We forecast realized volatilities by developing a time-varying heterogeneous autoregressive(HAR)latent factor model with dynamic model average(DMA)and dynamic model selection(DMS)approaches.The number of latent factor...We forecast realized volatilities by developing a time-varying heterogeneous autoregressive(HAR)latent factor model with dynamic model average(DMA)and dynamic model selection(DMS)approaches.The number of latent factors is determined using Chan and Grant's(2016)deviation information criteria.The predictors in our model include lagged daily,weekly,and monthly volatility variables,the corresponding volatility factors,and a speculation variable.In addition,the time-varying properties of the best-performing DMA(DMS)-HAR-2FX models,including size,inclusion probabilities,and coefficients,are examined.We find that the proposed DMA(DMS)-HAR-2FX model outperforms the competing models for both in-sample and out-of-sample forecasts.Furthermore,the speculation variable displays strong predictability for forecasting the realized volatility of financial futures in China.展开更多
Network autoregression and factor model are effective methods for modeling network time series data.In this study,we propose a network autoregression model with a factor structure that incorporates a latent group stru...Network autoregression and factor model are effective methods for modeling network time series data.In this study,we propose a network autoregression model with a factor structure that incorporates a latent group structure to address nodal heterogeneity within the network.An iterative algorithm is employed to minimize a least-squares objective function,allowing for simultaneous estimation of both the parameters and the group structure.To determine the unknown number of groups and factors,a PIC criterion is introduced.Additionally,statistical inference of the estimated parameters is presented.To assess the validity of the proposed estimation and inference procedures,we conduct extensive numerical studies.We also demonstrate the utility of our model using a stock dataset obtained from the Chinese A-Share stock market.展开更多
Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient'...Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient's distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients' current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.展开更多
We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment.The treatment rate has at most a finite number of jump discontinuities in every compact interv...We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment.The treatment rate has at most a finite number of jump discontinuities in every compact interval.By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis,the basic reproductive number Ro is proved to be a sharp threshold value which completely determines the dynamics of the model.If Ro<1,then there exists a disease-free equilibrium which is globally stable.If Ro>1,the disease-free equilibrium becomes unstable and there exists an endemic equilibrium which is globally stable.We discuss that the disease will die out in a finite time which is impossible for the corresponding SEIR model with continuous treatment.Furthermore,the numerical simulations indicate that strengthening treatment measure after infective individuals reach some level is beneficial to disease control.展开更多
An epidemic model with vaccination and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible steady states to this model is discussed. The exist...An epidemic model with vaccination and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible steady states to this model is discussed. The existence of a traveling wave solution is established by using the technique of upper and lower solutions and Schauder＇s fixed point theorem. Numerical simulations are carried out to illustrate the main results.展开更多
基金supported by grants from the National Natural Science Foundation of China(72171088,71803049,72003205)the Ministry of Education of the People's Republic of China of Humanities and Social Sciences Youth Fundation(20YJC790142)the General Project of Social Science Planning in Guangdong Province,China(GD22CYJ12).
文摘We forecast realized volatilities by developing a time-varying heterogeneous autoregressive(HAR)latent factor model with dynamic model average(DMA)and dynamic model selection(DMS)approaches.The number of latent factors is determined using Chan and Grant's(2016)deviation information criteria.The predictors in our model include lagged daily,weekly,and monthly volatility variables,the corresponding volatility factors,and a speculation variable.In addition,the time-varying properties of the best-performing DMA(DMS)-HAR-2FX models,including size,inclusion probabilities,and coefficients,are examined.We find that the proposed DMA(DMS)-HAR-2FX model outperforms the competing models for both in-sample and out-of-sample forecasts.Furthermore,the speculation variable displays strong predictability for forecasting the realized volatility of financial futures in China.
基金Supported by National Natural Science Foundation of China(72222009,71991472)。
文摘Network autoregression and factor model are effective methods for modeling network time series data.In this study,we propose a network autoregression model with a factor structure that incorporates a latent group structure to address nodal heterogeneity within the network.An iterative algorithm is employed to minimize a least-squares objective function,allowing for simultaneous estimation of both the parameters and the group structure.To determine the unknown number of groups and factors,a PIC criterion is introduced.Additionally,statistical inference of the estimated parameters is presented.To assess the validity of the proposed estimation and inference procedures,we conduct extensive numerical studies.We also demonstrate the utility of our model using a stock dataset obtained from the Chinese A-Share stock market.
基金supported by National Cancer Institute(Grant No.U01CA079778)
文摘Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient's distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients' current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.
基金supported by the National Nature Science Foundation of China(11271154).
文摘We consider a SEIR epidemic model with infectious force in latent period and infected period under discontinuous treatment.The treatment rate has at most a finite number of jump discontinuities in every compact interval.By using Lyapunov theory for discontinuous differential equations and other techniques on non-smooth analysis,the basic reproductive number Ro is proved to be a sharp threshold value which completely determines the dynamics of the model.If Ro<1,then there exists a disease-free equilibrium which is globally stable.If Ro>1,the disease-free equilibrium becomes unstable and there exists an endemic equilibrium which is globally stable.We discuss that the disease will die out in a finite time which is impossible for the corresponding SEIR model with continuous treatment.Furthermore,the numerical simulations indicate that strengthening treatment measure after infective individuals reach some level is beneficial to disease control.
文摘An epidemic model with vaccination and spatial diffusion is studied. By analyzing the corresponding characteristic equations, the local stability of each of feasible steady states to this model is discussed. The existence of a traveling wave solution is established by using the technique of upper and lower solutions and Schauder＇s fixed point theorem. Numerical simulations are carried out to illustrate the main results.
