Temporal Correlation

Deformation of semi-circle law for the correlated time series and Phase transition ArXiv ID: 2508.07192 “View on arXiv” Authors: Masato Hisakado, Takuya Kaneko Abstract We study the eigenvalue of the Wigner random matrix, which is created from a time series with temporal correlation. We observe the deformation of the semi-circle law which is similar to the eigenvalue distribution of the Wigner-Lèvy matrix. The distribution has a longer tail and a higher peak than the semi-circle law. In the absence of correlation, the eigenvalue distribution of the Wigner random matrix is known as the semi-circle law in the large $N$ limit. When there is a temporal correlation, the eigenvalue distribution converges to the deformed semi-circle law which has a longer tail and a higher peak than the semi-circle law. When we created the Wigner matrix using financial time series, we test the normal i.i.d. using the Wigner matrix. We observe the difference from the semi-circle law for FX time series. The difference from the semi-circle law is explained by the temporal correlation. Here, we discuss the moments of distribution and convergence to the deformed semi-circle law with a temporal correlation. We discuss the phase transition and compare to the Marchenko-Pastur distribution(MPD) case. ...

TCGPN: Temporal-Correlation Graph Pre-trained Network for Stock Forecasting ArXiv ID: 2407.18519 “View on arXiv” Authors: Unknown Abstract Recently, the incorporation of both temporal features and the correlation across time series has become an effective approach in time series prediction. Spatio-Temporal Graph Neural Networks (STGNNs) demonstrate good performance on many Temporal-correlation Forecasting Problem. However, when applied to tasks lacking periodicity, such as stock data prediction, the effectiveness and robustness of STGNNs are found to be unsatisfactory. And STGNNs are limited by memory savings so that cannot handle problems with a large number of nodes. In this paper, we propose a novel approach called the Temporal-Correlation Graph Pre-trained Network (TCGPN) to address these limitations. TCGPN utilize Temporal-correlation fusion encoder to get a mixed representation and pre-training method with carefully designed temporal and correlation pre-training tasks. Entire structure is independent of the number and order of nodes, so better results can be obtained through various data enhancements. And memory consumption during training can be significantly reduced through multiple sampling. Experiments are conducted on real stock market data sets CSI300 and CSI500 that exhibit minimal periodicity. We fine-tune a simple MLP in downstream tasks and achieve state-of-the-art results, validating the capability to capture more robust temporal correlation patterns. ...

Deformation of Marchenko-Pastur distribution for the correlated time series ArXiv ID: 2305.12632 “View on arXiv” Authors: Unknown Abstract We study the eigenvalue of the Wishart matrix, which is created from a time series with temporal correlation. When there is no correlation, the eigenvalue distribution of the Wishart matrix is known as the Marchenko-Pastur distribution (MPD) in the double scaling limit. When there is temporal correlation, the eigenvalue distribution converges to the deformed MPD which has a longer tail and higher peak than the MPD. Here we discuss the moments of distribution and convergence to the deformed MPD for the Gaussian process with a temporal correlation. We show that the second moment increases as the temporal correlation increases. When the temporal correlation is the power decay, we observe a phenomenon such as a phase transition. When $γ>1/2$ which is the power index of the temporal correlation, the second moment of the distribution is finite and the largest eigenvalue is finite. On the other hand, when $γ\leq 1/2$, the second moment is infinite and the largest eigenvalue is infinite. Using finite scaling analysis, we estimate the critical exponent of the phase transition. ...