Forecasting comparisons using a hybrid ARFIMA and LRNN models

In this article, an autoregressive fractionally integrated moving average model (ARFIMA) and a layer recurrent neural network (LRNN) were combined to form a hybrid forecasting model. The hybrid model was applied on the daily crude oil production data of the Nigerian National Petroleum Corporation (NNPC) to forecast the daily crude oil production of the NNPC. The Bayesian model averaging technique was used to obtain a combined forecast from the two separate methods. A comparison was made between the hybrid model with standalone ARFIMA and LRNN methods in which the hybrid model produced better forecasting performance than the standalone methods.     

Model averaging for multivariate multiple regression models

The theories and applications of model averaging have been developed comprehensively in the past two decades. In this paper, we consider model averaging for multivariate multiple regression models. In order to make use of the correlation information of the dependent variables sufficiently, we propose a model averaging method based on Mahalanobis distance which is related to the correlation of the dependent variables. We prove the asymptotic optimality of the resulting Mahalanobis Mallows model averaging (MMMA) estimators under certain assumptions. In the simulation study, we show that the proposed MMMA estimators compare favourably with model averaging estimators based on AIC and BIC weights and the Mallows model averaging estimators from the single dependent variable regression models. We further apply our method to the real data on urbanization rate and the proportion of non-agricultural population in ethnic minority areas of China.     

Can Long-Term Exposure Distributions Be Predicted from Short-Term Measurements?

A method for estimating long-term distributions of exposure based on repeated short-term measurements within the same population is developed. If the short-term measurements span seasonal variation, and if the distributions are log-normal or nearly so, then long-term distributions can be estimated from as few as two visits to the same population. The method is illustrated using examples drawn from EPA's TEAM Study of exposures to volatile organic compounds.     

Bayesian neural networks for nonlinear time series forecasting

In this article, we apply Bayesian neural networks (BNNs) to time series analysis, and propose a Monte Carlo algorithm for BNN training. In addition, we go a step further in BNN model selection by putting a prior on network connections instead of hidden units as done by other authors. This allows us to treat the selection of hidden units and the selection of input variables uniformly. The BNN model is compared to a number of competitors, such as the Box-Jenkins model, bilinear model, threshold autoregressive model, and traditional neural network model, on a number of popular and challenging data sets. Numerical results show that the BNN model has achieved a consistent improvement over the competitors in forecasting future values. Insights on how to improve the generalization ability of BNNs are revealed in many respects of our implementation, such as the selection of input variables, the specification of prior distributions, and the treatment of outliers.     

Model averaging by jackknife criterion for varying-coefficient partially linear models

Abstract

This paper is concerned with model averaging procedure for varying-coefficient partially linear models. We proposed a jackknife model averaging method that involves minimizing a leave-one-out cross-validation criterion, and developed a computational shortcut to optimize the cross-validation criterion for weight choice. The resulting model average estimator is shown to be asymptotically optimal in terms of achieving the smallest possible squared error. The simulation studies have provided evidence of the superiority of the proposed procedures. Our approach is further applied to a real data.     

Model averaging procedure for varying-coefficient partially linear models with missing responses

This paper is concerned with model averaging procedure for varying-coefficient partially linear models with missing responses. The profile least-squares estimation process and inverse probability weighted method are employed to estimate regression coefficients of the partially restricted models, in which the propensity score is estimated by the covariate balancing propensity score method. The estimators of the linear parameters are shown to be asymptotically normal. Then we develop the focused information criterion, formulate the frequentist model averaging estimators and construct the corresponding confidence intervals. Some simulation studies are conducted to examine the finite sample performance of the proposed methods. We find that the covariate balancing propensity score improves the performance of the inverse probability weighted estimator. We also demonstrate the superiority of the proposed model averaging estimators over those of existing strategies in terms of mean squared error and coverage probability. Finally, our approach is further applied to a real data example.     

Bayesian Stacked Parametric Survival with Frailty Components and Interval‐Censored Failure Times: An Application to Food Allergy Risk

To better understand the risk of exposure to food allergens, food challenge studies are designed to slowly increase the dose of an allergen delivered to allergic individuals until an objective reaction occurs. These dose‐to‐failure studies are used to determine acceptable intake levels and are analyzed using parametric failure time models. Though these models can provide estimates of the survival curve and risk, their parametric form may misrepresent the survival function for doses of interest. Different models that describe the data similarly may produce different dose‐to‐failure estimates. Motivated by predictive inference, we developed a Bayesian approach to combine survival estimates based on posterior predictive stacking, where the weights are formed to maximize posterior predictive accuracy. The approach defines a model space that is much larger than traditional parametric failure time modeling approaches. In our case, we use the approach to include random effects accounting for frailty components. The methodology is investigated in simulation, and is used to estimate allergic population eliciting doses for multiple food allergens.     

Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local‐to‐Continuity Theory for the Pre‐Averaging Method

We develop an asymptotic theory for the pre‐averaging estimator when asset price jumps are weakly identified, here modeled as local to zero. The theory unifies the conventional asymptotic theory for continuous and discontinuous semimartingales as two polar cases with a continuum of local asymptotics, and explains the breakdown of the conventional procedures under weak identification. We propose simple bias‐corrected estimators for jump power variations, and construct robust confidence sets with valid asymptotic size in a uniform sense. The method is also robust to certain forms of microstructure noise.     

A modification of the Box–Meyer method for finding the active factors in screening experiments

Screening experiments are conducted to identify a few active factors among a large number of factors. For the objective of identifying active factors, Box and Meyer provided an innovative approach, the Box–Meyer method (BMM). With the use of means models, we propose a modification of the BMM in this paper. Compared with the original BMM, the modified BMM (MBMM) can circumvent the problem that the original BMM runs into, namely that it may fail to identify some active factors due to the ignorance of higher order interactions. Furthermore, the number of explanatory variables in the MBMM is smaller. Therefore, the computational complexity is reduced. Finally, three examples with different types of designs are used to demonstrate the wide applicability of the MBMM.     

Bayesian Nonlinear Regression for the Air Pollution Effects on Daily Clinic Visits in Small Areas of Taiwan

We consider the complete clinic visit records and environmental monitoring data at 50 townships and city districts where ambient air monitoring stations of Taiwan Air Quality Monitoring Stations are located. A Bayesian analysis is carried out using regression spline model on principal components obtained from several pollutant covariables. The appropriate model is selected using Bayesian model averaging. A brief account of our results is provided for the elderly patients group.