A hidden semi-Markov model for chart pattern matching in financial time series

Abstract

Many pattern matching approaches have been applied in financial time series to detect chart patterns and predict price trends. In this paper, we propose an extended hidden semi-Markov model for chart pattern matching (HSMM-CP). In our approach, a hidden semi-Markov model is trained and a Viterbi algorithm is used to detect chart patterns. The proposed approach not only simplifies the traditional way of training an HSMM, but also reduces potential biases in parameter initialisation. We compare the proposed model with current approaches on a set of templates selected from 53 chart patterns. Experiments on a synthetic dataset show that the proposed approach has the highest average accuracy and recall among other pattern matching approaches. Specifically, the HSMM-CP approach achieves highest accuracy for “Triangles, Ascending”, “Head-and-Shoulders Tops”, “Triple Tops” and “Cup with Handle” patterns. Moreover, experiments results show that the HSMM-CP performs significantly better than other approaches in distinguishing patterns with similar shapes such as “Head-and-Shoulders Tops” and “Triple Tops”. Experiments are also conducted on a real dataset comprising the historical prices of several stocks.

Appendices

Appendix A: How to set thresholds for the TB, ED and DTW approaches

Fig. 14

Similarity calculation results using the TB approach for the four datasets of varying sub-sequence length. The y-axis denotes the similarity, and the x-axis denotes the case identification. The red crosses are the similarities calculated for the 50 positive cases, and the green crosses are the similarities calculated for the 50 negative cases. The blue lines are the thresholds, which were found to be constant

Fig. 15

Similarity calculation results using the ED approach on the four datasets of varying sub-sequence length. The y-axis denotes the similarity, and the x-axis denotes the case identification. The red crosses are the similarities calculated for the 50 positive cases, and the green crosses are the similarities calculated for the 50 negative cases. The blue lines are the thresholds, which increased when the length of the sub-sequence increased

Fig. 16

Similarity calculation results using the DTW approach on the four datasets of varying sub-sequence length. The y-axis denotes the similarity, and the x-axis denotes the case identification. The red crosses are the similarities calculated for the 50 positive cases, and the green crosses are the similarities calculated for the 50 negative cases. The blue lines are the thresholds, which increased when the length of the sub-sequence increased

We use the H&S-T pattern as an example to illustrate how we set the thresholds in the experiment. We began by generating four datasets containing one hundred time series (the top fifty were H&S-T positive time series and the bottom fifty were randomly generated negative time series) with different lengths of 19, 43, 85 and 127. We used the TB, ED and DTW approaches, respectively, to calculate the similarities between each time series in the four datasets. The top 50 were positive cases, and the distances had to be smaller than those in the bottom 50. As shown in Fig. 14a–d, the TB approach had a fixed threshold as the length of the time series increased. The threshold of the H&S-T pattern for TB $\theta =0.1$. As shown in Fig. 15a–d, the threshold of the ED approach increased with the length of the time series. As shown in Fig 16a–d, the threshold of the DTW approach increased with the length of the time series. We modelled the threshold of the ED and DTW approach by a linear function of length. In Fig. 15a–d, the thresholds for the ED approach are 20, 40, 85 and 143 for lengths of 19, 43, 85 and 127, respectively. We regressed the threshold as a linear function of length, where the slope $\alpha =1.1417$ and the intercept $\beta =-6.2079$. For the DTW approach, in Fig 16a–d, the thresholds 6, 10, 22 and 34 and correspond to lengths of 19, 43, 85 and 127. In the regression linear function of length, the slope $\gamma =0.2649$ and the intercept $\varepsilon =-0.1457$.

Appendix B: Experimental settings for a synthetic dataset

The experiment settings are shown in Table 16

Table 16 In the experiment conducted to distinguish H&S and Trip-T, the setting was (Distinguish, 100, 115, 7, 0.1 1.1417, -6.2079, 0.2649, -0.1457). Distinguish was a dataset containing 50 H&S-T and 50 Trip-T time series. As we designed the H&S-T patterns as positive cases, the threshold settings for the TB, ED and DTW approaches matched those in the H&S-T pattern recognition experiment