Error estimation properties of Gaussian process models in stochastic simulations

The theoretical relationship between the prediction variance of a Gaussian process model (GPM) and its mean square prediction error is well known. This relationship has been studied for the case when deterministic simulations are used in GPM, with application to design of computer experiments and metamodeling optimization. This article analyzes the error estimation of Gaussian process models when the simulated data observations contain measurement noise. In particular, this work focuses on the correlation between the GPM prediction variance and the distribution of prediction errors over multiple experimental designs, as a function of location in the input space. The results show that the error estimation properties of a Gaussian process model using stochastic simulations are preserved when the signal-to-noise ratio in the data is larger than 10, regardless of the number of training points used in the metamodel. Also, this article concludes that the distribution of prediction errors approaches a normal distribution with a variance equal to the GPM prediction variance, even in the presence of significant bias in the GPM predictions.     

Evaluating Kohonen’s learning rule: An approach through genetic algorithms

This paper examines the technical foundations of the self-organising map (SOM). It compares Kohonen’s heuristic-based training algorithm with direct optimisation of a locally-weighted distortion index, also used by Kohonen. Direct optimisation is achieved through a genetic algorithm (GA). Although GAs have been used before with the SOM, this has not been done in conjunction with the distortion index. Comparing heuristic-based training and direct optimisation for the SOM is analogous to comparing the Backpropagation algorithm for feedforward networks with direct optimisation of RMS error. Our experiments reveal lower values of the distortion index with direct optimisation. As to whether the heuristic-based algorithm is able to provide an approximation to gradient descent, our results suggest the answer should be in the negative. Theorems for one-dimensional and for square maps indicate that different point densities will emerge for the two training approaches. Our findings are in accordance with these results.     

A new method to mitigate data fluctuations for time series prediction

Although the classic exponential-smoothing models and grey prediction models have been widely used in time series forecasting, this paper shows that they are susceptible to fluctuations in samples. A new fractional bidirectional weakening buffer operator for time series prediction is proposed in this paper. This new operator can effectively reduce the negative impact of unavoidable sample fluctuations. It overcomes limitations of existing weakening buffer operators, and permits better control of fluctuations from the entire sample period. Due to its good performance in improving stability of the series smoothness, the new operator can better capture the real developing trend in raw data and improve forecast accuracy. The paper then proposes a novel methodology that combines the new bidirectional weakening buffer operator and the classic grey prediction model. Through a number of case studies, this method is compared with several classic models, such as the exponential smoothing model and the autoregressive integrated moving average model, etc. Values of three error measures show that the new method outperforms other methods, especially when there are data fluctuations near the forecasting horizon. The relative advantages of the new method on small sample predictions are further investigated. Results demonstrate that model based on the proposed fractional bidirectional weakening buffer operator has higher forecasting accuracy.     

A better measure of relative prediction accuracy for model selection and model estimation

Surveys show that the mean absolute percentage error (MAPE) is the most widely used measure of prediction accuracy in businesses and organizations. It is, however, biased: when used to select among competing prediction methods it systematically selects those whose predictions are too low. This has not been widely discussed and so is not generally known among practitioners. We explain why this happens. We investigate an alternative relative accuracy measure which avoids this bias: the log of the accuracy ratio, that is, log (prediction/actual). Relative accuracy is particularly relevant if the scatter in the data grows as the value of the variable grows (heteroscedasticity). We demonstrate using simulations that for heteroscedastic data (modelled by a multiplicative error factor) the proposed metric is far superior to MAPE for model selection. Another use for accuracy measures is in fitting parameters to prediction models. Minimum MAPE models do not predict a simple statistic and so theoretical analysis is limited. We prove that when the proposed metric is used instead, the resulting least squares regression model predicts the geometric mean. This important property allows its theoretical properties to be understood.     

A novel hybrid decomposition-ensemble model based on VMD and HGWO for container throughput forecasting

This paper built a hybrid decomposition-ensemble model named VMD-ARIMA-HGWO-SVR for the purpose of improving the stability and accuracy of container throughput prediction. The latest variational mode decomposition (VMD) algorithm is employed to decompose the original series into several modes (components), then ARIMA models are built to forecast the low-frequency components, and the high-frequency components are predicted by SVR models which are optimized with a recently proposed swarm intelligence algorithm called hybridizing grey wolf optimization (HGWO), following this, the prediction results of all modes are ensembled as the final forecasting result. The error analysis and model comparison results show that the VMD is more effective than other decomposition methods such as CEEMD and WD, moreover, adopting ARIMA models for prediction of low-frequency components can yield better results than predicting all components by SVR models. Based on the results of empirical study, the proposed model has good prediction performance on container throughput data, which can be used in practical work to provide reference for the operation and management of ports to improve the overall efficiency and reduce the operation costs.     

Prediction error criterion for selecting variables in a linear regression model

Several criteria, such as CV, C _p , AIC, CAIC, and MAIC, are used for selecting variables in linear regression models. It might be noted that C _p has been proposed as an estimator of the expected standardized prediction error, although the target risk function of CV might be regarded as the expected prediction error R _PE. On the other hand, the target risk function of AIC, CAIC, and MAIC is the expected log-predictive likelihood. In this paper, we propose a prediction error criterion, PE, which is an estimator of the expected prediction error R _PE. Consequently, it is also a competitor of CV. Results of this study show that PE is an unbiased estimator when the true model is contained in the full model. The property is shown without the assumption of normality. In fact, PE is demonstrated as more faithful for its risk function than CV. The prediction error criterion PE is extended to the multivariate case. Furthermore, using simulations, we examine some peculiarities of all these criteria.     

Thermal behaviour prediction utilizing artificial neural networks for an open office

This study investigates a neural network-based non-linear autoregressive model with external inputs (NNARX), a non-linear autoregressive moving average model with external inputs (NNARMAX), and a non-linear output error model (NNOE) to predict the thermal behaviour of an open-plan office in a modern commercial building. External and internal climate data recorded over one summer, autumn and winter season were used to build and validate the models. The paper illustrates the potential of using these models to predict room temperature and relative humidity for different time scales ahead (30 min or 2 h ahead). The prediction performance is evaluated using the criteria of goodness of fit, coefficient of determination, mean absolute error and mean squared error between predicted model output and real measurements. To obtain an optimal network structure (avoiding overfitting) after training, a pruning algorithm called optimal brain surgeon (OBS) was used to remove unnecessary input signals, weights and hidden neurons. The results demonstrate that all models provide reasonably good predictions but the NNARX and NNARMAX models outperform the NNOE model. These models can all potentially be used for improving the performance of thermal environment control systems.     

基于多项式混沌拓展模型和bootstrap的结构可靠性分析方法

多项式混沌拓展(polynomial chaos expansion,PCE)模型现已发展为全局灵敏度分析的强大工具,却很少作为替代模型用于可靠性分析。针对该模型缺乏误差项从而很难构造主动学习函数来逐步更新的事实,在结构可靠性分析的框架下提出了基于PCE模型和bootstrap重抽样的仿真方法来计算失效概率。首先,对试验设计(experimental design)使用bootstrap重抽样步骤以刻画PCE模型的预测误差;其次,基于这个局部误差构造主动学习函数,通过不断填充试验设计以自适应地更新模型,直到能够精确地逼近真实的功能函数;最后,当PCE模型具有足够精确的拟合、预测能力,再使用蒙特卡洛仿真方法来计算失效概率。提出的平行加点策略既能在模型更新过程中找到改进模型拟合能力的"最好"的点,又考虑了模型拟合的计算量;而且,当失效概率的数量级较低时,PCE-bootstrap步骤与子集仿真(subset simulation)的结合能进一步加速失效概率估计量的收敛。本文方法将PCE模型在概率可靠性领域的应用从灵敏度分析延伸到了可靠性分析,同时,算例分析结果显示了该方法的精确性和高效性。     

基于ARIMA与信息粒化SVR组合的股指预测研究

对于证券市场投资者而言,基于合理假设准确预测资产价格未来发展方向与趋势关乎投资成败。本文通过构建一个基于ARIMA与信息粒化SVR的组合预测模型,对股票市场指数价格和收益变化的趋势进行预测。实证研究结果表明:基于ARIMA与信息粒化SVR组合的股指预测模型相较于传统时间序列模型而言,在预测精度和效度方面有较大提升,能够在一定时间周期内对股票等风险资产的价格波动区间进行较为可靠地预测,但目前还只能大致确定时间序列波动的区间范围而不能精确地预测具体点位。未来仍需结合其他预测模型和预判技术进一步深入研究,以有效提升股指趋势预测的准确性和实际指导性。     

COVID-19 Epidemic Prediction Based on Deep Learning

In this paper, a multi-layer gated recurrent unit neural network (multi-head GRU) model is proposed to predict the confirmed cases of the new crown epidemic (COVID-19). We extract the time series relationship in the data, and the rolling prediction method is adopted to ensure the simple structure of the model and achieve higher precision and interpretability. The prediction results of this model are compared with the LSTM model, the Transformer model and the infectious disease model (SIR). The results show that the proposed model has higher prediction accuracy. The mean absolute error (MAE) of epidemic prediction in most countries (the United States, Brazil, India, the United Kingdom and Russia) is respectively 197.52, 68.02, 200.67, 24.78 and 123.50, which is much smaller than the prediction error of the SIR model, LSTM model and Transformer model. For the spread of the COVID-19 epidemic, traditional infectious disease models and machine learning models cannot achieve more accurate predictions. In this paper, we use a GRU model to predict the real-time spread of COVID-19, which has fewer parameters and reduces the risk of overfitting to train faster. Meanwhile, it can make up for the shortcoming of the transformer model to capture local features.     

Variable selection in high‐dimensional regression: a nonparametric procedure for business failure prediction

Business failure prediction models are important in providing warning for preventing financial distress and giving stakeholders time to react in a timely manner to a crisis. The empirical approach to corporate distress analysis and forecasting has recently attracted new attention from financial institutions, academics, and practitioners. In fact, this field is as interesting today as it was in the 1930s, and over the last 80 years, a remarkable body of both theoretical and empirical studies on this topic has been published. Nevertheless, some issues are still under investigation, such as the selection of financial ratios to define business failure and the identification of an optimal subset of predictors. For this purpose, there exist a large number of methods that can be used, although their drawbacks are usually neglected in this context. Moreover, most variable selection procedures are based on some very strict assumptions (linearity and additivity) that make their application difficult in business failure prediction. This paper proposes to overcome these limits by selecting relevant variables using a nonparametric method named Rodeo that is consistent even when the aforementioned assumptions are not satisfied. We also compare Rodeo with two other variable selection methods (Lasso and Adaptive Lasso), and the empirical results demonstrate that our proposed procedure outperforms the others in terms of positive/negative predictive value and is able to capture the nonlinear effects of the selected variables. Copyright © 2017 John Wiley & Sons, Ltd.     

Interval statistic based reliability analysis method on small sample hot test of satellite thruster

As one of the most important components of satellites, the thruster must maintain high reliability, but the assessment is difficult when lacking test failure data. When conducting hot test of the satellite thruster, we encountered the problem of reliability assessment on type-I censored data with only one failure, which is common for small sample tests. This paper proposes a novel interval statistic based reliability analysis method, which can fulfill the life information from the failure time to the censored time ignored by conventional methods, and improve the assessment accuracy. In this paper, a life distribution model is established by proper failure mechanism analysis and prior test information exploitation. As thrust chamber burning-through has been considered as the main failure mode, life test of the chamber coating was conducted under different thermal conditions to obtain the model parameter. Based on the interval statistic theory, a detailed derivation is illustrated. Then, reliability assessment and life prediction for the satellite thruster in both transfer orbit phase and synchronous orbit phase have been achieved, and the results show that our method performs very well, which provides an important way for dealing with test data with only one failure.     

An adaptive estimation of MAVE

Minimum average variance estimation (MAVE, Xia et al. (2002) [29]) is an effective dimension reduction method. It requires no strong probabilistic assumptions on the predictors, and can consistently estimate the central mean subspace. It is applicable to a wide range of models, including time series. However, the least squares criterion used in MAVE will lose its efficiency when the error is not normally distributed. In this article, we propose an adaptive MAVE which can be adaptive to different error distributions. We show that the proposed estimate has the same convergence rate as the original MAVE. An EM algorithm is proposed to implement the new adaptive MAVE. Using both simulation studies and a real data analysis, we demonstrate the superior finite sample performance of the proposed approach over the existing least squares based MAVE when the error distribution is non-normal and the comparable performance when the error is normal.     

A comparison of univariate methods for forecasting container throughput volumes

In this paper, six univariate forecasting models for the container throughput volumes in Taiwan’s three major ports are presented. The six univariate models include the classical decomposition model, the trigonometric regression model, the regression model with seasonal dummy variables, the grey model, the hybrid grey model, and the SARIMA model. The purpose of this paper is to search for a model that can provide the most accurate prediction of container throughput. By applying monthly data to these models and comparing the prediction results based on mean absolute error, mean absolute percent error and root mean squared error, we find that in general the classical decomposition model appears to be the best model for forecasting container throughput with seasonal variations. The result of this study may be helpful for predicting the short-term variation in demand for the container throughput of other international ports.     

On the relationship between the proportional hazards and accelerated failure time models in survival analysis

The slope parameters in the proportional hazards and accelerated failure time models are shown to be proportional if and only if the error variable in the accelerated failure time model has a generalized extreme value distribution. A differential equation relating the two score functions φ(u) and Φ(u) is established. The error distribution is characterized when φ (u) and Φ(u) are linearly related; subject to this restriction, censored data linear rank procedures are studied.     

A novel car-following inertia gray model and its application in forecasting short-term traffic flow

Real-time and accurate short-term traffic flow prediction results can provide real-time and effective information for traffic information systems. Based on classic car-following models, this paper establishes differential equations according to the traffic state and proposes a car-following inertial gray model based on the information difference of the differential and gray system, in combination with the mechanical characteristics of traffic flow data and the characteristics of an inertial model. Furthermore, analytical methods are used to study the parameter estimation and model solution of the new model, and the important properties, such as the original data, inertia coefficient and simulation accuracy, are studied. The effectiveness of the model is verified in two cases. The performance of the model is better than that of six other prediction models, and the structural design of the new model is more reasonable than that of the existing gray models. Moreover, the new model is applied to short-term traffic flow prediction for three urban roads. The results show that the simulation and prediction effects of the model are better than those of other gray models. In terms of the traffic flow state, an optimal match between short-term traffic flow prediction and the new model is achieved.     

Regression based reserving models and partial information

We consider a class of distribution-free regression models only defined in terms of moments, which can be used to model separate reported but not settled reserves, and incurred but not reported reserves. These regression models can be estimated using standard least squares and method of moments techniques, similar to those used in the distribution-free chain-ladder model. Further, these regression models are closely related to double chain-ladder type models, and the suggested estimation techniques could serve as alternative estimation procedures for these models. Due to the simple structure of the models it is possible to obtain Mack-type mean squared error of prediction estimators. Moreover, the analysed regression models can be used on different levels of detailed data, and by using the least squares estimation techniques it is possible to show that the precision in the reserve predictor is improved by using more detailed data. These regression models can be seen as a sequence of linear models, and are therefore also easy to bootstrap non-parametrically.     

自适应灰色欧拉模型的优化及其应用

灰色预测模型已经在很多领域获得成功的应用,但是该方法的模型性能还可以进一步提高.为此,提出了一种新的灰色欧拉模型GEM(1,1)和OSGEM(1,1),给出了参数的最小二乘法计算公式,并以微分方程为推理过程,得到了GEM(1,1)模型和OSGEM(1,1)模型的时间响应序列.利用2002-2015年的数据建立预测模型,利用2016-2018年的数据评估模型的准确性.结果表明,OSGEM(1,1)模型优于其他模型.     

Bayesian Variable and Transformation Selection in Linear Regression

This article suggests a method for variable and transformation selection based on posterior probabilities. Our approach allows for consideration of all possible combinations of untransformed and transformed predictors along with transformed and untransformed versions of the response. To transform the predictors in the model, we use a change-point model, or “change-point transformation,” which can yield more interpretable models and transformations than the standard Box–Tidwell approach. We also address the problem of model uncertainty in the selection of models. By averaging over models, we account for the uncertainty inherent in inference based on a single model chosen from the set of models under consideration. We use a Markov chain Monte Carlo model composition (MC³) method which allows us to average over linear regression models when the space of models under consideration is very large. This considers the selection of variables and transformations at the same time. In an example, we show that model averaging improves predictive performance as compared with any single model that might reasonably be selected, both in terms of overall predictive score and of the coverage of prediction intervals. Software to apply the proposed methodology is available via StatLib.     

Tracking error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.