Using a Graph-based Method for Detecting the Optimal Turning Points of Financial Time Series

Abstract

Objective: One of the concerns of financial market investors is adopting a profitable trading strategy, which is based on profitable turning points (TPs). To achieve this target, it is necessary to predict TPs. The first step for predicting TPs is to detect TPs from the history of the corresponding time series. The profitability of the predicted TPs depends on the profitability of the detected TPs. Hence, the academic literature has always tried to enhance the performance of TPs detection methods or improve the profitability of the detected TPs. Yet, to the best of our knowledge, none of the existing methods can detect the most profitable and optimal TPs. The current paper aims to fill this research gap. Methods: Our proposed method seeks the optimal TPs from the history of time series, by implementing the detection problem in the context of the graph and solving it by searching the longest path. Results: The proposed graph-based TPs detection method, in contrast to the existing detection methods, is able to detect the optimal TPs from the history of the corresponding financial time series. The optimality of this method is based on its graph-based specific structure. In this method, the only potentially valuable trading points (breakpoints, i.e., BPs) are considered as the corresponding graph's vertices and connections between the entire pair of BPs form the corresponding graph's edge set. Considering the vertex and edge set, the proposed graph-based TPs detection method optimizes the detection process, by finding the longest path existing in the corresponding graph and extracting the vertices existing in the longest path (as the optimal TPs). It is worth noticing that due to the structure of the corresponding graph, the longest path is equal to the most profitable set of BPs and the most profitable trading strategy available in the history of time series. Hence, the vertices existing in the longest path are the most profitable and the optimal TPs. Conclusion: To evaluate the performance of the proposed graph-based TPs detection method, it was applied to real-world data set, and thereafter its detection results were benchmarked against other detection models. Constraints considered for modeling the proposed graph-based TPs detection method were applied to the comparative detection models, as well. These constraints included the possibility of short-selling the financial asset, the impossibility of detecting consecutive buying or selling TPs, and considering no time value for the investment money. Results from applying the proposed method to NASDAQ and New York Stock Exchange indicated the efficiency of the proposed method in the problem of detecting the optimal TPs. Besides, comparison results revealed the superiority of the proposed graph-based TPs detection method, in comparison with other detection models available in the existing literature.

Keywords

• financial time series
• graph
• optimal
• trading strategy
• turning points (tps) detection