Volatility forecasting using stochastic conditional range model with leverage effect

Stock market indices often serve as indicators of a country's economic conditions. Therefore, analysing the trends of stock market indices can assist individuals, institutions, and even governments in comprehending the state of the economy and developing suitable investment strategies or economic policies. However, accurately predicting these indices poses a significant challenge. In recent years, machine learning has displayed remarkable learning capabilities in various industries, making it an intriguing and viable avenue for trend prediction. In this article, we have selected two closely linked data sources, namely monetary supply and consumer price index, which are highly correlated with economic operations. By combining these data with regression models, we have developed an algorithm for predicting China's Shanghai Stock Exchange Composite Index (SSECI). Experimental results illustrate a strong correlation between the collected data and the index, highlighting their value in indicating economic conditions.

Binomial Markov-Switching Multifractal model with Skewed t innovations and applications to Chinese SSEC Index

We provide new empirical evidence on volatility forecasting in relation to asymmetries present in the dynamics of both return and volatility processes. Leverage and volatility feedback effects of the S&P 500 price and volatility dynamics are examined using recently developed methodologies to detect jumps and to disentangle their size from continuous return and continuous volatility. Granted that jumps in both return and volatility are important components for generating the two effects, we find jumps in return can improve forecasts of volatility, while jumps in volatility improve volatility forecasts to a lesser extent. Moreover, disentangling jump and continuous variations into signed semivariances further improve the out-of-sample performance of volatility forecasting models, with negative jump semivariance being highly more informative then positive jump semivariance. The model proposed is able to capture many empirical stylized facts while still remaining parsimonious in terms of number of parameters to be estimated.

Conditional Autoregressive (CAR) models have been widely used in various disciplines, including epidemiological studies. The application of the CAR model in epidemiological studies is often associated with the relative risk of an infectious disease. This relative risk value can be estimated using the CAR models. Here, we evaluate four commonly used CAR models: the Intrinsic CAR, the Besag-York-Mollié CAR (BYM CAR), the BYM-modified CAR (BYM2 CAR), and the Leroux CAR (LCAR). To estimate CAR model parameters, Bayesian inference and the Integrated Nested Laplace Approximation (INLA) concept are used. The selected model was then used to model the number of dengue hemorrhagic fever (DHF) cases in Central Java Province in 2024. To support this analysis, we used 50 datasets simulated for each sample size (n), ranging from 10 to 100. The results of the study showed that of the four models compared, the best model was BYM2. This model was then used to model DHF cases in 2024 in Central Java Province. The research findings indicate the necessity of controlling population density, optimizing the role of medical personnel, and preparing for increased rainfall to curb the spread of dengue fever. Comprehensive detection and control measures through medical facilities are also required. Meanwhile, based on the coefficient of the altitude variable in the model, altitude has a positive influence on the number of dengue fever cases. Therefore, the conflicting conclusions between the model results and the medical perspective require data verification and further study of this variable.

A Bayesian conditional autoregressive geometric process model for range data

China’s Hang Seng Index (HSI) represents the mature market, and its Shanghai Stock Exchange Composite Index (SSE), the emerging market. I utilize six market timing (MT) methods and one dollar cost average (DCA) method to invest in the two stock indexes respectively. It is assumed that investors make a series of monthly cash contributions to an equity index in the long term. They do not possess lump-sum cash and cannot borrow cash. They buy and hold equity till the end of an investment period. The DCA method is simple, and it is to invest every monthly cash contribution immediately in an equity index. The six MT methods are complicated, and they are to invest more (less) than the monthly cash contribution, under the cash constraint, if the equity price has declined (risen). Empirical tests have been conducted for the 5-year, 10-year, and 20-year rolling investments during 1991-2022. My findings show that for both the HSI and SSE, the net returns generated by the six MTs are similar to those created by the DCA. In addition, the differences (MT-DCA) in the average monthly returns and modified Sharpe ratios are either statistically insignificant or negative and significant. Therefore, regardless the differences between the Hong Kong and mainland China markets, the complicated MTs do not outperform the simple CA in China’s mature and emerging stock indexes.

This paper discusses a variety of conditional autoregressive (CAR) models for mapping disease rates, beyond the usual first-order intrinsic CAR model. We illustrate the utility and scope of such models for handling different types of data structures. To encourage their routine use for map production at statistical and health agencies, a simple algorithm for fitting such models is presented. This is derived from penalized quasi-likelihood (PQL) inference which uses an analogue of best-linear unbiased estimation for the regional risk ratios and restricted maximum likelihood for the variance components. We offer the practitioner here the use of the parametric bootstrap for inference. It is more reliable than standard maximum likelihood asymptotics for inference purposes since relevant hypotheses for the mapping of rates lie on the boundary of the parameter space. We illustrate the parametric bootstrap test of the practically relevant and important simplifying hypothesis that there is no spatial autocorrelation. Although the parametric bootstrap requires computational effort, it is straightforward to implement and offers a wealth of information relating to the estimators and their properties. The proposed methodology is illustrated by analysing infant mortality in the province of British Columbia in Canada.

In the paper, we reviewed hierarchical statistical modeling about conditional autoregressive models method for spatial data located in Yellow River Delta. Moreover, we also proposed a new method about the evaluation and prediction of per capita grain possession on county-level in the high-efficiency ecological zone. With the support of MCMC approaches and conditional auto-regressive (CAR) Model, we estimated the posterior distribution through iterative sampling among per capita grain possession and the correlated factors. As a useful tool, the spatial bayesian model appeared to gain insights into per capita grain possession on spatio-temporal variability related to the grain sowing area, efficient irrigation area, agriculture machinery conditions. The study results showed that auto correlation characteristics and the posterior density distribution were described by the quantity method with CAR model, correspondingly the posterior mean of observed value and the posterior mean of predicted value of per capita grain possession were developed in Yellow River Delta. The posterior probability was more evident statistical significance on basis of prior information and sample characteristics in credible interval. Apparently, three factors of the grain sowing area, efficient irrigation area and agriculture machinery resulted in complex random effects on per capita grain possession. The results also indicated that bayesian method was not only the more quantitative evaluation, but also the more estimated accuracy for the per capita grain possession on country level in Yellow River Delta.KeywordsYellow River DeltaPer capita grain possessionCAR modelBayesian

Most spatial models include a spatial weights matrix (W) derived from the first law of geography to adjust the spatial dependence to fulfill the independence assumption. In various fields such as epidemiological and environmental studies, the spatial dependence often shows clustering (or geographic discontinuity) due to natural or social factors. In such cases, adjustment using the first‐law‐of‐geography‐based W might be inappropriate and leads to inaccuracy estimations and loss of statistical power. In this work, we propose a series of data‐driven Ws (DDWs) built following the spatial pattern identified by the scan statistic, which can be easily carried out using existing tools such as SaTScan software. The DDWs take both the clustering (or discontinuous) and the intuitive first‐law‐of‐geographic‐based spatial dependence into consideration. Aiming at two common purposes in epidemiology studies (ie, estimating the effect value of explanatory variable X and estimating the risk of each spatial unit in disease mapping), the common spatial autoregressive models and the Leroux‐prior‐based conditional autoregressive (CAR) models were selected to evaluate performance of DDWs, respectively. Both simulation and case studies show that our DDWs achieve considerably better performance than the classic W in datasets with clustering (or discontinuous) spatial dependence. Furthermore, the latest published density‐based spatial clustering models, aiming at dealing with such clustering (or discontinuity) spatial dependence in disease mapping, were also compared as references. The DDWs, incorporated into the CAR models, still show considerable advantage, especially in the datasets for common diseases.

This study describes the spatio-temporal dynamics of new visceral leishmaniasis (VL) cases notified in Brazil between 2001 and 2020. Data on the occurrence of the disease were obtained by means of the Notifiable Diseases Information System of the Brazilian Ministry of Health. Joinpoint, temporal generalized additive models and conditional autoregressive (CAR) models were used to analyse the temporal evolution of the rates in Brazil, states and regions. Spatio-temporal generalized additive and CAR models were used to identify the distribution of annual risks of VL occurrence in the Brazilian territory in relation to variation in the spatial average. There were 63,966 VL cases in the target period (3.198 cases/year), corresponding to a mean incidence rate of 1.68 cases/100,000 inhabitants. Of these, 4451 resulted in deaths, which gives a mean mortality rate of 0.12 deaths/100,000 inhabitants and a case fatality of 6.96%. The highest incidence rate was found in the North region, followed closely by the Northeast region, which presented the second and first highest mortality rates, respectively. For all of Brazil, and in the Northeast region, there were stability in the incidence rates, while the other regions showed an increasing trend in different time segments in the period: Central-West up to 2011, North up to 2008, Southeast up to 2004, and South up to 2010. On the other hand, all regions experienced a reduction in incidence rate during the last years of the series. The Northeast region had the highest number of municipalities with statistically significant elevated relative risks. The spatio-temporal analysis showed the highest risk area predominantly in the Northeast region in the beginning of the time series. From 2002 to 2018, this area expanded to the interior of the country. The present study has shown that VL has expanded in Brazil. However, the North and Northeast regions continue to have the highest incidence, and the risk of infection has decreased in recent years.

A number of previous studies on Covid-19 have used Bayesian spatial Conditional Autoregressive (CAR) models. However, basic CAR models are at risk of over-smoothing if adjacent areas genuinely differ in risk. More complex forms, such as localised CAR models, allow for sudden disparities, but have rarely been applied to modelling Covid-19, and never with covariates. This study aims to evaluate the most suitable Bayesian spatial CAR localised models in modelling the number of Covid-19 cases with and without covariates, examine the impact of covariates and spatial priors on the identified clusters and which factors affect the Covid-19 risk in South Sulawesi Province. Data on the number of confirmed cases of Covid-19 (19 March 2020 -25 February 2022) were analyzed using the Bayesian spatial CAR localised model with a different number of clusters and priors. The results show that the Bayesian spatial CAR localised model with population density included fits the data better than a corresponding model without covariates. There was a positive correlation between the Covid-19 risk and population density. The interplay between covariates, spatial priors, and clustering structure influenced the performance of models. Makassar city and Bone have the highest and the lowest relative risk (RR) of Covid-19 respectively.

This paper investigates the return, volatility, and trading on the Shanghai Stock Exchange with high-frequency intraday five-minute Shanghai Stock Exchange Composite Index (SHCI) data. The random walk hypothesis is rejected, indicating there are predictable components in the index. We adopt a time-inhomogeneous diffusion model using log penalized splines (log P-splines) to estimate the volatility. A GARCH volatility model is also fitted for comparison. A de-volatilized series are obtained by using the de-volatilization technique of Zhou (1991) that resample the data into different de-volatilized series with more desired properties for trading. A trading program based on local trends extracted with a State Space model is then implemented on the de-volatilized five-minute SHCI return series for profit. Volatility estimates from both models are found to be competitive for the purpose of trading.

Increasing attention has been focused on the analysis of the realized volatility, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data (from 1-min to 60- min) based on the trust region method. Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency and the volatility persistence becomes weaker at the lower sampling frequency.

This study evaluates the performance of four models for predicting daily realized volatility of S&P 500 index (SPX), Dow Jones Industry Average (DJIA), Canadian dollar (CAD/USD) and British Pound (USD/GBP) exchange rates. The competing models include a Simple Regression Model (SRM), Stochastic Volatility model with Lagged inter-temporal dependence (SVL), Stochastic Volatility model with Contemporaneous dependence (SVC), and a Heterogeneous Autoregressive (HAR) model. The main purpose is to examine whether allowing asymmetric relationships between return and volatility and leptokurtosis, or modelling the long-memory behaviour of volatility, would result in an improvement in forecast accuracy. Different approaches are considered when constructing daily realized volatility. Employing realized volatility in the in-sample estimation, the procedure is straightforward. The famous Diebold and Mariano's (1995) robust tests are applied to investigate whether the competing models provide equally accurate forecasts. ...

A note on the properties of power-transformed returns in long-memory stochastic volatility models with leverage effect