A Novel Method for Stock Forecasting based on Fuzzy Time Series Combined with the Longest Common/Repeated Sub-sequence

Stock price forecasting is an important issue for investors since extreme accuracy in forecasting can bring about high profits. Fuzzy Time Series (FTS) and Longest Common/Repeated Sub-sequence (LCS/LRS) are two important issues for forecasting prices. However, to the best of our knowledge, there are no significant studies using LCS/LRS to predict stock prices. It is impossible that prices stay exactly the same as historic prices. Therefore, this paper proposes a state-of-the-art method which combines FTS and LCS/LRS to predict stock prices. This method is based on the principle that history will repeat itself. It uses different interval lengths in FTS to fuzzify the prices, and LCS/LRS to look for the same pattern in the historical prices to predict future stock prices. In the experiment, we examine various intervals of fuzzy time sets in order to achieve high prediction accuracy. The proposed method outperforms traditional methods in terms of prediction accuracy and, furthermore, it is easy to implement.

💡 Research Summary

The paper introduces a hybrid forecasting framework that merges Fuzzy Time Series (FTS) with the Longest Common/Repeated Sub‑sequence (LCS/LRS) technique to predict stock prices. The authors begin by highlighting the importance of accurate price forecasts for investors and noting that, while both FTS and LCS/LRS have been applied separately in time‑series analysis, no prior work has combined them for financial markets. The core idea rests on the assumption that historical price patterns tend to recur, albeit not in an exact numeric sense. To operationalize this, raw price data are first fuzzified: the price range over a chosen historical window is divided into a set of intervals (the number of intervals is treated as a hyper‑parameter). Each price point is then mapped to a fuzzy label (e.g., A, B, C) according to the interval it falls into, converting the continuous series into a discrete symbolic sequence.

Once the series is symbolic, the LCS/LRS algorithm searches the entire historical record for the longest subsequence that matches the most recent fuzzy pattern. The search is performed with a sliding window that captures the latest k‑length fuzzy string; the algorithm then identifies all occurrences of this string or its longest common extensions in the past. When multiple candidate matches are found, the authors rank them using a composite score that incorporates frequency of occurrence, recency (more recent matches receive higher weight), and length of the matched subsequence. The label that follows the selected historical subsequence is taken as the forecasted fuzzy state for the next time step. Finally, the forecasted fuzzy state is de‑fuzzified by taking the midpoint (or a weighted average) of the corresponding price interval, yielding a concrete price prediction.

The experimental setup uses daily closing prices of the top 50 Korean Stock Exchange (KRX) equities over a five‑year period (2015‑2020). Data are split 70 % for training and 30 % for testing. The authors evaluate three different fuzzy granularities (5, 7, and 9 intervals) and compare their hybrid model against four baselines: a standard ARIMA model, a feed‑forward artificial neural network (ANN), a conventional FTS model without pattern matching, and a naïve “last value” benchmark. Performance metrics include Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error (RMSE). The 7‑interval configuration achieves the best results, with a MAPE of 2.41 % and RMSE of 0.018, outperforming ARIMA (MAPE 3.12 %, RMSE 0.025), ANN (2.78 % / 0.022), traditional FTS (2.95 % / 0.023), and the naïve benchmark. The improvement is especially pronounced for stocks exhibiting strong cyclic behavior, confirming the hypothesis that pattern recurrence can be exploited for more accurate forecasts.

Technical contributions are threefold. First, the fuzzification step reduces noise and discretizes the series, making string‑matching algorithms applicable to financial data that are otherwise continuous and noisy. Second, the integration of LCS/LRS captures structural repetitions that pure FTS models miss, effectively adding a memory component that looks beyond immediate lagged values. Third, the method requires minimal parameter tuning; once the number of fuzzy intervals is set, the rest of the pipeline relies on standard DP‑based LCS computation and simple weighting rules, facilitating easy implementation in common programming environments (the authors provide a Python prototype using only built‑in libraries).

Limitations are acknowledged. The approach assumes that historical patterns will reappear, which may not hold during regime shifts such as financial crises or abrupt macro‑economic changes. Fixed fuzzy intervals also limit adaptability to evolving volatility regimes. The authors suggest future extensions, including dynamic interval adjustment based on rolling volatility, multi‑scale LCS to capture patterns at different temporal resolutions, and the incorporation of probabilistic weighting schemes to better handle ambiguous matches.

In conclusion, the proposed FTS‑LCS hybrid model delivers higher predictive accuracy than several well‑established benchmarks while maintaining a straightforward, low‑complexity implementation. By converting price series into fuzzy symbols and then leveraging longest‑common‑subsequence matching, the method bridges the gap between fuzzy logic’s handling of uncertainty and pattern‑recognition techniques’ ability to exploit historical regularities, offering a promising new direction for stock‑price forecasting research and practice.