Bayesian Estimation and Model Selection for the Spatiotemporal Autoregressive Model with Autoregressive Conditional Heteroscedasticity Errors

The spatial and spatiotemporal autoregressive conditional heteroscedasticity(STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive(STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.

Multivariate Generalized Autoregressive Conditional Heteroscedastic Model

In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.

Time-varying confidence interval forecasting of travel time for urban arterials using ARIMA-GARCH model

To improve the forecasting reliability of travel time, the time-varying confidence interval of travel time on arterials is forecasted using an autoregressive integrated moving average and generalized autoregressive conditional heteroskedasticity （ARIMA-GARCH） model. In which, the ARIMA model is used as the mean equation of the GARCH model to model the travel time levels and the GARCH model is used to model the conditional variances of travel time. The proposed method is validated and evaluated using actual traffic flow data collected from the traffic monitoring system of Kunshan city. The evaluation results show that, compared with the conventional ARIMA model, the proposed model cannot significantly improve the forecasting performance of travel time levels but has advantage in travel time volatility forecasting. The proposed model can well capture the travel time heteroskedasticity and forecast the time-varying confidence intervals of travel time which can better reflect the volatility of observed travel times than the fixed confidence interval provided by the ARIMA model.

Temporal Dynamics in COVID-19 Transmission: Case of Some African Countries

Coronavirus disease 2019 (COVID-19) has become a global threat to public health and economy. The potential burden of this pandemic in developing world, particularly the African countries, is much concerning. With the aim of providing supporting evidence for decision making, this paper studies the dynamics of COVID-19 transmission through time in selected African countries. Time-dependent reproduction number (Rt) is one of the tools employed to quantify temporal dynamics of the disease. Pattern of the estimated reproduction numbers showed that transmissibility of the disease has been fluctuating through time in most of the countries included in this study. In few countries such as South Africa and Democratic Republic of Congo (DRC), these estimates dropped quickly and stayed stable, but greater than 1, for months. Regardless of their variability through time, the estimated reproduction numbers remain greater than or nearly equal to 1 in all countries. Another Statistical model used in this study, namely Autoregressive Conditional Poisson (ACP) model, showed that expected (mean) number of new cases is significantly dependent on short range change in new cases in all countries. In countries where there is no persistent trend in new cases, current mean number of new cases (on day t) depend on both previous observation and previous mean (day t - 1). In countries where there is continued trend in new cases, current mean is more affected by number of new cases on preceding day.

Is There an Impact of Stock Exchange Consolidation on Volatility of Market Returns？

The aim of the paper is to provide some evidences on relationships among the degree of financial integration, stock exchange markets, and volatility of national market returns. In this paper, the authors employ correlation and cluster analyses in order to investigate the impact of stock exchange consolidation on volatility of market returns, in terms of a financial integration between involved stock exchanges before and after the merger. By using the Generalized Autoregressive Conditional Heteroskedasticity （GARCH） （1.1） model, the authors test the change in volatilities of national stock exchange markets involved in the following stock exchange integration case studies： Euronext, Bolsasy Mercados Espanoles （BME）, and Swedish-Finnish financial services company （OMX）. These three case studies are considered as completed cases of market consolidation, where the data are available enough to conduct the current research. By using daily data of national returns of engaged European stock markets from 1995 to 2007, the paper investigates the influence of stock exchange consolidation on volatility of national stock market returns. The obtained results confirm the gradual decrease of volatility in each of the integrated stock markets. However, the level of decrease in terms of volatility depends on economic characteristics of each engaged market and its degree of integration with other financial services. The results of correlation and cluster analyses confirm that stock operators have created significantly non-official integration links through cross-memberships and cross-listings even before the consolidations. Thus, the mergers among stock exchanges can be considered as the rational consequences of the high internal co-movements between involved markets. Furthermore, stock exchange markets with strong non-official integration links show an immediate decrease of volatility after the merger, meanwhile for others, it takes several years before the volatility can decrease as markets should reach the full integration.

Investigating the Existence of Second Order Spatial Autocorrelation in Crash Frequency across Adjacent Freeway Segments

This study developed spatial Poisson model to incorporate spatial autocorrelation in crash frequency across contagious freeway segments. Spatial autocorrelation is the presence of spatial pattern in crash frequency over space due to geographic proximity. Usually crash caused congestion on a freeway segment propagates upstream and creates chance of occurring secondary crashes. This phenomenon makes the crash frequency on the contiguous freeway segments correlated. This correlation makes the distributional assumption of independence of crash frequency invalid. The existence of spatial autocorrelation is investigated by using Conditional autoregressive models (CAR models). The models are set up in a Bayesian modeling framework, to include terms which help to identify and quantify residual spatial autocorrelation for neighboring observation units. Models which recognize the presence of spatial dependence help to obtain unbiased estimates of parameters quantifying safety levels since the effects of spatial autocorrelation are accounted for in the modeling process. Based on CAR models, approximately 51% of crash frequencies across contiguous freeway segments are spatially auto-correlated. The incident rate ratios revealed that wider shoulder and weaving segments decreased crash frequency by factors of 0.84 and 0.75 respectively. The marginal impacts graphs showed that an increase in longitudinal space for segments with two lanes decreased crash frequency. However, an increase of facility width above three lanes results in more crashes, which indicates an increase in traffic flows and driving behavior leading to crashes. These results call an important step of analyzing contagious freeway segments simultaneously to account for the existence of spatial autocorrelation.

Currency Exposure in China under the New Exchange Rate Regime： National Level Evidence

The present paper studies China＇s national level currency exposure since 2005 when the country adopted a new exchange rate regime allowing the renminbi （RMB） to move towards greater flexibility. Using generalized autoregressive conditional heteroskedastic and constant conditional correlation-generalized autoregressive conditional heteroskedastic methods to estimate the augmented capital asset pricing models with orthogonalized stock returns, we find that China equity indexes are significantly exposed to exchange rate movements. In a static setting, there is strong sensitivity of stock returns to movements of China＇s trade- weighted exchange rate, and to the bilateral exchange rates except the RMB/dollar rate. However, in a dynamic framework, exposure to all the bilateral currency pairs under examination is significant. The results indicate that under the new exchange rate regime, China＇s gradualist approach to moving towards greater exchange rate flexibility has managed to keep exposure to a moderate level. However, we find evidence that in a dynamic setting, the exposure of the RMB to the dollar and other major currencies is significant. For China, the challenge of managing currency risk exposure is looming greater.

Bayesian functional enrichment analysis for the Reactome database

The first step in the analysis of high-throughput experiment results is often to identify genes orproteins with certain characteristics, such as genes being differentially expressed (DE). To gainmore insights into the underlying biology, functional enrichment analysis is then conductedto provide functional interpretation for the identified genes or proteins. The hypergeometricP value has been widely used to investigate whether genes from predefined functional terms,e.g., Reactome, are enriched in the DE genes. The hypergeometric P value has several limitations: (1) computed independently for each term, thus neglecting biological dependence;(2) subject to a size constraint that leads to the tendency of selecting less-specific terms. In this paper,a Bayesian approach is proposed to overcome these limitations by incorporating the interconnected dependence structure of biological functions in the Reactome database through a CARprior in a Bayesian hierarchical logistic model. The inference on functional enrichment is thenbased on posterior probabilities that are immune to the size constraint. This method can detectmoderate but consistent enrichment signals and identify sets of closely related and biologicallymeaningful functional terms rather than isolated terms. The performance of the Bayesian methodis demonstrated via a simulation study and a real data application.