Applied Soft Computing 7 (2007) 1197–1208 www.elsevier.com/locate/asoc Automatic extraction and identification of chart patterns towards financial forecast James N.K. Liu *, Raymond W.M. Kwong Department of Computing, The Hong Kong Polytechnic University, Hong Kong Available online 20 March 2006 Abstract Technical analysis of stocks mainly focuses on the study of irregularities, which is a non-trivial task. Because one time scale alone cannot be applied to all analytical processes, the identification of typical patterns on a stock requires considerable knowledge and experience of the stock market. It is also important for predicting stock market trends and turns. The last two decades has seen attempts to solve such non-linear financial forecasting problems using AI technologies such as neural networks, fuzzy logic, genetic algorithms and expert systems but these, although promising, lack explanatory power or are dependent on domain experts. This paper presents an algorithm, PXtract to automate the recognition process of possible irregularities underlying the time series of stock data. It makes dynamic use of different time windows, and exploits the potential of wavelet multi-resolution analysis and radial basis function neural networks for the matching and identification of these irregularities. The study provides rooms for case establishment and interpretation, which are both important in investment decision making. # 2006 Elsevier B.V. All rights reserved. Keywords: Forecasting; Wavelet analysis; Neural networks; Radial basis function network; Chart pattern extraction; Stock forecasting; CBR 1. Introduction According to the efficient market theory, it is practically impossible to infer a fixed long-term global forecasting model from historical stock market information. It is said that if the market presents some irregularities, someone will take advantages of it and this will cause the irregularities to disappear. But it does not exclude that hidden short-term local conditional irregularities may exist; this means that we can still take advantage from the market if we have a system which can identify the hidden underlying short-term irregularities when they occur. The behavior of these irregularities is mostly non-linear amid many uncertainties inherent in the real world. In general, the response to those irregularities will follow the golden rule — ‘‘buy low, sell high’’ for most investors. If one foresees that the stock prices will have a certain degree of upward movement, one will buy the stocks. In contrast, if one foresees that a certain degree of drop will happen, one will sell the stocks on hand. This gives arise the problems of what irregularities we should focus on, forecasting techniques we can deplore, effective indicators we can assemble, data information and features we can select to facilitate the modeling and making of sound investment decision. * Corresponding author. E-mail addresses: csnkliu@comp.polyu.edu.hk (James N.K. Liu), cskwong@comp.polyu.edu.hk (Raymond W.M. Kwong). 1568-4946/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2006.01.007 Since the late 1980s, advances in technology have allowed researchers in finance and investment to solve non-linear financial forecasting problems using artificial intelligence technologies including neural networks [1–4], fuzzy logic [5– 7], genetic algorithms and expert systems [8]. These methods have all shown promise, but each has its own advantages and disadvantages. Neural networks and genetic algorithms have produced promisingly accurate and robust predictions, yet they lack explanatory power and investors show little confidence in their recommendations. Expert systems and fuzzy logic provide users with explanations but usually require experts to set up the domain knowledge. At last but not least, none of these expert systems can learn. In this paper we introduce an algorithm, PXtract to automate the recognition process of possible irregularities underlying the time series of stock data. It makes dynamic use of different time windows, and exploits the potential of using wavelet multiresolution analysis and radial basis function neural networks for the matching and identification of these irregularities. 2. Related work Many of financial researchers believe that there are some hidden indicators and patterns underlying stocks [9]. Weinstein [10] found that every stock has its own characteristics. It mainly 1198 J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 falls into five categories, they are: finance, utilities, property, and commercial/industrial and technology. Stocks’ price movements in different categories are depending on different factors. It is difficult to identify which factors will affect a particular stock’s price movement. To address the problem, we explored the use of genetic algorithm to provide a dynamic mechanism for selecting appropriate factors from available fundamental data and technical indicators [11]. Our investigation of the HK stock market included potential parameters in fundamental data such as daily high, daily low, daily opening, daily closing, daily turnover, gold price, oil price, HK/US dollar exchange rate, HK deposit call, HK interbank call, HK prime rate, silver price, and Hang Seng index comprising 33 stocks from the said five categories. The aggregate market capitalization of these stocks accounts for about 79% of the total market capitalization on The Stock Exchange of Hong Kong Limited (SEHK). On the other hand, for the technical indicators, we examined the influences of popular indicators such as the relative strength index (RSI), moving average (MA), stochastic and Ballinger bands, prices/index movements, time lags and several data transformations [12,13]. Each of these indicators provides guidance for investors to analyze the trend of the stocks’ prices movements. In particularly, the RSI is quite useful to technical analyst in chart interpretation. The theoretical basis of the relative strength index is the concept of momentum. A momentum oscillator is used to measure the velocity or rate of change of price over time. It is essentially a short-term trading indicator and also quite effective in extracting price information for a non-trending market. In short, the total number of potential inputs being tested was 57 [11]. We applied GAs to determine which input parameters are optimal for different stock modeling in Hong Kong. The fitness value of the chromosome in the genetic algorithm was the classification rate of the neural network. It was calculated by counting on how many days the network’s output matched the derived ‘‘best strategy’’. We defined the best strategy at trading time t as: 8 priceðt þ 1Þ priceðtÞ > > buy if > z% > > < priceðtÞ best strategy ¼ priceðt þ 1Þ priceðtÞ > sell if < z% > > priceðtÞ > : hold otherwise where z is the decision threshold, and the output of the network is encoded as 1, 0, and 1 corresponding to the suggested investment strategies ‘buy’, ‘hold’, ‘sell’, respectively. We observed that the daily closing price and its transformation were the most sensitive input parameters for the stock forecast. In contrast, technical indicators such as RSI and MA were not critical in those experiments. As such, we feel confident to concentrate on the investigation of the closing price movements for possible trends and irregularities. This will be the subject of chart pattern analysis below. 3. Wave pattern identification According to Thomas [14], there are up to 47 different chart patterns, which can be identified in stock price charts. These chart patterns play a very important role in technical analysis with different chart patterns revealing different market trends. For example, a head-and-shoulders tops chart pattern reveals that the market will most likely to have a 20–30% rise in the coming future. Successfully identifying the chart pattern is said to be the crucial step towards the win. Fig. 1 shows 16 samples of typical chart patterns. However, the analysis and identification of wave patterns is difficult for two reasons. Firstly, there exists no single time scale that works for all analytical purposes. Secondly, any stock chart may exhibit countless different pattern combinations, some containing sub-patterns. Choosing the most representative presents quite a dilemma. Furthermore, there is no readily report of research development on the automatic process of identifying chart patterns. We address this problem using the following algorithm. 3.1. The PXtract algorithm The PXtract algorithm extracts wave patterns from stock price charts based on the following phases: 3.1.1. Window size phase As there is hardly a single time scale that works for all analytical purposes in a wave identification process [2,29], a set of time window sizes W={fw1 ; w2 ; . . . ; wn g j w1 > w2 > . . . > wn is defined (wi is the window size for 1 < = i< = n). Different window sizes are used to determine whether a wave pattern occurs in a specific time range. For example, in a shortterm investment strategy, a possible window size can be defined as Wi 2 W = {40, 39, . . ., 10}. 3.1.2. Time subset generation phase Stock price trading data contain a set of time data T = {t1, t2, . . ., tn} j t1 > t2 > . . . > tn. For a given time window size wi , T will be divided into a temporary subset T0. A set P is also defined, where P T. It contains the time ranges in which previously identified wave patterns have occurred. Set P is f in the beginning. It is said that any large change in a trend plays a more important role in the prediction process [13]. A range which has previously been discovered to contain a wave pattern will not be tested again (i.e. If T0 P, tests will not be carried out). Details about time subset T0 generation processes are shown in Fig. 2. For example, T = {10 Jan, 9 Jan, 8 Jan, 7 Jan, 6 Jan, 5 Jan, 4 Jan, 3 Jan, 2 Jan, 1 Jan}, the current testing window size is 3 (w ¼ 3), and P = {9 Jan, 8 Jan, 7 Jan, 6 Jan}. After the time subset generation process, T0 = {(5 Jan, 4 Jan, 3 Jan), (4 Jan, 3 Jan, 2 Jan), (3 Jan, 2 Jan, 1 Jan)}. 3.1.3. Pattern recognition For a given set of time T00 j T00 T0, apply the wavelet theory to identify the desired sequences. If a predefined wave pattern is discovered, add T00 to P. Details are described below. The proposed algorithm PXtract is given in Fig. 3. The function genSet(wi ) is the subset generation process discussed J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 1199 Fig. 1. Samples of typical chart patterns [14]. earlier. At the end of the algorithm, all the time information of the identified wave pattern is stored in set P. Pattern matching can be carried out using simple multiresolution (MR) matching (or radial basis function neural network (RBFNN) matching. Details of the wavelet recognition and simple MR matching can be found in our previous work [15]. univariate function c, defined on R when subjected to fundamental operations of shifts and dyadic dilation, yielding an orthogonal basis of L2(R). The orthonormal basis of compactly supported wavelets of L2(R) is formed by the dilation and translation of a single function c (x). 4. Wavelet recognition and matching where j, k 2 Z. Vanishing moments means that the basis functions are chosen to be orthogonal to the low degree polynomials. It is said that a function w(x) has a vanishing kth moment at point t0 if the following equality holds with the integral converging absolutely: Z ðt t0 Þk ’ðtÞdt ¼ 0 Wavelet analysis is a relatively recent development of applied mathematics in 1980s. It has since been applied widely with encouraging results in signal processing, image processing and pattern recognition [16]). As the waves in stock charts are 1D patterns, no transformation from higher dimension to 1D is needed. In general, wavelet analysis involves the use of a Fig. 2. Time subset generation. c j;k ðxÞ ¼ 2i=2 cð2 j x kÞ Fig. 3. Algorithm PXtract. 1200 J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 The function c(x) has a companion, the scaling function f(x), and these functions satisfy the following relations: fðxÞ ¼ L1 pﬃﬃﬃX 2 hk fð2x kÞ k¼0 ’ðxÞ ¼ L1 pﬃﬃﬃX 2 gk fð2x kÞ ing to the wavelet orthonormal decomposition as shown in Eq. (1), Vj is first decomposed orthogonally into a high-frequency sub-space Vj+1 and Wj+1. The low-frequency sub-space Vj+1 is further decomposed into Vj+2 and Wj+2 and the processes can be continued. The above wavelet orthonormal decomposition can be represented by V j ¼ W jþ1 V jþ1 ¼ W jþ1 W jþ2 V jþ2 k¼0 where hk and gk are the low- and high-pass filter coefficients, respectively, L is related to the number of vanishing moments k and L is always even. For example, L = 2k in the Daubechies wavelets. gk ¼ ð1Þk hLk1 ; þ1 Z k ¼ 0; . . . ; L 1 ¼ W jþ1 W jþ2 W jþ3 V jþ3 ¼ . . . According to Tang et al. [16], projective operators Aj and Dj are defined as: A j : L2 ðRÞ V j projective operator from L2 ðRÞ to V j D j : L2 ðRÞ W j projective operator from L2 ðRÞ to W j Since f ðxÞ 2 V j L2 ðRÞ : X c j;k f j;k ðxÞ ¼ A jþ1 f ðxÞ þ D jþ1 f ðxÞ f ðxÞ ¼ A j f ðxÞ ¼ fðxÞdx ¼ 1 1 The filter coefficients are assumed to satisfy the orthogonality relations: X hn hnþ2 j ¼ dð jÞ X ¼ k 2 ZZ c jþ1;m f jþ1;m ðxÞ þ m 2 ZZ X d jþ1;m c jþ1;m ðxÞ m 2 ZZ Also, Tang et al. [16] has proved the following equations: n X c jþ1;m ¼ hn gnþ2 j ¼ 0 X hk c j;kþ2m (2) gk c j;kþ2m (3) n for all j, where d(0) = 1 and d(j) = 0 for j 6¼0. d jþ1;m ¼ X 4.1. Multi-resolution analysis Multi-resolution analysis (MRA) was formulated based on the study of orthonormal, compactly supported wavelet bases [17]. The wavelet basis induces a MRA on L2(R), the decomposition of the Hilbert space L2(R), into a chain of closed sub-space: V4 V3 V2 V1 V0 such that \ j 2 Z V j ¼ f0g and [ j 2 Z V j ¼ L2 ðRÞ f ðxÞ 2 V j , f ð2xÞ 2 V jþ1 f ðxÞ 2 V0 , f ðx kÞ 2 V0 9 c 2 V0 ; fcðx kÞgk 2 Z is an orthogonal basis of V0 In pattern recognition, an 1D pattern, f(x), can always be viewed as a signal of finite energy; such that, þ1 Z j f ðxÞj2 < þ 1 1 It is mathematically equivalent to f(x) 2 L2(R). It means that MRA can be applied to the function f(x) and can decompose it to L2(R) space. In MRA, closed sub-space Vj1 can be decomposed orthogonally as: V j ¼ V jþ1 W jþ1 (1) Vj contains the low-frequency signal component of Vj1 and Wj contains the high-frequency signal component of Vj1. Accord- According to the wavelet orthonormal decomposition as shown in Eq. (1), the original signal V0 can be decomposed orthogonally into a high-frequency sub-space W0 and a low-frequency sub-space V0 by using the wavelet transform Eqs. (2) and (3). In the chart pattern recognition process, V0 should be the original wave pattern, while V1 and W1 should be the wavelet-transformed sub-patterns. If we want to analyze the current data to determine whether it is a predefined chart pattern, a template of the chart pattern is needed. According to the noisy input data, direct comparing the data with the template will lead to an incorrect result. Therefore, wavelet decomposition should be applied to both the input data and the template. Example of matching the input data to a ‘‘head-and-shoulder, top’’ pattern is illustrated in Fig. 4. We can match sub-patterns using either a range of coarse-tofine scales, or by matching the input data with features in the pattern template. The matching process will only be terminated if the target is accepted or rejected. If the result is undetermined, it continues to at the next, finer scale. The coarse scale coefficients obtained from the low pass filter represent the global features of the signal. For a high-resolution scale, the intraclass variance will be larger than for a low resolution scale. A threshold scale should be defined to determine the acceptance level. For example, scale n is defined as the lowest resolution. The resolution threshold is t and t > n. At each resolution t, its root-means-square should be greater than another threshold J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 Fig. 4. Wavelet decomposition in both input data and chart pattern template. value l, which called the level threshold. It is difficult to derive optimal thresholds; therefore, we need to determine this through empirical testing. Fig. 5 illustrates the details of the process. 4.2. Radial basis function neural network (RBFNN) Neural networks are widely used to provide non-linear forecasts [18–20] and have been found to be good in pattern recognition and classification problems. Radial basis function neural network (RBFNN), its universal approximation capabilities have been proven by Park and Sandberg [21,22] to be suitable for solving our pattern/signal matching problem [23]. We have created different RBFNNs for recognizing different patterns at different resolution levels. The input of the network is the wavelet-transformed values in a particular resolution. As shown in Fig. 6, a typical network consists of three layers. The first layer is the input layer having two portions: (1) past 1201 network outputs that feedback to the network; (2) major corelative variables that are concerned with the prediction problem. Past network outputs enter into the network by means of time-delay unit as the first inputs. These outputs are also affected by a decay factor g ¼ aelk , where l is the decay constant, a is the normalization constant, and k is the forecast horizon. In general, the time series prediction of the proposed network is to predict the outcome of the sequence x1i+k at the time t + k that is based on the past observation sequence of size n, i.e. x1t, x1t1, x1t2, x1t3, . . ., x1tn+1 and on the major variables that influence the outcome of the time series at time t. The numbers of input nodes in the first and second portions are set to n and m, respectively. The number of hidden nodes is set to p. The predictive steps are set to k, so the number of output nodes is k. At time t, the input will be [x1t, x1t1, x1t2, x1t3, . . ., x1tn+1] and [x21, x22, . . ., x2m], respectively. The output is given by xt+k, denoted by pkt for simplicity, wijt denotes the connection weight between the ith node and the jth node at time t. To simplify the network, the choice of the centers of the Gaussian functions is determined by the K-means algorithm [24]. The variances of the Gaussians are chosen to be equal to the mean distance of every Gaussian center from its neighboring Gaussian centers. A constructive learning approach is used to select the number of hidden units in the RBFNN. The hidden nodes can be created one at a time. During the iteration we add one hidden node and check the new network for errors. This procedure is repeated until the error goal is met, or until the preset maximum number of hidden nodes is reached. Normally, the preset maximum number of hidden nodes should be less than the total number of input patterns. The existence of fewer hidden nodes shows that the network generalizes well though it may not be accurate enough. 5. Training set collections Stock chart pattern identification is highly subjective and humans are far better than machines at recognizing stock patterns, which are meaningful to investors. Moreover, Fig. 5. The multi-resolution matching. 1202 J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 Fig. 6. Schematic diagram of a typical RBFNN. extracting chart patterns in the stock time series data is a time consuming and expensive operation. We have examined five typical stocks for the period 1 January 1995 to 31 December 2001 (see Table 1). A summary of the total numbers of real training data for fourteen different chart patterns is shown in Table 2. The training set of the chart patterns is collected based on the judgment of a human critic following the rules suggested by Thomas [14] from the real and deformed data described in the following. The training set contains totally 308 records. A quarter of the training set is extracted as the validation set. We set the wavelet resolution equal to 8. We found that the signal/ pattern for the resolution 1–3, was too smooth and each pattern was similar to each others at those levels. The network was not able to recognize different patterns well. Therefore, only four RBFNNs were created for training different chart patterns at the resolution levels 4–7. The performance of the networks at different resolution levels and the classification results are shown in Section 6. In our training set, the initial quantity of data is insufficient for training the system well. If we tried to extract over 200 chart patterns in the time series data, it would be infeasible, time consuming and expensive. In order to expand the training set, we use a simple but powerful mechanism to generate more training data based on the real data. To generate more training samples, a radial deformation method is introduced. Here are the major steps of the radial deformation process: (a) P = {p1, p2, p3, . . ., pn} is a set of data points containing a chart pattern. (b) Randomly pick i points (i< = n) in set P for deformation. (c) Randomly generate a set of the radial deformation distance D = {d1, d2, . . ., di}. (d) For each point in P, a random step dr is taken in a random direction. The deformed pattern is constructed by joining consecutive points with straight lines. Details are depicted in Fig. 7. (e) Justify the deformed pattern using human critics. Psychophysical studies [25] tell us that humans are better than machines at recognizing objects, which are more Table 1 The five different stocks and their stock IDs Stock ID Stock name 00341 00293 00011 00005 00016 CAFÉ DE CORAL HOLDINGS Ltd. CATHAY PACIFIC AIRWAYS Ltd. HANG SENG BANK Ltd. HSBC HOLDINGS PLC. SUN HUNG KAI PROPERTIES Ltd. Fig. 7. Radial deformation. (a) An example of accepted deformed pattern. (b) An example of NOT accepted deformed pattern. J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 1203 Table 2 Total numbers of training patterns in fourteen typical chart patterns of five different stocks meaningful to humans. In assessing the generated training data, the whole training set (including real and generated data) is accepted and selected based on the opinion of the human critic. In the training set, 64 chart patterns have been extracted from five different stocks in Hong Kong stock market. By applying the radial deformation technique, the 64 real training patterns were extended to a total of 308 patterns. All of the patterns generated by radial deformation must be judged by humans to identify whether a human would accept the deformed pattern or find it meaningful. Fig. 8 illustrates examples of (a) an accepted and (b) a NOT accepted of deformed pattern. Fig. 9 shows the training set from both the real and deformed chart patterns. 6. Experimental results Two set of experiments have been conducted to evaluate the accuracy of the proposed system. The first set evaluates whether the algorithm PXtract is scaleable, and the second set evaluates the performance comparison between using simple multiresolution matching and RBFNN matching. Algorithm PXtract uses different time window sizes to locate any occurrence of a specific chart pattern. The major concern is the performance of the algorithm. To assess the relative performance of the algorithms and to investigate their scale-up properties, we performed experiments on an IBM PC workstation with 500 MHz CPU, 128 MB memory. To evaluate the performance of the algorithm using RBFNN Matching over Table 3 Optimal wavelet and thresholds setting found by empirical testing Wavelet family Resolution threshold Threshold value Accuracy (%) Total number of patterns discovered Daubechies (DB2) 4 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 0.3 0.2 0.15 0.1 6.2 7.1 14.2 43.1 7.1 9.4 17.4 53 8.9 13.5 19.9 56.9 10.5 14.5 18.5 48.3 8932 7419 3936 543 7734 6498 2096 420 7146 5942 1873 231 6023 5129 1543 194 5 6 7 Processing time (s) 312 931 3143 8328 1204 J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 Fig. 8. Accepted and NOT accepted deformed patterns by radial transformation. a large range of widow’s sizes, we used typical stock prices of SUN HUNG KAI and Co. Ltd. (0086) for the period from 2 January 1992 to 31 December 2001. As shown in Fig. 10, the algorithm scales linearly as the size of the time window increases. In the experiments on wavelet chart patterns recognition, different wavelet families were selected as the filter. The maximum resolution level was set to be 7. The highest resolution level 8 is taken as the raw input. The left hand side of Fig. 11 shows the price of the stock CATHAY PACIFIC (00293) for the period from 7 June 1999 to 22 July 1999. This period contains the ‘Double Tops’ pattern. For the identification of the chart patterns, two matching methods were studied — simple multi-resolution (MR) matching and RBFNN matching, respectively. For the simple MR matching, similarity between the input and the template is measured by mean absolute percentage error (MAPE). A low MAPE denotes that they are similar. The performance of simple MR matching was tested in experiments using different resolution threshold t and different level threshold l. Table 3 shows the most accurate combinations. We note that the accuracy using simple MR matching is not accurate J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 1205 Fig. 9. Training set from both the real and deformed chart patterns. Fig. 10. Execution time of algorithm PXtract using RBFNN matching under different time window sizes. with an average recognition rate of just 30%. Furthermore, the calculation of MAPE between the input data and the pattern templates creates a heavy workload. Although it is possible to reach a recognition rate of more than 50%, if we set a level threshold at a low value (about 0.1) and a highresolution threshold (above 6), the processing time is unacceptably long (about 3143 s). This illustrates that simple MR matching is not a good choice for use in the matching process. Table 4 illustrates the overall classification results. It shows that the classification rate is over 90% and the optimal recognition resolution level is 6. Four wavelet families were tested, and their performances were more or less the same except that the Haar wavelet was found to be not suitable for use. 1206 J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 Fig. 11. Algorithm PXtract using wavelet multi-resolutions analysis on the pattern ‘‘double tops’’ template. Having found the appropriate setting for the RBFNN, we applied it to extract all the chart patterns from 10 different stocks over the last 10 years. Table 5 shows the accuracy of the 14 different chart patterns. The RBFNN is on average 81% accurate. Multi-resolution RBFNN matching has a high accuracy in recognizing different chart patterns. However, the accuracy Table 4 RBFNNs: accuracy in different wavelet families and at different resolution levels Wavelet Families Resolution level Training set (%) Validation set (%) Haar DB1 4 5 6 7 66 75 81 87 64 72 78 74 Daubechies DB2 4 5 6 7 73 85 95 97 64 78 91 85 Coiflet C1 4 5 6 7 77 86 95 98 72 81 90 84 Symmlet S8 4 5 6 7 75 84 93 96 68 78 89 82 Table 5 Accuracy of identifying the fourteen different chart patterns using RBFNN extraction methods Chart pattern Accuracy (%) Broadening bottoms Broadening formations, right-angled and ascending Broadening formations, right-angled and descending Broadening tops Broadening wedges, ascending Bump-and-run reversal bottoms Bump-and-run reversal tops Cup with handle Double bottoms Double tops Head-and-shoulders, top Head-and-shoulders, bottoms Triangles, ascending Triangles, descending 73 84 81 79 86 83 82 63 92 89 86 87 73 76 of the recognition process is heavily dependent on the resolution level. Once the resolution level has been identified, based on empirical testing, the proposed method is highly accurate. 7. Conclusion and future works In this paper, we examined the sensitive factors associated with stock forecast and stressed the importance of chart pattern J.N.K. Liu, R.W.M. Kwong / Applied Soft Computing 7 (2007) 1197–1208 identification. We have demonstrated how to automate the process of chart pattern extraction and recognition, which has not been discussed in previous studies. The PXtract algorithm provides a dynamic means for extracting all the possible chart patterns underlying stock price charts. It is shown that PXtract consistently achieves high accuracy with a desirable result. Currently, we have analyzed only 14 of the representatives of chart patterns and templates from a total of 308 training samples. According to Thomas [14], there are totally 47 different chart patterns, which can be extracted from the time series data. In order to complete the system, the future direction of work will be to build templates for the remaining chart patterns. On the other hand, the identification and extraction of the chart patterns enable us to establish cases for interpretation and stock forecast. We regard these chart patterns as potentially suitable for case representation in a CBR system. It may be worthwhile revisiting the selection of indicators associated with the relevant chart patterns in order to form feature vector (e.g. time range, RSI, OBV, prices moving average, wave pattern). We might then compare these feature vectors, v1 ; v2 2 ½a; b, such that the similarity of v1 and v2 is computed by the following expression: simðv1 ; v2 Þ ¼ 1 jv1 v2 j ba for b 6¼ a For the attribute ‘‘class pattern’’ in the feature vector, the similarity measure of the attribute between the two cases can be measured by the following expression: 1 if v1 ¼ v2 simðv1 ; v2 Þ ¼ 0 otherwise The overall similarity between two cases c1 and c2 is measured by the weighted-sum metric shown below: P w simðv1i ; v2i Þ Pi simðc1 ; c2 Þ ¼ i¼1...n i¼1...n wi The system retrieves the updated stock data and converts them into case knowledge. It then studies the new current status of the cases and appends the new result set into the result database for users’ direct query. The system can be set to refer to three successive cases within a series of stock cases as one complete CASE for the purposes of prediction. Further exploration in this area is ongoing. 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