Modeling opening price spread of Shanghai Composite Index based on ARIMA-GRU/LSTM hybrid model.

In the dynamic landscape of financial markets, accurate forecasting of stock indices remains a pivotal yet challenging task, essential for investors and policymakers alike. This study is motivated by the need to enhance the precision of predicting the Shanghai Composite Index's opening price spread, a critical measure reflecting market volatility and investor sentiment. Traditional time series models like ARIMA have shown limitations in capturing the complex, nonlinear patterns inherent in stock price movements, prompting the exploration of advanced methodologies. The aim of this research is to bridge the gap in forecasting accuracy by developing a hybrid model that integrates the strengths of ARIMA with deep learning techniques, specifically Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) networks. This novel approach leverages the ARIMA model's proficiency in linear trend analysis and the deep learning models' capability in modeling nonlinear dependencies, aiming to provide a comprehensive tool for market prediction. Utilizing a comprehensive dataset covering the period from December 20, 1990, to June 2, 2023, the study develops and assesses the efficacy of ARIMA, LSTM, GRU, ARIMA-LSTM, and ARIMA-GRU models in forecasting the Shanghai Composite Index's opening price spread. The evaluation of these models is based on key statistical metrics, including Mean Squared Error (MSE) and Mean Absolute Error (MAE), to gauge their predictive accuracy. The findings indicate that the hybrid models, ARIMA-LSTM and ARIMA-GRU, perform better in forecasting the opening price spread of the Shanghai Composite Index than their standalone counterparts. This outcome suggests that combining traditional statistical methods with advanced deep learning algorithms can enhance stock market prediction. The research contributes to the field by providing evidence of the potential benefits of integrating different modeling approaches for financial forecasting, offering insights that could inform investment strategies and financial decision-making.

Socio-economic and demographic impacts on the full awareness of the methods for controlling/preventing the spread of COVID-19 among social media users in some African countries at the onset of the pandemic.

OBJECTIVE: In Africa, most countries continue to battle COVID-19 with cases of newly infected still being recorded. In this note, we investigate how socioeconomic and demographic factors affected individuals awareness on the methods for controlling/preventing the spread of COVID-19 in some parts of Africa at the onset of the pandemic. RESULTS: Based on regression modelling, we find that having full awareness does not depend on religious affiliation. Men, urban dwelling, holding bachelors or higher degrees, operating multiple social media accounts or being employed are associated with having full awareness of the recommended practices for the prevention and control of COVID-19 at the early stage of the pandemic. No occupation, business or older people are associated with not having full awareness.

The impact of socio-demographic factors on the survival of cancer patients in Zimbabwe.

We provide a survival analysis of cancer patients in Zimbabwe. Our results show that young cancer patients have lower but not significant hazard rate compared to old cancer patients. Male cancer patients have lower but not significant hazard rate compared to female cancer patients. Race and marital status are significant risk factors for cancer patients in Zimbabwe.

Compound distributions for financial returns.

In this paper, we propose six Student's t based compound distributions where the scale parameter is randomized using functional forms of the half normal, Fréchet, Lomax, Burr III, inverse gamma and generalized gamma distributions. For each of the proposed distribution, we give expressions for the probability density function, cumulative distribution function, moments and characteristic function. GARCH models with innovations taken to follow the compound distributions are fitted to the data using the method of maximum likelihood. For the sample data considered, we see that all but two of the proposed distributions perform better than two popular distributions. Finally, we perform a simulation study to examine the accuracy of the best performing model.

AdequacyModel: An R package for probability distributions and general purpose optimization.

Several lifetime distributions have played an important role to fit survival data. However, for some of these models, the computation of maximum likelihood estimators is quite difficult due to presence of flat regions in the search space, among other factors. Several well-known derivative-based optimization tools are unsuitable for obtaining such estimates. To circumvent this problem, we introduce the AdequacyModel computational library version 2.0.0 for the R statistical environment with two major contributions: a general optimization technique based on the Particle Swarm Optimization (PSO) method (with a minor modification of the original algorithm) and a set of statistical measures for assessment of the adequacy of the fitted model. This library is very useful for researchers in probability and statistics and has been cited in various papers in these areas. It serves as the basis for the Newdistns library (version 2.1) published in an impact journal in the area of computational statistics, see https://CRAN.R-project.org/package=Newdistns. It is also the basis of the Wrapped library (version 2.0), see https://CRAN.R-project.org/package=Wrapped. A third package making use of the AdequacyModel library can be found in https://CRAN.R-project.org/package=sglg. In addition, the proposed library has proved to be very useful for maximizing log-likelihood functions with complex search regions. The library provides a greater control of the optimization process by introducing a stop criterion based on a minimum number of iterations and the variance of a given proportion of optimal values. We emphasize that the new library can be used not only in statistics but in physics and mathematics as proved in several examples throughout the paper.

Statistical distribution of the measure of coherence.

The recent papers by Miranda de Sa et al. (2001) and Miranda de Sa (2004) proposed a new measure of coherence between two signals. In this paper, we derive the exact probability density function and moments of the measure. We also provide simple programs for computing the associated cumulative distribution function and percentile points as well as for generating random samples of the measure.

Stochastic inequality probabilities for adaptively randomized clinical trials.

We examine stochastic inequality probabilities of the form P (X > Y) and P (X > max (Y, Z)) where X, Y, and Z are random variables with beta, gamma, or inverse gamma distributions. We discuss the applications of such inequality probabilities to adaptively randomized clinical trials as well as methods for calculating their values.