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The purpose of this paper is to discuss the interval forecasting, prediction interval and its reliability. When the predicted interval and its reliability are construction, the general rule which must satisfy is studied, grey wrapping band forecasting method is perfect.

A forecasting method puts forward a process of prediction interval. It also elaborates on the meaning of interval (the probability of the prediction interval including the real value of predicted variable). The general rule is abstracted and summarized by many forecasting cases. The general rule is discussed by axiomatic method.

The prediction interval is categorized into three types. Three axioms that construction predicted interval must satisfy are put forward. Grey wrapping band forecasting method is improved based on the proposed axioms.

Take the Shanghai composite index as the example, according to the K-line diagram from 4 January 2013 to 9 May 2013, the reliability of predicted rebound height of subsequent two or three trading day does not exceed the upper wrapping curve is 80 per cent. It is significant to understand the forecasting range correctly, build a reasonable range forecasting method and to apply grey wrapping band forecasting method correctly.

Grey wrapping band forecasting method is improved based on the proposed axioms.

In contrast to point forecasts, interval forecasts provide information on future variability. This research thus aimed to develop interval prediction models by addressing two significant issues: (1) a simple average with an additive property is commonly used to derive combined forecasts, but this unreasonably ignores the interaction among sequences used as sources of information, and (2) the time series often does not conform to any statistical assumptions.

To develop an interval prediction model, the fuzzy integral was applied to nonlinearly combine forecasts generated by a set of grey prediction models, and a sequence including the combined forecasts was then used to construct a neural network. All required parameters relevant to the construction of an interval model were optimally determined by the genetic algorithm.

The empirical results for tourism demand showed that the proposed non-additive interval model outperformed the other interval prediction models considered.

The private and public sectors in economies with high tourism dependency can benefit from the proposed model by using the forecasts to help them formulate tourism strategies.

In light of the usefulness of combined point forecasts and interval model forecasting, this research contributed to the development of non-additive interval prediction models on the basis of combined forecasts generated by grey prediction models.

Because of short life cycle and fluctuating greatly in total sales volumes (TSV), it is difficult to accumulate enough sales data and mine an attribute set reflecting the common needs of all consumers for a kind of experiential product with short life cycle (EPSLC). Methods for predicting TSV of long-life-cycle products may not be suitable for EPSLC. Furthermore, point prediction cannot obtain satisfactory prediction results because information available before production is inadequate. Thus, this paper aims at proposing and verifying a novel interval prediction method (IPM).

Because interval prediction may satisfy requirements of preproduction investment decision-making, interval prediction was adopted, and then the prediction difficult was converted into a classification problem. The classification was designed by comparing similarities in attribute relationship patterns between a new EPSLC and existing product groups. The product introduction may be written or obtained before production and thus was designed as primary source information. IPM was verified by using data of crime movies released in China from 2013 to 2017.

The IPM is valid, which uses product introduction as input, classifies existing products into three groups with different TSV intervals, mines attribute relationship patterns using content and association analyses and compares similarities in attribute relationship patterns – to predict TSV interval of a new EPSLC before production.

Different from other studies, the IPM uses product introduction to mine attribute relationship patterns and compares similarities in attribute relationship patterns to predict the interval values. It has a strong applicability in data content and structure and may realize rolling prediction.

The purpose of this paper is to improve the information quality of bankruptcy prediction models proposed in the literature by building prediction intervals around the point estimates generated by these models and to determine if the use of the prediction intervals in conjunction with the point estimated yields an improvement in predictive accuracy over traditional models. The authors calculated the point estimates and prediction intervals for a sample of firms from 1991 to 2008. The point estimates and prediction intervals were used in concert to classify firms as bankrupt or non-bankrupt. The accuracy of the tested technique was compared to that of a traditional bankruptcy prediction model. The results indicate that the use of upper and lower bounds in concert with the point estimates yield an improvement in the predictive ability of bankruptcy prediction models. The improvements in overall prediction accuracy and non-bankrupt firm prediction accuracy are statistically significant at the 0.01 level. The authors present a technique that (1) provides a more complete picture of the firm’s status, (2) is derived from multiple forms of evidence, (3) uses a predictive interval technique that is easily repeated, (4) can be generated in a timely manner, (5) can be applied to other bankruptcy prediction models in the literature, and (6) is statistically significantly more accurate than traditional point estimate techniques. The current research is the first known study to use the combination of point estimates and prediction intervals to in bankruptcy prediction.

With the rise in wine consumption, accurate wine price forecasts have significantly impacted restaurant and hotel purchasing decisions and inventory management. This study aims to develop a precise and effective wine price point and interval forecasting model.

The proposed forecast model uses an improved hybrid kernel extreme learning machine with an attention mechanism and a multi-objective swarm intelligent optimization algorithm to produce more accurate price estimates. To the best of the authors’ knowledge, this is the first attempt at applying artificial intelligence techniques to improve wine price prediction. Additionally, an effective method for predicting price intervals was constructed by leveraging the characteristics of the error distribution. This approach facilitates quantifying the uncertainty of wine price fluctuations, thus rendering decision-making by relevant practitioners more reliable and controllable.

The empirical findings indicated that the proposed forecast model provides accurate wine price predictions and reliable uncertainty analysis results. Compared with the benchmark models, the proposed model exhibited superiority in both one-step- and multi-step-ahead forecasts. Meanwhile, the model provides new evidence from artificial intelligence to explain wine prices and understand their driving factors.

This study is a pioneering attempt to evaluate the applicability and effectiveness of advanced artificial intelligence techniques in wine price forecasts. The proposed forecast model not only provides useful options for wine price forecasting but also introduces an innovative addition to existing forecasting research methods and literature.

The purpose of this paper is to construct a prediction model of three-parameter interval grey number based on kernel and double information domains to expand the modeling object of grey prediction model from interval grey number to three-parameter interval grey number.

First, the study decomposes the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point and defines the upper and lower information domains of the three-parameter interval grey number. Second, it calculates the kernel, the upper and lower information domains of the three-parameter interval grey number. Then, it constructs the prediction model for kernel sequence and upper and lower information domain sequences, respectively. By deducing the time response expressions of “center of gravity”, lower and upper limits of three-parameter interval grey number, a prediction model of three-parameter interval grey number based on kernel and double information domains is obtained.

This paper provides a prediction model of three-parameter interval grey number based on kernel and double information domains, and the example analysis shows that the method proposed in this paper has higher prediction accuracy and practicality.

In this paper, the modeling object of grey prediction model is extended to the three-parameter interval grey number, so it can be used for the prediction of uncertainty problems, such as stock changing trend, temperature and so on.

By decomposing the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point, gives the definition of upper and lower information domains and then obtains a new method for whitening the three-parameter interval grey number.

The effective prediction of crude oil futures prices can provide a reference for relevant enterprises to make production plans and investment decisions. To the nonlinearity, high volatility and uncertainty of the crude oil futures price, a matrixed nonlinear exponential grey Bernoulli model combined with an exponential accumulation generating operator (MNEGBM(1,1)) is proposed in this paper.

First, the original sequence is processed by the exponential accumulation generating operator to weaken its volatility. The nonlinear grey Bernoulli and exponential function models are combined to fit the preprocessed sequence. Then, the parameters in MNEGBM(1,1) are matrixed, so the ternary interval number sequence can be modeled directly. Marine Predators Algorithm (MPA) is chosen to optimize the nonlinear parameters. Finally, the Cramer rule is used to derive the time recursive formula.

The predictive effectiveness of the proposed model is verified by comparing it with five comparison models. Crude oil futures prices in Cushing, OK are predicted and analyzed from 2023/07 to 2023/12. The prediction results show it will gradually decrease over the next six months.

Crude oil futures prices are highly volatile in the short term. The use of grey model for short-term prediction is valuable for research. For the data characteristics of crude oil futures price, this study first proposes an improved model for interval number prediction of crude oil futures prices.

The purpose of this paper is to construct an unbiased interval grey number prediction model with new information priority for dealing with the jumping errors from difference equation to the differential equation in the prediction model of interval grey number.

First, this study obtains a set of linear equations about the model parameters by taking the minimum error sum of squares between the accumulative sequence and its simulation values as criterion, and solves them on the basis of the Crammer rule. Then, according to the new information priority principle, it selects the last number of the accumulated generation sequence as the initial value and gives the expression of the time response function by the recursive iteration method to establish the interval grey number prediction model.

This paper provides an unbiased interval grey number prediction model with new information priority, and the example analysis shows that the method proposed in this paper has higher prediction precision and practicality.

If there is a better method to whiten the interval grey number, so as to fully tap the grey information contained in it, the accuracy of the model will be higher.

The model proposed in this paper can avoid the error caused by jumping from difference equation to differential equation and make full use of new information. It can be better used in a problem where new information has a great influence on prediction results.

This paper selects the last number of the accumulated generation sequence as the initial value and gives the expression of the time response function by the recursive iteration method. Then, it constructs an unbiased interval grey number prediction model with new information priority.

The purpose of this paper is to critically analyze the common assumption, made by many credit risk models such as the Moody's KMV Loss‐Calc model, of a β distribution for the loss‐given default (LGD). The paper shows that this assumption does not perform well in constructing analytic prediction intervals for LGD.

Simulation experiments were conducted to highlight the potential problems associated with this distributional assumption in constructing prediction intervals for LGD.

The simulation experiments show that, when starting from a different assumption concerning the shape of the population distribution, the beta distribution does not perform well in constructing prediction intervals for LGD.

The analysis performed in this study addresses a relevant subject. Indeed, a correct estimate of a credit exposure LGD is particularly relevant not only for internal risk management and management purposes, but also for regulatory reasons within the context of the internal ratings based approach of the recently approved capital regulation framework (Basel II).

This study aims to propose the adoption of artificial neural network (ANN)-based prediction intervals (PIs) to give more reliable prediction of labour productivity using historical data.

Using the proposed PI method, various sources of uncertainty affecting predictions can be accounted for, and a PI is proposed instead of a less reliable single-point estimate. The proposed PI consists of a lower and upper bound in which the realization of the predicted variable, namely, labour productivity, is anticipated to fall with a defined probability and represented in terms of a confidence level (CL).

The proposed PI method is implemented on a case study project to predict labour productivity. The quality of the generated PIs for the labour productivity is investigated at three confidence levels. The results show that the proposed method can predict the value of labour productivity efficiently.

This study is the first attempt in construction management to undertake a shift from deterministic point predictions to interval forecasts to improve the reliability of predictions. The proposed PI method will help project managers obtain accurate and credible predictions of labour productivity using historical data. With a better understanding of future outcomes, project managers can adopt appropriate improvement strategies to enhance labour productivity before commencing a project.

Point predictions provided by traditional deterministic ANN-based forecasting methodologies may be unreliable due to the different sources of uncertainty affecting predictions. The current study proposes ANN-based PIs as an alternative and robust tool to give a more reliable prediction of labour productivity using historical data. Using the proposed method, various sources of uncertainty affecting the predictions are accounted for, and a PI is proposed instead of a less reliable single point estimate.