Dynamic Correlation between the Chinese and the US Financial Markets: From Global Financial Crisis to COVID-19 Pandemic

Stochastic differential equations and Copula theories are important topics that have many advantages for applications in almost every discipline. Many studies in forestry collect longitudinal, multi-dimensional, and discrete data for which the amount of measurement of individual variables does not match. For example, during sampling experiments, the diameters of all trees, the heights of approximately 10% of the trees, and the tree crown base height and crown width for a significantly smaller number of trees are measured. In this study, for estimating five-dimensional dependencies, we used a normal copula approach, where the dynamics of individual tree variables (diameter, potentially available area, height, crown base height, and crown width) are described by a stochastic differential equation with mixed-effect parameters. The approximate maximum likelihood method was used to obtain parameter estimates of the presented stochastic differential equations, and the normal copula dependence parameters were estimated using the pseudo-maximum likelihood method. This study introduced the normalized multi-dimensional interaction information index based on differential entropy to capture dependencies between state variables. Using conditional copula-type probability density functions, the exact form equations defining the links among the diameter, potentially available area, height, crown base height, and crown width were derived. All results were implemented in the symbolic algebra system MAPLE.

Section: Discussionmentioning

confidence: 99%

“…The normal copula function is defined using a multi-dimensional standard normal probability density function and a marginal probability density function to obtain the joint distribution. It can be used to model multi-dimensional joint distributions and is suitable for forest growth analysis studies [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

A Statistical Dependence Framework Based on a Multivariate Normal Copula Function and Stochastic Differential Equations for Multivariate Data in Forestry

Krikštolaitis

Mozgeris

Petrauskas

et al. 2023

“…We focus on the COVID-19 and Russia-Ukraine (RU) War periods. The sudden COVID-19 pandemic severely affected financial markets, causing significant disruptions (Choi [53], Szczygielski et al [54], Liu et al [55]). The RU War also led to increased market volatility, characterized supply chain disruptions and energy concerns (Umar et al [56], Lo et al [57], Alam et al [58]).…”

Section: Model Performance In Crisis Periodsmentioning

confidence: 99%

Forecasting the S&P 500 Index Using Mathematical-Based Sentiment Analysis and Deep Learning Models: A FinBERT Transformer Model and LSTM

Kim,

Choi

2023

Stock price prediction has been a subject of significant interest in the financial mathematics field. Recently, interest in natural language processing models has increased, and among them, transformer models, such as BERT and FinBERT, are attracting attention. This study uses a mathematical framework to investigate the effects of human sentiment on stock movements, especially in text data. In particular, FinBERT, a domain-specific language model based on BERT tailored for financial language, was employed for the sentiment analysis on the financial texts to extract sentiment information. In this study, we use “summary” text data extracted from The New York Times, representing concise summaries of news articles. Accordingly, we apply FinBERT to the summary text data to calculate sentiment scores. In addition, we employ the LSTM (Long short-term memory) methodology, one of the machine learning models, for stock price prediction using sentiment scores. Furthermore, the LSTM model was trained by stock price data and the estimated sentiment scores. We compared the predictive power of LSTM models with and without sentiment analysis based on error measures such as MSE, RMSE, and MAE. The empirical results demonstrated that including sentiment scores through the LSTM model led to improved prediction accuracy for all three measures. These findings indicate the significance of incorporating news sentiment into stock price predictions, shedding light on the potential impact of psychological factors on financial markets. By using the FinBERT transformer model, this study aimed to investigate the interplay between sentiment and stock price predictions, contributing to a deeper understanding of mathematical-based sentiment analysis in finance and its role in enhancing forecasting in financial mathematics. Furthermore, we show that using summary data instead of entire news articles is a useful strategy for mathematical-based sentiment analysis.

“…This paper aims to distinguish between long memory and regime switching based on the second moment of the financial return series (it is widely recognized that the definitions of long memory and regime switching may be referred to much broader non-linear concepts; as explained in the paper, we focus on fractional integration (long memory) and Markov switching-type non-linearity (regime switching) of financial data). Among the existing models of financial volatility, the GARCH family models [16] have enjoyed great popularity because of their ability to capture the properties of financial volatility, such as timevarying heteroskedasticity and volatility clustering [8,[17][18][19][20][21][22][23]. In particular, to incorporate long-memory persistence in the GARCH framework, the Fractionally Integrated GARCH (FIGARCH) model has been proposed [1].…”

Section: Introductionmentioning

confidence: 99%

Modeling Long Memory and Regime Switching with an MRS-FIEGARCH Model: A Simulation Study

Zhang

Shi

2023

Recent research suggests that long memory can be caused by regime switching and is easily confused with it. However, if the causes of confusion were properly controlled, they could be distinguished. Motivated by this idea, our study aims to distinguish between the long memory and regime switching of financial volatility. We firstly modeled the long memory and regime switching of volatility using the Fractionally Integrated Exponential GARCH (FIEGARCH) and Markov Regime-Switching EGARCH (MRS-EGARCH) frameworks, respectively, and performed a simulation study on their finite-sample properties when innovations followed a non-normal distribution. Subsequently, we demonstrated the confusion between the FIEGARCH and MRS-EGARCH processes using simulations. A recent study theoretically proved that the time-varying smoothing probability series can induce the presence of significant long memory in the regime-switching process. To control for its effect, the two-stage two-state FIEGARCH and MRS-FIEGARCH frameworks are proposed. The Monte Carlo studies showed that both frameworks can effectively distinguish between the pure FIEGARCH and pure MRS-EGARCH processes. When the MRS-FIEGARCH model was further employed to fit series generated with the MRS-FIEGARCH process, it outperformed the ordinary FIEGARCH model. Finally, an empirical study of NASDAQ index return was conducted to demonstrate that our MRS-FIEGARCH model can provide potentially more reliable long-memory estimates, identify the volatility states and outperform both the FIEGARCH and MRS-EGARCH models.