Abstract
In this study, a new idea is proposed to analyze the financial market and detect price fluctuations, by integrating the technology of PSR (phase space reconstruction) and SOM (self organizing maps) neural network algorithms. The prediction of price and index in the financial market has always been a challenging and significant subject in time-series studies, and the prediction accuracy or the sensitivity of timely warning price fluctuations plays an important role in improving returns and avoiding risks for investors. However, it is the high volatility and chaotic dynamics of financial time series that constitute the most significantly influential factors affecting the prediction effect. As a solution, the time series is first projected into a phase space by PSR, and the phase tracks are then sliced into several parts. SOM neural network is used to cluster the phase track parts and extract the linear components in each embedded dimension. After that, LSTM (long short-term memory) is used to test the results of clustering. When there are multiple linear components in the m-dimension phase point, the superposition of these linear components still remains the linear property, and they exhibit order and periodicity in phase space, thereby providing a possibility for time series prediction. In this study, the Dow Jones index, Nikkei index, China growth enterprise market index and Chinese gold price are tested to determine the validity of the model. To summarize, the model has proven itself able to mark the unpredictable time series area and evaluate the unpredictable risk by using 1-dimension time series data.
Highlights
Nonlinear models, such as LSTM and deep learning algorithms, have been widely used and proven effective to train and predict time series [1,2,3]
By calculating the Hurst index with MF-DFA [5], or using PSR technology to restore the dynamic system of time series, and calculate the Lyapunov index and K entropy, the complexity of time series and the size of predictable range of time series needs to be acquired [6]
The other is to predict the predictable part of clustering results by a supervised learning neural network, and a flow chart is given as Figure 1
Summary
Nonlinear models, such as LSTM and deep learning algorithms, have been widely used and proven effective to train and predict time series [1,2,3]. It is the outstanding prediction results which are contrary to the initial sensitivity law of chaotic system and the principle of long-term immeasurability [4]. The fact is, the dynamic properties of a chaotic financial time series should be restored first before it is analyzed. The predictable range of a time series is reflected by the reciprocal of the Lyapunov index The chaos degree of a time series system can be described with Lyapunov index, which means that the more chaotic the system is, the more difficult it is to predict the time series.
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