particles 4 24 18 particles 5 Γι7~ lir

It can be carried out by the fuzzy prediction rules listed above; = ' Technical personnel should be aware that if there is no particle, then the choice of fuzzy prediction rule is not limited to the above table data. According to this, for example, according to the mean square error (MSE) value of equation (1) and (2), the following formula is calculated:

f 20 (four)-7D,) 2 £ (four)-22),) 2

Nt MSE: V forecasted 20 20 ' ~ = 4497.87 where the forecasted quantity is 乂. ...heart thought 2〇, i < as) indicates the predicted value of 7(8/5/1998+/); τ^· indicates the corresponding historical training data about ^: (ie r(8/5/1998+0) It should be noted that FZ) 2i represents the predicted value of the new test material (ie, Γ(9/1/1998)) and thus is not used in this example 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; as shown in the following table: —-—- bi b 2 b3 b4 b 5 Be MSE Particle 1 ---__ 6657 6814 697 1 7 128 7285 7442 4497.87 Particle 2 _ 6590 6680 6790 6895 7000 73 00 7091.33 25 201039264 Particle 3 66 10 6750 6900 7000 7 150 7400 5613.6 Particle 4 6 6 8 0 6 8 00 6940 7 160 73 20 748 0 4494.03 Particles 5 6640 67 8 0 6925 7095 7280 75 10 5035.16 Six τ, m workers and peasants / 7 Γ 不 不 不 不 贳 全 邵 5 5 5 5 于 于 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 (ie, the corpse ge^ of equation (1)) is the particle 4 (since its 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), and the historical data exemplified in the embodiment is calculated, second. The location and its mean squared difference are listed below:

5 2 7 3 · 1--------- # ^ ° According to all the current best solutions shown in the table (ie, the coffee of equation (1)), it is still particle 4. Here, in the actualization, according to the foregoing steps, all particles are adjusted to the third position by equations (1), (7) and the mean square error of the relevant position is obtained according to equation (3), and = open loop calculation until the stop condition is satisfied. When the stop condition is over 1 and the prediction rule has not been completed, the test data prediction is performed by the pre-test rule of the completed training. According to the specific 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:

Date Actual Data Linear Polynomial of degree 2 PolyiK^nial ofdegr^S ^bving Awage (pmod**3) HPSO NPSO 雠1998 6890.0 6333.0 6923.4361 8032.7297 6879.7 6861.0 6878.3 9/25/1998 6871.0 6305.7 6958.7064 8266.964 6889.3 6897.8 6906.1 9/28/ 1998 6840.0 6278.3 6996.5325 8522.4575 6871.0 6912.8 6866.8 9/29/1998 6806.0 6251.0 7036.9144 8799.9584 6867.0 6858.4 6844J 9/30/1998 6787.0 6223.6 7079.8521 9100.2149 6839.0 6800.6 6820.8 MSE 314130.5 34479J 3082409.0 1565.8 1955.9 938.9 R2 0.6435 0.7713 0.8778 ❹ where, listed above The prior technologies are:

Linear model: y = -27.348 jc + 7509 Polynomial model of degree 2: y = 1.2779 x2 - 75.907 jc + 7824.6 Polynomial model of degree 3: y = 0.1247 x3 - 5.8308 jc2 + 33.592 χ + 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. It will be appreciated by those skilled in the art that the present invention is described by way of example only. However, the skilled person with the usual knowledge in this field is not out of this issue.

Claims (1)

201039264 ==::Γ, change. BRIEF DESCRIPTION OF THE DRAWINGS [Brief Description of the Drawings] A preferred embodiment of the present invention will be described in the following description and the accompanying drawings in which: FIG. 1 is a flow chart of a conventional fuzzy time series prediction method of the prior art. / < The second figure is a flow chart of the prediction method according to the present invention. 0 [Description of main component symbols] 1 〇Historical data 201 defines the number of particles program 202 sets the particle interval and blurs the program 2 0 3 fuzzy relationship group establishment procedure 2 0 state state basic estimation scheme calculation program 205 mother voting scheme calculation program 206 particle fuzzy prediction rule establishing procedure 207 207 mean square error calculating program 208 stop condition achievement 2 0 9 stop condition not reached 210 particle position moving program 2 11 prediction rule completion training 2 1 2 test data prediction program 7. Patent application scope: 1. A method for predicting the futures of Taiwan stock index based on the particle swarm optimization algorithm 28 201039264 The method includes: based on historical training data, using the particle swarm optimization algorithm to train fuzzy prediction rules; and the fuzzy prediction rules After the training is completed, the test data is predicted using the fuzzy prediction rules of the completed training. 2. For example, the method for predicting the futures index of the Taiwan stock index, which is based on the historical training data, the step of using the particle swarm optimization to train the fuzzy prediction rules includes: using the interval represented by the parent particle to generate blur An independent group of prediction rules is used to predict all training data; and each particle is moved to another position according to the first equation and the second equation, wherein the first equation is ^ + C, x W() x (Pw -xirf) + c2, Rand〇HPgbest # where the second equation is ^id~Xid+Vid, where factory W represents the rate of a particle M, (7) represents the inertial weight coefficient, and C! represents the degree of confidence. Self confidence coefficient ' C2 denotes a social confidence coefficient, which is a Random Number Generator, which produces a random real number between 0 and 1 under normal distribution. The current position of the particle ,, Λν represents the best solution of the particle W, which represents one of the best solutions for all particles. 3. If the scope of applying for patents is 2, the steps of using the group represented by each particle include: the method for predicting the index of the stock index of the item, wherein the interval is independent of the fuzzy prediction rule, and the minimum and maximum values in the historical data are respectively reduced. Add and adjust an value to define the domain of the historical data; divide the historical data into n intervals, define the area 〇 = 7 '09 and H "]; ... to represent the interval as a third-party program Fuzzy set, where the third-party program is =/1/W1 + /2/w2 H3/M3 + /4/...+ + + /7/1/7; establish a level 2 fuzzy relationship 'to (F(i_ J), F (Bu J +1), , F (Bu 2) F(i-1)) means "current state", p(7) means "next state", and the fuzzy relationship is F ( Bu 2), factory (Bu 1)) 4F (7) is the representation; ' ' Based on the 2 levels of fuzzy relations to establish fuzzy prediction rules, including the calculation of predicted values using the fourth equation for the trained fuzzy prediction rules, untrained fuzzy prediction rules The predicted value is calculated by the fifth equation. 4. For the forecast method of Taiwan stock index futures in the third application patent scope, the fourth equation is, 30 201039264 Less submidk+midk Forcasted Value = M---, n where 'ForecaWec? Ffl/we indicates the predicted value, w Indicates the total number of next states in the same group, m/heart (1 $ moxibustion $ indicates the midpoint of the secondary state moxibustion corresponding to the interval, and (10) indicates the number of the state number A: the corresponding interval The midpoint of one of the three sub-intervals. 5. The method for predicting the futures index of the stock index in item 3 of the patent application scope, wherein the fifth equation is Forcasted X%) +, where /M represents the predicted value, % means that the preset maximum number of votes refers to the fuzzy relationship series 'Wtl and Wtk (2aq) indicate the current past (4) state), the latest past text representation value and other past text representation values correspond to the midpoint of the interval. ❹ 6. For the method of predicting the futures index of Taiwan stock index in the second paragraph of the patent application, based on the training data, the steps of using the cabin + following the rules of the rule of the night to modify the fuzzy prediction rules include: The mean square defined by the six equations should not be the prediction accuracy of each particle, where the sixth equation is ^forecasted MSE Σ(^ ~TD.ff^.1 N forecasted where the mean mean square representation is expressed_number of documents 31 201039264 • Representation /th forecast data, ji /) Zhi-n, Cai Ye table does not refer to the TM 丨 · corresponding training 7.t application for patent range item 1 of the Taiwan stock index futures forecasting method, where = training: data based The step of using the particle swarm optimization to train the fuzzy prediction rule further includes repeating the steps described in items 2 and 6 of the patent application until a predetermined stop condition is satisfied. 0 8. Shen Shen: The method for predicting the futures index of the Taiwan stock index in item 7 of the patent scope, wherein the pre-sufficient condition includes that the movement of all the particles reaches the maximum value or the optimal solution of the obtained particles is obtained. 9. If you apply for a patent scope! The step of predicting the test data using the fuzzy prediction rule of the completed training includes: 5 the corresponding part of the test data conforms to the trained fuzzy prediction rule The prediction rule obtains the predicted value of the test data; 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 the fifth equation.