This study aims to address the challenges of financial price prediction in high-frequency trading (HFT) by introducing a novel continual learning framework based on factor predictors via graph neural networks. The model integrates multi-factor pricing theory with real-time market dynamics, effectively bypassing the limitations of conventional time series forecasting methods, which often lack financial theory guidance and ignore market correlations. We propose three heterogeneous tasks, including price gap regression, changepoint detection, and price moving average regression to trace the short-, intermediate-, and long-term trend factors present in the data. We also account for the cross-sectional correlations inherent in the financial market, where prices of different assets show strong dynamic correlations. To accurately capture these dynamic relationships, we resort to spatio-temporal graph neural network (STGNN) to enhance the predictive power of the model. Our model allows a continual learning strategy to simultaneously consider these tasks (factors). To tackle the catastrophic forgetting in continual learning while considering the heterogeneity of tasks, we propose to calculate parameter importance with mutual information between original observations and the extracted features. Empirical studies on the Chinese futures data and U.S. equity data demonstrate the superior performance of the proposed model compared to other state-of-the-art approaches.

It is challenging to predict futures prices with traditional econometric models as it necessitates a comprehensive consideration of both historical observations and correlations among various futures. Spatial-temporal graph neural networks (STGNNs) offer a promising approach for modeling such complex spatio-temporal data. Nevertheless, the direct application of STGNNs to high-frequency futures data remains a challenge, as traders must account for both short- and long-term characteristics when making decisions. To capture these distinct timeframes, we leverage additional label information by devising four heterogeneous tasks: price regression, price gap regression, price moving average regression, and change-point detection. To make full use of these labels, we train the model in a continual manner. Traditional continual GNNs define the gradient of losses as parameter importance to overcome the catastrophic forgetting (CF) issue, while this is unsuitable for our heterogeneous tasks with losses in distinct spaces. Therefore, we propose to calculate the parameter importance with mutual information between the original observations and the extracted features. The empirical results based on 49 varieties of commodity futures demonstrate that our model achieves superior performance compared to the leading approaches, highlighting the effectiveness of our approach in modeling the intricate dynamics of the futures market.

In this paper, two different n -order topological circuit networks are connected by diodes to establish a unified network model, which is a previously unexplored problem. The network model includes not only five resistive elements but also diode devices, so the network contains many different network types. This problem can be solved through three main steps: First, the network is simplified into two different equivalent circuit models. Second, the nonlinear difference equation model is established by applying Kirchhoff’s law. Finally, the two equations with similar structures are processed uniformly, and the general solutions of the nonlinear difference equations are obtained by using the transformation technique. As an example, several interesting specific results are deduced. Our study on the network model has significant value, as it can be applied to relevant interdisciplinary research.

Considerable progress has been made recently in the development of techniques to determine exactly two-point resistances in networks of various topologies. In particular, a general resistance formula of a non-regular m × n resistor network with an arbitrary boundary is determined by the recursion-transform (RT) method. However, research on the complex impedance network is more difficult than that on the resistor network, and it is a problem worthy of study since the equivalent impedance has many different properties from equivalent resistance. In this study, the equivalent impedance of a non-regular m × n RLC network with an arbitrary boundary is studied based on the resistance formula, and the oscillation characteristics and resonance properties of the equivalent impedance are discovered. In the RLC network, it is found that our formula leads to the occurrence of resonances at the boundary condition holding a series of specific values with an external alternating current source. This curious result suggests the possibility of practical applications of our formula to resonant circuits.

We investigate a multifunctional n -step honeycomb network which has not been studied before. By adjusting the circuit parameters, such a network can be transformed into several different networks with a variety of functions, such as a regular ladder network and a triangular network. We derive two new formulae for equivalent resistance in the resistor network and equivalent impedance in the LC network, which are in the fractional-order domain. First, we simplify the complex network into a simple equivalent model. Second, using Kirchhoff’s laws, we establish a fractional difference equation. Third, we construct an equivalent transformation method to obtain a general solution for the nonlinear differential equation. In practical applications, several interesting special results are obtained. In particular, an n -step impedance LC network is discussed and many new characteristics of complex impedance have been found.