KR102198459B1 - Clustering method and system for financial time series with co-movement relationship - Google Patents

Abstract

The present invention relates to a clustering method and system for a financial time series having a synergistic relationship, comprising the steps of: pre-processing financial data; Clustering using the preprocessed data; And interpreting the clustering result.

Description

Clustering method and system for financial time series with synergistic relationship {CLUSTERING METHOD AND SYSTEM FOR FINANCIAL TIME SERIES WITH CO-MOVEMENT RELATIONSHIP}

The present invention relates to a clustering method and system for a financial time series having a synergistic relationship, which is a clustering system and method for removing noise and finding a time series cluster having a higher synergistic relationship.

A time series is a set observed sequentially over time. With the development of information devices, time series observed in real time in various fields such as finance, communication, medicine, health, and transportation are being used in various fields of application. Among them, for financial applications, time series is one of the most important applications. Financial applications include exchange rates, currency volumes, stock indexes, stock prices, commodity prices, and derivatives. Therefore, it is very important to consider the important functions of financial time series in developing an efficient analysis method for applying financial time series.

The financial time series is abnormal because it has random walking characteristics. Therefore, it is very difficult to make investment decisions by analyzing financial time series. However, despite the fact that financial time series are abnormal and have, as a result of a linear combination of the two Spread of financial time series it has been found to satisfy the normal conditions in many situations. In this case, the two financial time series is called a cointegration relationship and is considered to share the same trend. The cointegration is used as a measure of the degree of cavitation of two abnormal time series. Because financial time series clusters with high cavitation can be widely applied to financial time series applications, the clustering algorithm that generates clusters is an important research topic in financial applications. These results can be useful in predicting the future prices of financial portfolio selection and financial policy formulation.

The main problems of the existing time series clustering algorithm and the existing financial time series clustering algorithm are as follows. First, Euclidean distance and Dynamic Time Warping are used as the distance calculation method, but the distance calculation method does not consider the time weight of time series data. Second, the importance of the ratio of increase or decrease in future value compared to past value in the trend component analysis of financial time series is ignored. Third, they allow too much information loss in the dimensionality reduction process. Fourth, they create clusters containing too much noise with a low degree of co-movement. Fifth, useful information for financial analysis may be lost because time series cannot be duplicated in multiple clusters.

For example, Korean Patent Laid-Open No. 102017-0078256 discloses a method and an apparatus for predicting time series data. Specifically, measurement values 　 time series 　 data in a predetermined period unit during a training period are clustered into a plurality of 　 clusters. step; Collecting a plurality of environmental data during the training period; Selecting at least some of the plurality of environmental data as a factor; Generating a classification model for optimally classifying the 　 cluster of the measured values 　 time series 　 data on a space or plane composed of axes indicating the factor; Determining a performance index value of the generated classification model; The selecting, generating the classification model, and determining the performance index value are repeated while changing the selection of the factor, and an optimal classification model among the generated classification models is determined based on the performance index value. Selecting; And predicting a cluster of measured values and time series data in a prediction period using the optimal classification model. A method for predicting time series data is disclosed. However, the clustering method has a problem in that a lot of noise may be generated when clustering is performed on a time series with cavitation.

Therefore, there is a need for a technology capable of solving the above problems.

Republic of Korea Patent Publication No. 102017-0078256

Accordingly, in order to overcome the above problems and limitations, the present invention aims to provide a clustering method and a clustering system capable of removing noise to increase accuracy and distinguishing data exhibiting higher cavitation compared to the conventional clustering method.

The present invention for solving the above problem includes the steps of pre-processing financial data;

Clustering using the preprocessed data; And interpreting the clustering result; and a clustering method for a financial time series having a synergistic relationship comprising: a preprocessor for preprocessing financial data; A clustering unit for clustering using the preprocessed data; And a result analysis unit for analyzing the clustering result.

The present invention can reduce noise and perform financial time series clustering having high synergism in a financial time series clustering method compared to the existing method.

The present invention provides a clustering method and system that compensates for the disadvantages of the existing time series clustering algorithm and creates a cluster having high coherence.

Meanwhile, the effects of the present invention are not limited to the above-mentioned effects, and various effects may be included within a range that will be apparent to a person skilled in the art from the contents to be described below.

1 illustrates the problem of density-based clustering.
2 shows the problem of partitioning-based clustering.
3 is a graph showing the problem of Z-transformation as a normalization method.
4 is a graph showing a band limit signal, a partial section (sub-interval), and a sampled point.
5 is a DRE result value for each dimension reduction method.
6 shows DRaE results (α=50) values for each dimension reduction method.
7 is a graph showing changes in cluster diameter.
8 shows the steps of estimating the diameter limit.
9 is a result of RMSE for each clustering method.
10 is a result of the diameter of each clustering method.
11 is a result of MSD for each clustering method.
12 is an ADF test result for each clustering method.
13 is a cluster created by YADING.
14 is a cluster created by 3PTC.
15 is a cluster created by a method according to an embodiment of the present invention.
16 is a block diagram of a clustering system for a financial time series having a synergistic relationship according to an embodiment of the present invention.
17 is a flowchart of a clustering method for a financial time series having a synergistic relationship according to an embodiment of the present invention.

Hereinafter, a'clustering method and system for a financial time series having a joint relationship' according to the present invention will be described in detail with reference to the accompanying drawings. The described embodiments are provided so that those skilled in the art can easily understand the technical idea of the present invention, and the present invention is not limited thereto. In addition, matters expressed in the accompanying drawings are schematic drawings for easy explanation of embodiments of the present invention and may be different from the actual implementation form.

Meanwhile, each component expressed below is only an example for implementing the present invention. Accordingly, in other implementations of the present invention, other components may be used without departing from the spirit and scope of the present invention.

In addition, each component may be implemented with purely hardware or software, but may be implemented with a combination of various hardware and software components that perform the same function. In addition, two or more components may be implemented together by one piece of hardware or software.

In addition, the expression'including' certain elements is an expression of'open type' and simply refers to the existence of the corresponding elements, and should not be understood as excluding additional elements.

1 illustrates the problem of density-based clustering.

Referring to FIG. 1, since time series has a high-dimensional characteristic, if raw time series data is directly used for time series analysis, expensive calculations and dimensional damage problems may occur. Dimension reduction methods used for time series analysis can be divided into data adaptation methods and non-data adaptation methods.

The data adaptation method is used when the size of data is variable. PCA (Piecewise Constant Approximation), APCA (Adaptive Piecewise Constant Approximation), SAX (Symbolic Aggregate Approximation) may be included. The non-data adaptation method can be used when the size of the data is fixed. These may include Random Mapping, Piecewise Aggregate Approximation (PAA), Discrete Fourier Transform (DFT), and Discrete Cosine Transform (DCT).

The existing technology has a density-based clustering algorithm using DBSCAN called YADING. The above existing technology uses a sampling method to reduce the execution time of the algorithm. They also used the inflection point to estimate the density radius.

In order to improve the performance of time series clustering with other conventional techniques, a multi-level clustering algorithm was developed. As a two-stage clustering method, time series data is transformed by SAX in the first step. Then the CAST algorithm creates a cluster. In the second step, each cluster is divided into sub-clusters using sub-sequence information of the time series data of each cluster.

Another existing technology is a three-stage clustering method called 3PTC. In the first step, the time series data is transformed by SAX. Then, the K-mode algorithm creates a pre-cluster. In the second step, each dictionary cluster is refined into sub-clusters by the PCS algorithm. In the third step, the similarity between sub-clusters is calculated using the similarity of the shape method. Finally, the final cluster is created by merging sub-clusters.

When considering the characteristics of financial time series, the key factors that should be considered as important factors in financial time series clustering are cluster size, data normalization, distance calculation, and redundant allocation of time series to multiple clusters.

The existing time series clustering method performs clustering without considering information on the appropriate size of the cluster. If the proper size of the cluster is not considered, a large amount of noise data may be included in the cluster. When financial data analysis is performed using clusters containing such noisy data, the results of financial data analysis are unreliable.

Density-based clustering, an existing technology, can create a cluster in an arbitrary shape within a continuously dense area in the data space. The size of clusters created in that area can be very small or very large in any shape. If the cluster size is very large, the degree of joint movement of the two furthest data in the cluster may be very different. 1 shows the problem of density-based clusters.

2 shows the problem of partitioning-based clustering.

Referring to FIG. 2, partition-based clustering creates a cluster by dividing a data space into K partitions. The number of partitions can be determined by the user. If the user does not properly select the number of partitions (K), the degree of joint movement of the two furthest data can be very different. 2 shows the problem of partition-based clustering.

3 is a graph showing the problem of Z-transformation as a normalization method.

Referring to FIG. 3, in financial time series trend analysis, a ratio indicating how much a future value increases or decreases compared to a past value is more important than the distribution and variance of the entire time series data. Also, financial time series have very different scales for each data. Therefore, the normalization step is essential in financial time series analysis. However, most time series analysis methods do not consider normalization of time series data or perform normalization using Z-transform. The Z-transform is defined as in Equation 1 below.

[Equation 1]

Here, Y _t represents the normalized time series at time t, X _t represents the unnormalized time series at time t, μ _t represents the mean of X data, and σ _X represents the standard deviation of X data.

Since the Z-transform is expressed as a multiple of the standard deviation of the time series values, it is not suitable as a normalization method for time series. 3 shows that even though the ratio indicating how much the future value increases or decreases in each time series compared to the past value is different, the change ratio of the two time series data is similar.

Time series data are observed over a long period of time. The state of the system that generates time series may change over time, so the time series analysis model may not work properly over time. Therefore, it makes more sense to give more weight to recent data than to give equal weight to all past data. In particular, since this phenomenon occurs very frequently in financial time series, time weights need to be changed when calculating concentric similarity.

The existing multi-level clustering algorithm uses a reduced-dimensional time series to obtain a pre-cluster in the pre-clustering step. In this case, SAX, PAA, DCT, and DFT are used as dimension reduction methods. However, using this method can lead to excessive loss of information.

Existing time series clustering algorithms cannot redundantly allocate time series to multiple clusters. However, there is a possibility that one time series is similar to a time series included in another cluster. Therefore, if redundant allocation of time series is not allowed, important information may be lost in time series analysis.

In consideration of such a problem, the present invention uses an efficient clustering method suitable for the characteristics of financial time series application.

4 is a graph showing a band limit signal, a partial section (sub-interval), and a sampled point.

Referring to FIG. 4, in data preprocessing, average scaling is defined as in Equation 2 below to indicate a ratio indicating how much future value increases or decreases relative to past value for data normalization.

[Equation 2]

Here, Y _t represents the normalized time series at time t, X _t represents the time series at time t, and μ _X represents the average of X.

In financial time series analysis, the more recent data, the more impact on future analysis results. A weighted time series is used to reflect this characteristic. The weighted time series transform produces a weighted time series. This transformation may involve two steps: partial interval (sub-interval) calculation and weight assignment.

N/2k, 2π/T_s ≥2Ω_max, 2π / T_s ≥2 * 2πk / N, T_s≤N / 2k). 그런 다음 각 샘플링 된 기간을 시계열의 부분 구간(서브 인터벌)으로 해석한다. 도 4는 대역 제한 신호의 부분 구간(서브 인터벌)을 보여준다.Based on the Nyquist Sampling Rate Condition and Parseval Theorem, we use a method to find the partial section (sub-interval) of the time section efficiently. When the sampling frequency is twice the maximum frequency under the Nyquist Sampling Rate condition, the band-limited signal can be completely reconstructed without frequency aliasing by the sampling point. Some time series are not perfectly band-limited signals, but high-frequency components can be considered noise. Therefore, most time series can be regarded as band-limited signals. According to the Parseval theorem, the sum of squares of time series values in time space is equal to the sum of squares of coefficients of frequency components in frequency space. Therefore, we use the Parseval theorem to find the maximum frequency (Ω_max) that conserves most of the energy of the original time series (about 80-90%). (Ω_max = 2πk / N, N corresponds to the total time interval of the time series, k is the multiple coefficient of the frequency 1 / N.) The sampling period (T _s) using the maximum frequency and Nyquist Sampling Rate conditions

N/2k, 2π/T _s ≥2Ω_max, 2π / T _s ≥2 * 2πk / N, T _s ≤N/2k). Then, each sampled period is interpreted as a sub-interval (sub-interval) of the time series. 4 shows a partial section (sub-interval) of a band-limited signal.

Weights are linearly assigned to partial intervals obtained by the Nyquist Sampling Rate Condition and Parseval Theorem. For example, when there are 4 sub-intervals, 1, 2, 3, and 4 weights are allocated to the sub-intervals according to the time sequence from the past to the latest.

Dimension reduction can be performed in the preprocessing step. The dimensional reduction method was selected by comparing DCT, PAA, PCA, and SAX. PCA (Principal Component Analysis) was selected as the dimension reduction method. PCA reduces the dimensions of the data by using an eigenvector that best represents the variability of the overall data. The number of dimensions reduced by PCA is determined experimentally using a Scree plot.

After the preprocessing is finished, the clustering step can be performed.

Important terms used in the clustering step are defined as follows.

Weighted Metric Space (WMS)

WMS is defined as follows. X = {(f (t))|(f (t)) is the weighted time series of (f (t)), t = 1, ..., T} SES (sum of Euclidean distances in partial interval time series) Street.

(f (t)) is the result of applying the weighted time series transformation to f (t).

SES distance

Where SIDIst _i is the Euclidean distance of the i-th sub-section time series of the weighted time series.

RDS (Reduced Dimensional Space)

X = (g (z) | g(z) is the reduced expression of (f(t)). T = 1, ..., T, z = 1, ..., rr << T}

g (z) is the result of applying the dimensionality reduction method to (f (t)).

Estimate the upper limit of the cluster diameter used in the weight space and the diameter limit of the cluster used in the reduced dimensional space. Time series can be regarded as a combination of a trend component and a noise component. You should find a time series with similar trend components and low enough noise. To do this, limit the cluster diameter. For calculation efficiency in the pre-clustering step, the financial time series is converted into reduced dimensional data. Then, clustering is performed on the reduced dimensional data. However, due to the reduction in dimensions, the pre-cluster may contain noise. Therefore, in the purification step, the pre-cluster is purified into a purified cluster.

Estimation of upper diameter limit

In the refinement step, an upper diameter limit is estimated to limit the size of the cluster. The upper limit of the area represents the maximum limit of SES_Distance between time series in the cluster. The upper diameter limit is estimated as follows. One sample is extracted from WMS. Then, the time series is sequentially included in the neighboring set in the order of the shortest distance from this sample. If the neighboring set has a time series that deviates significantly from the trend, the present invention removes the time series from the set and considers the maximum SES_Distance as a diameter candidate in the set. The average of several diameter candidate values obtained by iteratively working with several samples is estimated as the upper diameter limit.

Diameter limit estimation

The diameter limit used to limit the size of the cluster in the pre-clustering step is estimated as follows. S is the set of neighbors used to estimate the upper diameter limit (D) in WMS. There are two time series corresponding to the upper diameter limit of S. The present invention calculates the Euclidean distance in a reduced dimensional space. The obtained distance is taken as the diameter limit candidate (d'). Information is lost in the reduced dimensional space. When the maximum distance of the cluster is limited to the diameter restriction candidate d', not only data with noise may be included, but similar time series may not be included in the same cluster. Therefore, we use a value slightly larger than the diameter limit value (d = γd', γ> 1) as the diameter limit value.

In the pre-clustering step, the ADupClustering algorithm is performed on the data of Reduced Dimensional Space as follows. Agglomerative Clustering Algorithm creates clusters. For each cluster (R) created by the Agglomerative Clustering Algorithm, AdupClustering finds a cluster that should be included in cluster R among the time series included in other clusters. The distance from the cluster R should be less than the diameter limit (d). That is, ADupClustering Algorithm allocates one time series to several clusters. That is, redundant allocation.

Since the pre-cluster is created in the Reduced Dimensional Space, it is possible to include time series with different trends. In the purification step, each pre-cluster is purified into several purified clusters. Each refined cluster should contain only time series with similar trends (high degree of synchronization). For this, the ADupClustering algorithm is performed in a weighted metric space using the upper diameter limit (D).

In the ADupClustering Algorithm, we assume that R is a cluster created by integrated clustering. Let ρ be the diameter of R. Let σ be the diameter boundary, which can be the upper diameter limit (D) or the diameter limit (d). Then there are α, β in R where ρ = dist (α, β). ρ≤σ. Place c as the center of the diameter ((αβ)). Let x = R. Let l = dist (x, c). Let R'= R∪x. Let τ be the diameter of R'.

Lemma. If l> (√3 σ) / 2, then τ> σ

와

사이의 각도가 π / 2보다 크거나 같다면, dist (x, α)>

, 왜냐하면 τ≥dist (x, α)이기 때문이다. β의 경우 α의 경우와 동일하다.proof. 1> (√3 σ) / 2 and

Wow

If the angle between is greater than or equal to π/2, dist (x, α)>

, Because τ≥dist (x, α). In case of β, it is the same as in case of α.

Therefore, for l≤ (√3 σ) / 2, we must test whether τ is less than the diameter σ.

In order to prove the performance of the present invention, an experiment on the efficiency of dimensional reduction, an experiment on the diameter upperbound determination in WMS (Weighted Metric Space), an experiment on diameter limit determination in RDS (Reduction Dimensional Space), We performed an experiment comparing the algorithm.

Stock data from the Korean stock market (KOSPI, KOSDAQ) and UCR time series archives were used as experimental data. Korea's stock market data consists of 1,483 stocks in 2016, each with a scale of 4000 hours. In the UCR time series archive, ShapsAll (512 dimensions), word synonyms (270 dimensions), and 50 words (270 dimensions) were used. The experiment was performed on an Intel (R) Core (TM) i5-4570 CPU @ 3.20GHz, 4.00GB.

DCT, PAA, and PCA are compared to select the dimensionality reduction method used in the present invention. Dimensional reduction efficiency (DRE) and dimensional rank efficiency (DRaE) are used as comparison metrics. Dimension Reduction Efficiency (DRE) is defined as in Equation 3 below.

[Equation 3]

SSEW (sum of squared errors of WMS) is equal to Equation 4.

[Equation 4]

Here, μ represents a randomly selected reference time series in a weighted metric space, and SetW is a set of n time series closest to the reference time series.

5 is a DRE result value for each dimension reduction method.

Referring to FIG. 5, SSER (sum of squared errors of RDS) is shown in Equation 5.

[Equation 5]

Where SetR is a set of n time series.

μ is the time series closest to the reference time series in the reduced dimensional space. f _k , μ are expressed in a weighted metric space.

The meaning of DRE is as follows. SSER is an SSE (Square of Error) value obtained by using a k time series close to the reference time series in a reduced dimensional space. Therefore, the SSER is always greater than the SSEW value obtained using the k time series close to the reference time series in the weighted measurement reference space. As a result, the dimensional reduction method with the least information loss has a large DRE value. 5 shows the results of the DRE values for PCA, DCT and PAA in 2D, 4D and 6D.

6 shows DRaE results (α=50) values for each dimension reduction method.

Referring to FIG. 6, the dimensional ranking efficiency (DRaE) is defined as in Equation 6 below.

[Equation 6]

Here, N represents the number of time series included in SetW. d _k represents the k-th neighbor in μ in the weighted metric space. r(d _k ) is the rank of d _k in the reference time series in the weighted metric space. r(d _k ) = k. rr(d _k ) is the rank of d _k in the reference time series in the reduced dimensional space.

The meaning of DRaE is as follows. If r(d _k ) = rr(d _k ), ranking error does not occur because ranking information is not lost due to the dimension reduction method. Therefore, the value of DRaE is 100%. However, if r(d _k ) ≠ rr(d _k ), ranking error occurs because ranking information is lost due to the dimension reduction method. Therefore, the value of DRaE is less than 100%. Figure 6 shows DRaE results for PCA, DCT and PAA in 2,4,6 dimensions.

7 is a graph showing changes in cluster diameter.

Referring to FIG. 7, the present invention confirmed that the DRE and DRaE values of PCA are greater than those of DCT and PAA. Consequently, in the present invention, PCA was selected as the dimension reduction method.

7 shows an experiment for the estimation of the upper diameter limit. The present invention sequentially adds N neighbors to the neighbor set from the reference time series μ and identifies the change in the maximum distance (Diameter) between data in the neighbor set. At a certain maximum distance, a time series that has a very different trend from most of the time series of the neighbor set appears. The maximum distance is after the upper limit of the diameter.

8 shows the steps of estimating the diameter limit.

Referring to Fig. 8, a process for estimating the diameter limit used in the reduced dimensional space is shown. The graph on the right shows that the diameter of the neighbor set increases when the neighbor set of the reference time series is sequentially added to the neighbor set in the weighted metric space. The graph on the left is shown as follows. In the reduced dimensional space, when neighbors of the reference time series are sequentially added to the neighboring set, the diameter of the neighboring set increases. The diameter limit is estimated as follows. In the graph on the right, find a specific upper diameter limit, then find the kth time series corresponding to the specific upper diameter limit. Next, find the diameter corresponding to the kth time series from the left graph. In the present invention, a diameter corresponding to the k-th time series obtained from the left graph is regarded as a diameter limit candidate. As the diameter limit candidate, the diameter limit candidate × γ is used.

9 is a result of RMSE for each clustering method, FIG. 10 is a result of diameter of each clustering method, and FIG. 11 is a result of MSD for each clustering method.

9 to 11, in order to compare the method according to an embodiment of the present invention with other algorithms, 3PTC and YADING, which are the most recently announced technologies, were selected. 3PTC is the latest technology for financial time series clustering. YADING is the latest technology for density-based time series clustering. The present invention uses two evaluation methods to evaluate the degree of joint movement of a time series in a cluster.

RMSE (root mean square error) is defined as in Equation 7 below.

[Equation 7]

Here, |cluster| represents the number of time series in the cluster. f _i (t) represents the i-th time series of the cluster. P(t) represents the prototype time series of the cluster.

The prototype time series p (t) is defined as in Equation 8 below.

[Equation 8]

MSD (maximum standard deviation) is defined as in Equation 9 below.

[Equation 9]

RMSE is a measure of cluster consistency. Therefore, the smaller the value, the higher the joint movement of the cluster. However, since RMSE is an average value, it is not possible to distinguish the case where time series with significantly different degrees of synchronization are included in the cluster. MSD and diameter are indicators of maximum values. It does not measure the degree of consistency within a cluster, but it can measure the maximum variation of a time series within a cluster. Therefore, in order to evaluate the degree of pupil movement of the cluster, three values should be reduced at the same time.

As shown in Figs. 9 to 11, the three values of this method are smaller than that of other methods. Therefore, it can be seen that the degree of co-movement of the cluster generated by the method of the present invention is the highest.

12 is an ADF test result for each clustering method.

Referring to FIG. 12, cointegration may be used as an index of ball motion. Therefore, the present invention evaluates the degree of coherence of the time series in the cluster using the co-integral evaluation method (ADF test).

To check whether there is a co-integral relationship between the time series of the cluster generated by the algorithm, an ADF test is performed on all the time series pairs of the cluster. Then you get the P value. If the P value is lower than the threshold value, the null hypothesis is rejected. This means that there is a high probability that the two time series are in a cointegrating relationship. The ratio of rejecting the null hypothesis is obtained from the P value obtained by the ADF test. The higher the ratio, the more satisfactory the co-integral relationship of the time series pair of the cluster. Thus, we can see the degree of uniform shift of the time series in the cluster. The results of Fig. 12 mean the following.

It was found that the rejection rate of the null hypothesis for the cluster created by the method according to an embodiment of the present invention is greater than that of YADING and 3PTC. This means that the time series pairs of clusters generated by the method of the present invention are at a higher degree of synchronization than the time series pairs of clusters generated by other methods.

13 is a cluster created by YADING, FIG. 14 is a cluster created by 3PTC, and FIG. 15 is a cluster created by a method according to an embodiment of the present invention.

13 to 15 disclose representative clusters of each algorithm used in the evaluation of the clustering algorithm.

13 and 14, it can be seen that there are sub-clusters having various tendencies in the cluster. The time series pair of clusters created by YADING and 3PTC does not satisfy the high degree of coherence.

15 shows the results of the method of the present invention. It can be seen that the time series pairs of the clusters generated by our method satisfy a high level of synergism.

The present invention discloses a method of finding a financial time series cluster with high sociability. In particular, the present invention takes into account the characteristics of a financial time series. The clustering algorithm proposed in the present invention can be applied to various financial investments such as portfolio selection, risk management, asset allocation, and time series prediction. We are also convinced that our method is very valuable because it is likely to be used for macroeconomic purposes.

16 is a block diagram of a clustering system for a financial time series having a synergistic relationship according to an embodiment of the present invention.

Referring to FIG. 16, a clustering system for a financial time series having a synergistic relationship according to an embodiment of the present invention may include a preprocessor 1610, a clustering unit 1620, and a result analysis unit 1630.

The preprocessor 1610 may perform average scaling to indicate a ratio indicating how much a future value increases or decreases compared to a past value for data normalization. The average scaling is defined as in Equation 2 below.

[Equation 2]

Here, Y _t represents the normalized time series at time t, X _t represents the time series at time t, and μ _X represents the average of X.

In the financial time series analysis in the preprocessor 1610, the more recent data, the more the analysis results in the future are affected. A weighted time series is used to reflect this characteristic. The weighted time series transform produces a weighted time series. This transformation may involve two steps: partial interval (sub-interval) calculation and weight assignment.

N/2k, 2π/T_s ≥2Ω_max, 2π / T_s ≥2 * 2πk / N, T_s≤N / 2k). 그런 다음 각 샘플링 된 기간을 시계열의 부분 구간(서브 인터벌)으로 해석한다. 도 4는 대역 제한 신호의 부분 구간(서브 인터벌)을 보여준다.The preprocessor 1610 uses a method of efficiently finding a partial section (sub-interval) of a time section based on a Nyquist Sampling Rate condition and Parseval theorem. If the sampling frequency is twice the maximum frequency under the Nyquist Sampling Rate condition, the band-limited signal can be completely reconstructed without frequency aliasing by the sampling point. Some time series are not perfectly band-limited signals, but high-frequency components can be considered noise. Therefore, most time series can be regarded as band-limited signals. According to the Parseval theorem, the sum of squares of time series values in time space is equal to the sum of squares of coefficients of frequency components in frequency space. Therefore, we use the Parseval theorem to find the maximum frequency (Ω_max) that conserves most of the energy of the original time series (about 80-90%). (Ω_max = 2πk / N, N corresponds to the total time interval of the time series, k is the multiple coefficient of the frequency 1 / N.) The sampling period (T _s) using the maximum frequency and Nyquist Sampling Rate conditions

N/2k, 2π/T _s ≥2Ω_max, 2π / T _s ≥2 * 2πk / N, T _s ≤N/2k). Then, each sampled period is interpreted as a sub-interval (sub-interval) of the time series. 4 shows a partial section (sub-interval) of the band-limited signal.

The preprocessor 1610 linearly allocates weights to partial sections obtained by the Nyquist Sampling Rate condition and Parseval Theorem. For example, when there are 4 sub-intervals, 1, 2, 3, and 4 weights are allocated to the sub-intervals according to the time sequence from the past to the latest.

The preprocessor 1610 may perform dimension reduction in the preprocessing step. The dimensional reduction method was selected by comparing DCT, PAA, PCA, and SAX. PCA (Principal Component Analysis) was selected as the dimension reduction method. PCA reduces the dimensions of the data by using an eigenvector that best represents the variability of the overall data. The number of dimensions reduced by PCA is determined experimentally using a Scree plot.

The clustering unit 1620 estimates the upper limit of the diameter of the cluster used in the weight space and the limit of the diameter of the cluster used in the reduced dimensional space. Time series can be regarded as a combination of a trend component and a noise component. You should find a time series with similar trend components and low enough noise. To do this, limit the cluster diameter. For computational efficiency in the pre-clustering step, the financial time series is converted to reduced dimensional data. Then, clustering is performed on the reduced dimensional data. However, due to dimensional reduction, the pre-cluster may contain noise. Therefore, in the purification step, the pre-cluster is purified into a purified cluster.

The clustering unit 1620 may perform a diameter upper limit estimation.

The clustering unit 1620 estimates the upper limit of the diameter in order to limit the size of the cluster in the refining step. The upper limit of the area represents the maximum limit of SES_Distance between time series in the cluster. The upper diameter limit is estimated as follows. One sample is extracted from WMS. Then, the time series is sequentially included in the neighboring set in the order of the shortest distance from this sample. If the neighboring set has a time series that deviates significantly from the trend, the present invention removes the time series from the set and considers the maximum SES_Distance as a diameter candidate in the set. The average of several diameter candidate values obtained by iteratively working with several samples is estimated as the upper diameter limit.

The clustering unit 1620 may estimate a diameter limit.

The diameter limit used by the clustering unit 1620 to limit the size of the cluster in the pre-clustering step is estimated as follows. S is the set of neighbors used to estimate the upper diameter limit (D) in WMS. There are two time series corresponding to the upper diameter limit of S. The present invention calculates the Euclidean distance in a reduced dimensional space. The obtained distance is taken as the diameter limit candidate (d'). Information is lost in the reduced dimensional space. When the maximum distance of the cluster is limited to the diameter restriction candidate d', not only data with noise may be included, but similar time series may not be included in the same cluster. Therefore, we use a value slightly larger than the diameter limit value (d = γd', γ> 1) as the diameter limit value.

In the pre-clustering step of the clustering unit 1620, the ADupClustering algorithm is performed on the data of the Reduced Dimensional Space as follows. Agglomerative Clustering Algorithm creates clusters. For each cluster (R) created by the Agglomerative Clustering Algorithm, AdupClustering finds a cluster that should be included in cluster R among the time series included in other clusters. The distance from the cluster R should be less than the diameter limit (d). That is, ADupClustering Algorithm allocates one time series to several clusters. That is, redundant allocation.

The clustering unit 1620 may include time series having different trends since the pre-cluster is generated in the Reduced Dimensional Space. In the purification step, each pre-cluster is purified into several purified clusters. Each refined cluster should contain only time series with similar trends (high degree of synchronization). For this, the ADupClustering algorithm is performed in a weighted metric space using the upper diameter limit (D).

The result analysis unit 1630 may predict a financial time series, a portfolio selection, and a future price of establishing a financial policy using the clustering result.

17 is a flowchart of a clustering method for a financial time series having a synergistic relationship according to an embodiment of the present invention.

Referring to FIG. 17, a clustering method for a financial time series having a synergistic relationship according to an embodiment of the present invention may include preprocessing financial data (S1710).

In step S1710, the preprocessor 1610 may perform average scaling to indicate a ratio indicating how much a future value increases or decreases compared to a past value for data normalization. The average scaling is defined as in Equation 2 below.

[Equation 2]

Here, Y _t represents the normalized time series at time t, X _t represents the time series at time t, and μ _X represents the average of X.

In step S1710, the more recent data in the financial time series analysis in the preprocessor 1610, the more the analysis results in the future are affected. A weighted time series is used to reflect this characteristic. The weighted time series transform produces a weighted time series. This transformation may involve two steps: partial interval (sub-interval) calculation and weight assignment.

N/2k, 2π/T_s ≥2Ω_max, 2π / T_s ≥2 * 2πk / N, T_s≤N / 2k). 그런 다음 각 샘플링 된 기간을 시계열의 부분 구간(서브 인터벌)으로 해석한다. 도 4는 대역 제한 신호의 부분 구간(서브 인터벌)을 보여준다.In step S1710, the preprocessor 1610 uses a method of efficiently finding a partial section (sub-interval) of a time section based on a Nyquist Sampling Rate condition and Parseval theorem. If the sampling frequency is twice the maximum frequency under the Nyquist Sampling Rate condition, the band-limited signal can be completely reconstructed without frequency aliasing by the sampling point. Some time series are not perfectly band-limited signals, but high-frequency components can be considered noise. Therefore, most time series can be regarded as band-limited signals. According to the Parseval theorem, the sum of squares of time series values in time space is equal to the sum of squares of coefficients of frequency components in frequency space. Therefore, we use the Parseval theorem to find the maximum frequency (Ω_max) that conserves most of the energy of the original time series (about 80-90%). (Ω_max = 2πk / N, N corresponds to the total time interval of the time series, k is the multiple coefficient of the frequency 1 / N.) The sampling period (T _s) using the maximum frequency and Nyquist Sampling Rate conditions

N/2k, 2π/T _s ≥2Ω_max, 2π / T _s ≥2 * 2πk / N, T _s ≤N/2k). Then, each sampled period is interpreted as a sub-interval (sub-interval) of the time series. 4 shows a partial section (sub-interval) of the band-limited signal.

In step S1710, the preprocessor 1610 linearly allocates a weight to the partial section obtained by the Nyquist Sampling Rate condition and Parseval theorem. For example, when there are 4 sub-intervals, 1, 2, 3, and 4 weights are allocated to the sub-intervals according to the time sequence from the past to the latest.

In step S1710, the preprocessor 1610 may perform dimension reduction in the preprocessing step. The dimensional reduction method was selected by comparing DCT, PAA, PCA, and SAX. PCA (Principal Component Analysis) was selected as the dimension reduction method. PCA reduces the dimensions of the data by using an eigenvector that best represents the variability of the overall data. The number of dimensions reduced by PCA is determined experimentally using a Scree plot.

A clustering method for a financial time series having a synergistic relationship according to an embodiment of the present invention may include clustering using the preprocessed data (S1720).

In step S1720, the clustering unit 1620 estimates the upper limit of the diameter of the cluster used in the weight space and the limit of the diameter of the cluster used in the reduced dimensional space. Time series can be regarded as a combination of a trend component and a noise component. You should find a time series with similar trend components and low enough noise. To do this, limit the cluster diameter. For computational efficiency in the pre-clustering step, the financial time series is converted to reduced dimensional data. Then, clustering is performed on the reduced dimensional data. However, due to dimensional reduction, the pre-cluster can contain noise. Therefore, in the purification step, the pre-cluster is purified into a purified cluster.

In step S1720, the clustering unit 1620 may perform a diameter upper limit estimation.

The clustering unit 1620 estimates the upper limit of the diameter in order to limit the size of the cluster in the refining step. The upper limit of diameter represents the maximum limit of SES_Distance between time series within a cluster. The upper diameter limit is estimated as follows. One sample is extracted from WMS. Then, the time series is sequentially included in the neighboring set in the order of the shortest distance from this sample. If the neighboring set has a time series that deviates significantly from the trend, the present invention removes the time series from the set and considers the maximum SES_Distance as a diameter candidate in the set. The average of several diameter candidate values obtained by iteratively working with several samples is estimated as the upper diameter limit.

In step S1720, the clustering unit 1620 may estimate a diameter limit.

The diameter limit used by the clustering unit 1620 to limit the size of the cluster in the pre-clustering step is estimated as follows. S is the set of neighbors used to estimate the upper diameter limit (D) in WMS. There are two time series corresponding to the upper diameter limit of S. The present invention calculates the Euclidean distance in a reduced dimensional space. The obtained distance is taken as the diameter limit candidate (d'). Information is lost in the reduced dimensional space. When the maximum distance of the cluster is limited to the diameter restriction candidate d', not only data with noise may be included, but similar time series may not be included in the same cluster. Therefore, we use a value slightly larger than the diameter limit value (d = γd', γ> 1) as the diameter limit value.

In step S1720, the clustering unit 1620 performs the ADupClustering algorithm in the time series of the Reduced Dimensional Space as follows in the pre-clustering step. Agglomerative Clustering Algorithm creates clusters. For each cluster (R) created by the Agglomerative Clustering Algorithm, AdupClustering finds a cluster that should be included in cluster R among the time series included in other clusters. The distance from the cluster R should be less than the diameter limit (d). That is, ADupClustering Algorithm allocates one time series to several clusters. That is, redundant allocation.

In step S1720, the clustering unit 1620 may include time series having different trends because the pre-cluster is generated in the Reduced Dimensional Space. In the purification step, each pre-cluster is purified into several purified clusters. Each refined cluster should contain only time series with similar trends (high degree of synchronization). For this, the ADupClustering algorithm is performed in a weighted metric space using the upper diameter limit (D).

The clustering method for a financial time series having a synergistic relationship according to an embodiment of the present invention may include analyzing the clustering result (S1730).

In step S1730, the result analysis unit 1630 may predict the future price of financial time series, portfolio selection, and financial policy establishment using the clustering result.

So far, the present invention has been looked at around its preferred embodiments. Those of ordinary skill in the art to which the present invention pertains will be able to understand that the present invention may be implemented in a modified form without departing from the essential characteristics of the present invention. Therefore, the disclosed embodiments should be considered from an illustrative point of view rather than a limiting point of view. The scope of the present invention is shown in the claims rather than the foregoing description, and all differences within the scope equivalent thereto should be construed as being included in the present invention.

Claims (10)

As a clustering method for a financial time series performed by a cluster system for a financial time series including a data preprocessor and a clustering unit,
A data pre-processing step performed by the data pre-processing unit and a clustering step performed by the clustering unit,
The data preprocessing step,
Normalizing the financial time series by performing average scaling defined by Equation 2 below;
Performing a weighted time series transformation on the normalized financial time series to generate a weighted time series to which a greater weight is assigned from the past to the latest; And
Reducing the dimension of the weighted time series; Including,
The clustering step,
A pre-clustering step of generating a pre-cluster for a weighted time series whose dimensions have been reduced; And
Clustering method for a financial time series comprising; a refinement step of generating a refined cluster from each of the generated dictionary clusters:
<Equation 2>

(Where Y _t is the normalized financial time series at time t, X _t is the financial time series at time t, and μ _X is the mean of X).
The method of claim 1,
The clustering step
Performed before performing the pre-clustering step,
Estimating a diameter limit (D) limiting the size of the prior cluster and a diameter limit (d) limiting the size of the refined cluster; further comprising,
Estimating the upper diameter limit (D)
Selecting a maximum value of the SES_distance represented by Equation 1 below from an arbitrary time series to another time series constituting a neighboring set as a diameter upper limit candidate in the weight metric space; And estimating the average of the diameter upper limit candidates as the diameter upper limit (D); Including,
Estimating the diameter limit (d),
Calculating a Euclidean distance in a dimension reduction space for two time series used to estimate the upper diameter limit (D); Selecting the Euclidean distance as a diameter limit candidate (d'); And estimating a diameter limit (d) from the diameter limit candidate (d'); including, a clustering method for a financial time series:
<Equation 1>

(SIDIst _i is the Euclidean distance of the i-th sub-interval (sub-interval) time series of the weighted time series).
The method of claim 2,
The weight metric space is a space consisting of a weighted time series,
The dimensionality reduction space is a space consisting of a weighted time series whose dimensions are reduced, a clustering method for a financial time series.
The method of claim 1,
The cluster system further includes a result analysis unit, the clustering method for the financial time series
Analyzing the clustering result performed by the result analysis unit; further comprising, a clustering method for a financial time series.
In a cluster system for a financial time series including a data preprocessor and a clustering unit,
The data preprocessing unit,
Normalize the financial time series by performing average scaling defined by Equation 2 below,
A weighted time series transformation is performed on the normalized financial time series to generate a weighted time series with a greater weight from the past to the latest,
Reduce the dimension of the weighted time series,
The clustering unit,
Pre-cluster the weighted time series with reduced dimensions to create a pre-cluster,
A clustering system for a financial time series to generate a refined cluster by refining each of the prior clusters:
<Equation 2>

(Where Y _t is the normalized financial time series at time t, X _t is the financial time series at time t, and μ _X is the mean of X).
The method of claim 5,
The clustering unit
Before performing the pre-clustering,
Estimating an upper diameter limit (D) limiting the size of the pre-cluster and a diameter limit (d) limiting the size of the refined cluster,
The estimation of the upper diameter limit (D) is
In the weighted metric space, the maximum value of the SES_ distance represented by Equation 1 below from an arbitrary time series to another time series forming a neighboring set is selected as a diameter upper limit candidate, and the average of the diameter upper limit candidates is selected as the diameter upper limit (D). Is carried out in an estimate method,
Estimation of the diameter limit (d),
For the two time series used to estimate the upper diameter limit (D), the Euclidean distance in the dimension reduction space is calculated, the Euclidean distance is selected as a diameter limit candidate (d'), and the diameter limit candidate (d Clustering system for financial time series, performed by estimating diameter limit (d) from'):
<Equation 1>

(SIDIst _i is the Euclidean distance of the i-th sub-interval (sub-interval) time series of the weighted time series).
The method of claim 6,
The weight metric space is a space consisting of a weighted time series,
The dimensionality reduction space is a space consisting of a weighted time series whose dimensions are reduced, a clustering system for a financial time series.
The method of claim 5,
The clustering system for the financial time series
Clustering system for financial time series further comprising; a result analysis unit for analyzing the clustering result. delete delete

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