On the cone eigenvalue complementarity problem for higher-order tensors

In this paper, we consider the tensor generalized eigenvalue complementarity problem (TGEiCP), which is an interesting generalization of matrix eigenvalue complementarity problem (EiCP). First, we given an affirmative result showing that TGEiCP is solvable and has at least one solution under some reasonable assumptions. Then, we introduce two optimization reformulations of TGEiCP, thereby beneficially establishing an upper bound of cone eigenvalues of tensors. Moreover, some new results concerning the bounds of number of eigenvalues of TGEiCP further enrich the theory of TGEiCP. Last but not least, an implementable projection algorithm for solving TGEiCP is also developed for the problem under consideration. As an illustration of our theoretical results, preliminary computational results are reported.Comment: 26 pages, 2 figures, 3 table

On non-stationary threshold autoregressive models

In this paper we study the limiting distributions of the least-squares estimators for the non-stationary first-order threshold autoregressive (TAR(1)) model. It is proved that the limiting behaviors of the TAR(1) process are very different from those of the classical unit root model and the explosive AR(1).Comment: Published in at http://dx.doi.org/10.3150/10-BEJ306 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Forex Trading Signal Extraction with Deep Learning Models

The rise of AI technology has popularized deep learning models for financial trading prediction, promising substantial profits with minimal risk. Institutions like Westpac, Commonwealth Bank of Australia, Macquarie Bank, and Bloomberg invest heavily in this transformative technology. Researchers have also explored AI's potential in the exchange rate market. This thesis focuses on developing advanced deep learning models for accurate forex market prediction and AI-powered trading strategies. Three deep learning models are introduced: an event-driven LSTM model, an Attention-based VGG16 model named MHATTN-VGG16, and a pre-trained model called TradingBERT. These models aim to enhance signal extraction and price forecasting in forex trading, offering valuable insights for decision-making. The first model, an LSTM, predicts retracement points crucial for identifying trend reversals. It outperforms baseline models like GRU and RNN, thanks to noise reduction in the training data. Experiments determine the optimal number of timesteps for trend identification, showing promise for building a robotic trading platform. The second model, MHATTN-VGG16, predicts maximum and minimum price movements in forex chart images. It combines VGG16 with multi-head attention and positional encoding to effectively classify financial chart images. The third model utilizes a pre-trained BERT architecture to transform trading price data into normalized embeddings, enabling meaningful signal extraction from financial data. This study pioneers the use of pre-trained models in financial trading and introduces a method for converting continuous price data into categorized elements, leveraging the success of BERT. This thesis contributes innovative approaches to deep learning in algorithmic trading, offering traders and investors precision and confidence in navigating financial markets