Research Article  Open Access
Lv Tao, Yongtao Hao, Hao Yijie, Shen Chunfeng, "KLine Patterns’ Predictive Power Analysis Using the Methods of Similarity Match and Clustering", Mathematical Problems in Engineering, vol. 2017, Article ID 3096917, 11 pages, 2017. https://doi.org/10.1155/2017/3096917
KLine Patterns’ Predictive Power Analysis Using the Methods of Similarity Match and Clustering
Abstract
Stock price prediction based on Kline patterns is the essence of candlestick technical analysis. However, there are some disputes on whether the Kline patterns have predictive power in academia. To help resolve the debate, this paper uses the data mining methods of pattern recognition, pattern clustering, and pattern knowledge mining to research the predictive power of Kline patterns. The similarity match model and nearest neighborclustering algorithm are proposed for solving the problem of similarity match and clustering of Kline series, respectively. The experiment includes testing the predictive power of the Three Inside Up pattern and Three Inside Down pattern with the testing dataset of the Kline series data of Shanghai 180 index component stocks over the latest 10 years. Experimental results show that the predictive power of a pattern varies a great deal for different shapes and each of the existing Kline patterns requires further classification based on the shape feature for improving the prediction performance.
1. Introduction
A time series is a series of observations listed in time order. It is the most commonly encountered data type, touching almost every aspect of human life [1], for example, the meteorological time series, the time series of stock prices (stock time series for short) which are composed of stock price observations, and the time series of personal health that are consisted of the observation of blood pressure, temperature, white corpuscle, and so forth.
Researches show that the time series have two import features. (a) The historical information will affect the future trend [2]. That is, the historical values of observations will exert an influence on the future values in the time series. The influence can be described by time series’ period, nonstationarity, varying volatility, and so on. (b) History repeats itself [3]. That is to say, some special time subseries will repeat in the entire time series. Because of the two features, all kinds of time series forecasting have become a present hot research, one of which is the prediction of stock time series, stock prediction for short. As a typical time series, not only have stock time series the features of time series, but also the trend of stock prices is directly related to the people’s vital interests. Therefore, stock prediction has aroused the interest of a wide variety of researchers.
There are many technical analysis methods about stock prediction, the best known of which is candlestick technical analysis that is also called Kline technology analysis in Asia. In the stock market, in order to learn and study the fluctuation of stock prices in a more intuitive way, people invent a candlestick chart (also called Kline) to represent stock time series graphically. Taking a daily Kline, for example, a Kline represents the fluctuation of stock prices in one day, it not only shows the close price, open price, high price, and low price for the day but also reflects the difference and size between any two prices (all Klines given in the paper refer to daily Kline, unless otherwise indicated). If the Kline of a stock lists in time order, then a series used to reflect the fluctuation of the stock price for some time can be formed, which can be called Kline series. As each Kline consists of four prices, the essence of Kline series is stock series with four observations.
In Kline series, if a Kline subseries contains some knowledge used to predict stock, then this subseries is called a Kline pattern series, a Kline pattern for short. For instance, when a subseries appears, the stock price will often rise or descend. Then, this subseries is a typical pattern series. Stock prediction based on Kline patterns is the essence of Kline technology analysis. How to mine the Kline patterns and how to make use of these patterns for predicting are main research contents of Kline technology analysis.
By the artificial methods of observing the Kline series of stock market (or Japanese rice market), people (the leading character is the founder of Kline, Munehisa Honma, who was a Japanese rice trader in the 18th century) have found many Kline patterns. The literatures [4, 5] introduce the existing patterns and their features in detail, such as Three Inside Up (TIU), Three Inside Down (TID), and Doji. Some papers [6–10] conclude from the experiment that the existing Kline patterns have a good forecasting capability for forecasting stock trends. Some other papers [11–15] have studied the stock prediction based on these patterns and have achieved some research results. However, there are also a number of papers [5, 16–18] challenging these patterns’ predictive power. They argue that Kline technology analysis violates the efficient market hypothesis, so it is not feasible for stock investment based on Kline patterns. They also did some experiments, which show that the existing Kline patterns have no predictive power.
Based on the above analysis, it is obvious that there are some disputes on whether the Kline patterns have predictive power in academia. However, there are few papers analyzing the reason why there are two different positions regarding the patterns’ predictive power. Paper [19] also pays attention to the debate, while it does not analyze the Kline patterns themselves but attempts to obtain an answer to the following question: are the trend reversals accompanied more often by some types of candlesticks than by others? Finally, paper [19] has found that there exist types of candlesticks that frequently tend to appear close to the trendreversal regions and others that cannot be found in such regions. Although the paper’s research shows that the Kline patterns exist, it does not give the answer that why there is a debate on the Kline patterns’ predictive power.
Through reviewing the relevant literatures, this paper considers that the main reason is that the existing Kline patterns are lack of rigorous mathematical definition. For example, the shadow length and body size are not defined clearly in the definition of Kline patterns, which means that a Kline pattern has many different shapes. Because the predictive power of a pattern may vary a lot for different shapes. If we ignore the shape difference and research the predictive power of a pattern by taking all patterns with various shapes as a whole instead of classifying the pattern further based on its shape feature, then the study result of Kline patterns’ predictive power may produce deviations. For instance, a TIU pattern has three shapes: shape A, shape B, and shape C, as shown in Figure 1, where shape A is the generic form of TIU pattern, and shape B and C are infrequent form of which. Suppose that shape A has predictive power, and shape B and C do not have predictive power. When studying the predictive power of TIU pattern, if we ignore the shape difference between the three patterns and research them as a whole, then we will come to the wrong conclusion that TIU pattern has no predictive power. However, if the three patterns are classified further based on shape features and researched separately, then we can get the correct conclusion that TIU pattern has predictive power only at shape A.
(a) Shape A
(b) Shape B
(c) Shape C
In addition, another reason is that, as the existing Kline patterns are mined by artificial means, there may be some spurious pattern in them.
In order to resolve the debate and verify the two inferences, this paper presents the research of Kline patterns’ predictive power using the data mining related method, such as pattern recognition, pattern clustering, pattern knowledge mining, and statistical analysis. The rest of this paper is organized as follows. In Section 2, we firstly shortly introduce Kline, Kline technology analysis, and Kline patterns. Then we define the similarity match model and nearest neighborclustering algorithm of Kline series. In Section 3, we define the mining method of patterns’ predictive power. Section 4 presents the experimental result and discussion. Section 5 concludes the paper.
2. KLine and KLine Series Clustering
Firstly, we give the mathematic definition of Kline series. Let represent the th Kline series of any stock, and let represent tth Kline in ; thenwhere is the number of elements in , which is also called the length of . , , , and are the tth day’s close price, open price, high price, and low price in , respectively. In this paper, “” symbol indicates the number of elements in the set or series.
2.1. KLine
2.1.1. KLine Introduction
As defined in literature [4–6], the Kline is drawn by four basic elements: close price, open price, high price, and low price, where the part between the close price and open price is drawn into a rectangle called body of Kline and the part between the high price and body is drawn into a line called upper shadow of Kline. Moreover, the part between the lower price and body is drawn into a line called lower shadow of Kline. This kind of very personalized lines consisting of upper shadow, lower shadow, and body is called Kline.
In the Kline, if open price is lower than close price, Kline also called Yang line, the body is usually filled with white or green color, as shown in Figure 2(a). And if open price is higher than close price, Kline also called Yin line, the body is usually filled with black or red color, as shown in Figure 2(b). Moreover, if open price is equal to close price, Kline also called Doji line, the body then collapses into a single horizontal line, as shown in Figure 2(c). It is important to note that the body color of Yin line and Yang line is different in Chinese stock market and stock markets of European and American. In Chinese stock market, the body color of Yang line and Yin line is red and green, respectively. However, the body color of Yang line and Yin line is green and red, respectively, in the stock markets of European and American.
(a) Yang line
(b) Yin line
(c) Doji line
2.1.2. KLine Technology Analysis
Firstly, we introduce and define some key concepts of Kline technology analysis. Let represent the tth day’s Kline of any stock.
(1) Moving Average. It is the average of stock price for some time. The threeday moving average at time is defined bywhere denotes the close price of .
(2) KLine Trend. It is used to describe the Kline’s trend, including uptrend and downtrend. is said to be a downtrend ifwith at most one violation of the inequalities. Uptrend is defined analogously.
(3) Stock Price Trend. It is used to describe the general trend of stock prices for some time, including uptrend and downtrend. If the future trend of stock price is rising, it is called bullish market. In contrast, if the future trend of stock price is descending, it is called bearish market. Moreover, a more intense rising or descending trend indicates a more typical bullish or bearish market. The capability of a Kline patter for predicting the bullish market and bearish market is defined in formulas (17) and (18), respectively.
It is noted that the concepts of “moving average” and “Kline trend” are defined by the paper [6], while the concept of stock price trend is firstly defined by the paper.
2.1.3. KLine Patterns
Many Kline patterns have been mined up to now, as shown in literatures [4–6]. Limited by space, only the patterns of TIU and TID will be introduced in the next content. Let represent a threeday Kline series.
The conditions of becoming the TIU pattern are as follows: is a downtrend, and . , , and , where at most one of the two equalities holds. That is, the second day is Yang line and must be contained with the body of the first day. ; . That is, the third day is Yang line and closes above the open of the first day. A standard TIU pattern is shown in Figure 3(a).
(a) TIU
(b) TID
The predictive power of TIU pattern from the existing literature is that TIU is a trendreversal pattern, which gives the bullish market signal. This means when the TIU pattern appears, the stock prices will be likely to be transferred from downtrend into uptrend or the stock market would be changed from bearish market to bullish market, and the stock prices would rise gradually.
The conditions of becoming the TID pattern are as follows: (1) is an uptrend, and . (2) , , and , where at most one of the two equalities holds. That is, the second day is Yin line and must be contained within the body of the first day. (3) ; . That is, the third day is Yin line and its close is lower than the first day’s open. A standard TID pattern is shown in Figure 3(b).
The predictive power of TID pattern from the existing literature is that TID is a trendreversal pattern, which gives the bearish market signal. That means, after the TID pattern appears, the stock prices will be likely to be transferred from uptrend into downtrend or the stock market would be changed from bullish market to bearish market, and the stock prices would fall gradually.
2.2. Similarity Match of KLine Series
The similarity match of Kline series is an essential and basis task for Kline series clustering. In the literature, however, there are few papers focusing on the similarity match of Kline series. Only paper [20] studies the similarity match method and search algorithm of Kline series using image retrieval technology. In addition, paper [19, 21] proposes the similarity match model of Kline series based on the traditional Euclidean distance.
From the view of stock prediction, the Kline series’ similarity refers to the trend similarity of Kline in the Kline series. However, the Kline trend is determined by the close price change, open price change, high price change, low price change, and the size relationship between close price and open price. Therefore, if we want to match the similarity between two Kline series, we should calculate the similarity of Kline price changes instead of the similarity of price values. As the changes of Kline price are not shown in the Kline chart, Kline prices distance rather than Kline price changes distance is used in the similarity match model of literature [19–21]. This means that these match models belong to similarity match methods based on Kline price values rather than Kline price changes. Therefore, they cannot accurately measure the similarity of stock prices trend in the Kline series.
For example, assuming that there are two Kline series and needed to match their similarity, where and indicate their similarity. Let , , , , and indicate the close price change rate of at day , which is calculated by , denotes the similarity between and , then , and . We cannot calculate the correct result of by the similarity match model in literature [19–21]. Similarly, the same problems would occur for calculating the similarity of open price, high price, or low price.
Therefore, this paper proposes a new similarity match model based on Kline price changes to measure the trend similarity between two Kline series. In this model, the similarity of Kline series is composed of two parts: one is the shape similarity of Kline, which is the similarity of the corresponding Kline’s shape features in the two Kline series; the other is the position similarity of Kline, which is the similarity of the corresponding Kline’s position features in the two Kline series. Therefore, this paper will define Kline series’ shape similarity model and position similarity model, respectively. Then based on these two kinds of similarity models, the similarity model of the entire Kline series could be built.
2.2.1. The Shape Similarity of KLine Series
According to the shape feature of Kline, this paper proposes using the shape distance to measure the shape similarity between two Klines. Firstly, based on the shape structure of Kline, three components of Kline shape are extracted: the upper shadow shape, the lower shadow shape, and the body shape. Secondly, the similarity match methods of three shapes are defined, respectively. Finally, the shape similarity of Kline can be calculated by summing the three shapes’ similarity. Assuming that and denote the tth day’s Kline of and , respectively, the shape similarity model of Kline series is defined as follows:
Let denote the upper shadow length of , as defined in the following formula:where is used to normalize the upper shadow length. According to the related regulation of Chinese Ashare market, the range of daily fluctuations of stock prices cannot exceed 10% of the previous day’s close price. So can be used to normalize the length of the Kline’s upper shadow, lower shadow, and body.
Let denote the upper shadow similarity between and , as defined by
Let denote the lower shadow length of , as defined in the following formula:
Let denote the lower shadow similarity between and , as defined by
Let denote the body length of , as defined in the following formula:
Let denote the body similarity between and , as defined by
Let denote the shape similarity between and , as defined bywhere , , and represent the weight of , , and , respectively.
Let denote the shape similarity between and , as defined bywhere represent the weight of . Thanks to the idea that each Kline can be given different weight, the Kline series having special shape features could be identified well.
2.2.2. The Position Similarity of KLine Series
For computing the similarity between two Kline series, we not only consider the shape similarity of Kline series but also the position similarity. If we only consider the shape similarity, then it will cause the problem that two Kline series having same shape features but different position features will have the same similarity.
For example, supposing that the Kline series chart of and is shown in Figure 2, we can see that, according to the shape feature definition of Kline, all of the corresponding Klines of and have the same shape features. These mean that and have identical shape features; that is, . However, as is vividly shown in Figure 4, the relative positions of and are different though and have the same relative position in the Kline series. Therefor the stock price’s overall trend of and are not identical, that is, . If we only consider the shape similarity, we will draw the wrong conclusion that .
(a)
(b)
To solve this problem, the concept of Kline coordinate is introduced hoping to implement the position match of Kline by defining Kline’s coordinate in the Kline series. In this paper, the sequence of Kline in the Kline series is called coordinate of Kline; the increase range of close price is called coordinate of Kline; in addition the first Kline’s coordinate is set to 1 in the Kline series. Therefore, the position similarity model of Kline series based on Kline coordinate is defined as follows.
Let denote the coordinate of , which are defined in the following formula:
Let denote the position similarity between and , as defined by
Let denote the position similarity between and , as defined bywhere represents the weight of . Thanks to the idea that each Kline can be given different weight, the Kline series having special coordinates could be identified well.
2.2.3. The Similarity of KLine Series
Finally, based on the shape similarity and position similarity, the similarity of Kline series could be obtained. Therefore, the similarity match model between and is defined bywhere and represent the shape similarity weight and position similarity weight of Kline series, respectively.
2.3. Cluster of KLine Series
The more accurate classification result of Kline patterns can be gotten by clustering them using the nearest neighborclustering algorithm based on the similarity match model of Kline series. The Kline series’ nearest neighborclustering algorithm (KNNCA) is described as shown in Algorithm 1.

In addition, represents the number of elements in . As each Kline series will be matched once with all of the Kline series stored in the cluster, the time complexity and space complexity of KNNCA are both .
3. Mining of Patterns’ Predictive Power
We can mine and analyze the patterns’ predictive power according to the following steps.
(1) Pattern Recognition. Based on the definition of Kline patterns, we identify all the Kline series belonging to a pattern (such as TIU or TID), and then they form a set .
(2) Pattern Clustering. We use the KNSSC algorithm to cluster ; then the set of clusters can be gotten, in which different clusters represent the same pattern’s different shapes.
(3) Knowledge Mining. We define some statistical indicators about stock prices, which we use to mine stock prediction knowledge from each cluster.
The pattern’s predictive power is gotten primarily by analyzing the trend of the pattern’s consequent Kline series. Paper [22] found that Kline technology is suited for shortterm investment prediction and that the most efficient time period for prediction is 10 days. Therefore, we mainly analyze the close price trend of the pattern’s consequent Kline series in 10 days. Let denote a threeday Kline pattern; its consequent Kline series is denoted by . The statistical indicators of are defined as follows.
(a) Let denote the kth close price of , let denote that the probability of the trend of is uptrend, and let denote that the probability of the trend of is downtrend. and are calculated bywhere represents the number of patterns meeting the condition of in , represents the number of patterns meeting the condition of in , and represents the close price of . indicates that the future trend of is rising. indicates that the future trend of is descending.
(b) Let denote the probability that the close price will rise in the next days if the pattern appears. denotes the probability that the close price will fall in the next days if the pattern appears. and are calculated bywhere a higher value of or indicates a stronger capability for predicting bullish or bearish market.
(4) Analysis. Based on the statistical result, we analysis the pattern’s predictive power.
4. Experiment and Result Analysis
4.1. Experiment Data and Method
As Yahoo provides the finance stock API used to download the transaction data of Chinese stock market, the stock transaction data of Chinese Ashare market in any time can be acquired based on the API. To get a representative testing data, we select the Kline series data of Shanghai 180 index component stocks over the latest 10 years (from 20060104 to 20160824) as the test data. Limited by space, only the TIU and TID pattern’s predictive power will be analyzed in the experiment. And the parameters of KNSSC algorithm are set as follows: , , , , , , and ().
4.2. Experiment One
The aim of the first experiment is to analyze the TIU pattern’s predictive power based on the method defined in Section 3. Firstly, based on the definition of TIU, 1516 TIU patterns are identified from the test data. Then we cluster these patterns using the KNSSC algorithm, and finally 554 clusters are obtained. We choose the top 20 clusters with the most elements to conduct statistical analysis, as shown in Table 1.

In Table 1, represents the cluster composed of 1516 TIU Patterns. Its is only 0.5 which means that it may be a spurious pattern to predict bullish market. However, after further classifying the TIU patterns, we can see that (1) , , , and so forth have a strong capability for predicting bullish market, because their both are above 0.8, (2) , , , and so forth have a moderate capability for predicting bullish market, as their are only in 0.5~0.7, and (3) , , , and so forth have a weak capability for predicting bullish market, as their entire are below 0.5. Particularly for , its is only 0.1.
By comparing the predictive power of and , as shown in Figure 5, we can see that the predictive result of is bullish market while that of is bearish market, which means that their predictive power is opposite. The result of experiment one shows that (1) the predictive power of TIU varies a great deal for different shapes and (2) to be a better pattern for predicting bullish market, the TIU pattern badly needs to be further classified, which are consistent with the expected analysis.
4.3. Experiment Two
The aim of the second experiment is to analyze the TID pattern’s predictive power based on the method defined in Section 3. Firstly, based on the definition of TID, 1498 TID patterns are identified from the test data. Then we cluster these patterns using the KNSSC algorithm, and finally 572 clusters are obtained. We choose the top 20 clusters with the most elements to conduct statistical analysis, as shown in Table 2.

Similarly, the TID pattern may be also a spurious pattern to predict bearish market because of is 0, where represents the cluster composed of 1498 TID patterns. Moreover, after further classifying the TID patterns, we can see that except for and , almost all of the clusters have a weak capability for predicting bearish market, as their entire are below 0.5 and even and still not have a higher value of , which are only 0.5. Therefore, we can consider that the TID pattern is definitely a spurious pattern, which is also consistent with the expected analysis.
4.4. Experiment Conclusion
Through the above experiment, we can draw the following conclusion. (1) The predictive power of a pattern varies a great deal for different shapes. Take TIU; for example, some shapes’ TIU patterns have a strong capability for predicting bullish market, while some others have the opposite predictive power. Therefore, to analyze the predictive power of a pattern, we should make a concrete analysis of concrete shapes. (2) There are definitely some spurious patterns in the existing Kline patterns. Therefore, in order to improve the stock prediction performance based on Kline patterns, we need to further classify the existing patterns based on the shape feature, identify all the spurious patterns, and choose the patterns having stronger predictive power to predict the stock price.
5. Conclusion
Stock prediction is a popular research field in the time series prediction. As a primary technology analysis method of stock prediction, there is different option on the stock price prediction based on Kline patterns in the academic world, though it is widely used in reality. To help resolve the debate, this paper uses the data mining method, like pattern recognition, similarity match, cluster and statistical analysis, and so forth, to study the predictive power of Kline patterns. Experimental results show that one reason for the debate is that the definition of Kline patterns is more open and lack of mathematical rigor. The other is that there are some spurious patterns in the existing Kline patterns. In addition, the method presented in the paper can be used not only to test the predictive power of patterns but also for Kline patterns mining and stock prediction. Therefore, the future works as follows. It will be a necessary and significant task to identify the entire spurious pattern using the proposed method. On the basis of the proposed method, we can research an automatic pattern mining method to discover more useful patterns for stock prediction.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
The Key Basic Research Foundation of Shanghai Science and Technology Committee, China (Grant no. 14JC1402203), and the Science and Technology Support Program of China (Grant no. 2015BAF10B01) financially supported this work.
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Copyright
Copyright © 2017 Lv Tao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.