Interval Forecasts Research Articles

An intelligent interval forecasting system based on fuzzy time series and error distribution characteristics for air quality index

Due to the emergency environment pollution problems, it is imperative to understand the air quality and take effective measures for environmental governance. As a representative measure, the air quality index (AQI) is a single conceptual index value simplified by the concentrations of several routinely monitored air pollutants according to the proportion of various components in the air. With the gradual enhancement of awareness of environmental protection, air quality index forecasting is a key point of environment management. However, most of the traditional forecasting methods ignore the fuzziness of original data itself and the uncertainty of forecasting results which causes the unsatisfactory results. Thus, an innovative forecasting system combining data preprocessing technique, kernel fuzzy c-means (KFCM) clustering algorithm and fuzzy time series is successfully developed for air quality index forecasting. Concretely, the fuzzy time series that handle the fuzzy set is used for the main forecasting process. Then the complete ensemble empirical mode decomposition and KFCM are respectively developed for data denoising and interval partition. Furthermore, the interval forecasting method based on error distribution is developed to measure the forecasting uncertainty. Finally, the experimental simulation and evaluation system verify the great performance of proposed forecasting system and the promising applicability in a practical environment early warning system.

Using Monte-Carlo Dropout in Deep Neural Networks for Interval Forecasting of Durian Export

Interval forecasting is essential because it presents predictions with associated uncertainties, which are not captured by point forecasts alone. In nature, data contain variability due to measurement and random noise. In machine learning, most research focuses on point forecasts, with relatively few studies dedicated to interval forecasting, especially in areas such as agriculture. In this study, durian exports in Thailand are used as a case study. We employed Monte Carlo Dropout (MCDO) for interval forecasting and investigated the impact of various hyperparameters on the performance of Monte Carlo Dropout Neural Networks (MCDO-NNs). Our results were benchmarked against traditional models, such as the Seasonal Autoregressive Integrated Moving Average (SARIMA). The findings reveal that MCDO-NN outperforms SARIMA, achieving a lower root mean squared error of 9,570.24 and a higher R-squared value of 0.4837. The interval forecast width obtained from the MCDO-NN was narrower compared to that of SARIMA. Also, the impact of hyperparameters was observed, and it can serve as guidelines for applying MCDO-NNs to other agricultural datasets or datasets with seasonal and/or trend components.

Forecasting high-dimensional functional time series: Application to sub-national age-specific mortality

We study the modeling and forecasting of high-dimensional functional time series (HDFTS), which can be cross-sectionally correlated and temporally dependent. We introduce a decomposition of the HDFTS into two distinct components: a deterministic component and a residual component that varies over time. The decomposition is derived through the estimation of two-way functional analysis of variance. A functional time series forecasting method, based on functional principal component analysis, is implemented to produce forecasts for the residual component. By combining the forecasts of the residual component with the deterministic component, we obtain forecast curves for multiple populations. We apply the model to age- and sex-specific mortality rates in the United States, France, and Japan, in which there are 51 states, 95 departments, and 47 prefectures, respectively. The proposed method is capable of delivering more accurate point and interval forecasts in forecasting multi-population mortality than several benchmark methods considered.

Carbon price interval prediction method based on probability density recurrence network and interval multi-layer perceptron

Low-carbon development is an inevitable choice under global climate change, and carbon markets have emerged accordingly. Carbon price forecasting is a crucial aspect of research on carbon-reduction strategies. Traditional forecasting methods are mostly focused on point-valued time series and contain limited information, which causes point forecasting to lose volatility information. Such limitations highlight the importance of proposing a precise interval-valued time series prediction system. To address this issue, we propose a carbon price interval forecasting framework based on a probability density recurrence network and interval multi-layer perceptron (MLPI) from the perspective of uncertainty in the presence of carbon price fluctuations. First, we convert the original data into a probability density sequence using kernel density estimation and then build the network. To extract valid information and exclude abnormal data in the carbon price sample data, we clean the data using network topology and link prediction theory; then, the MLPI model is used for interval forecasting. To verify the forecasting performance of this method, we conduct an empirical analysis using real interval-valued carbon futures price data from the EU carbon market and compare its forecasting precision with other models under the same conditions. The results show that the proposed carbon price interval prediction framework is superior to traditional methods in terms of forecasting precision.

PREDICTIVE ANALYSIS OF CLIMATE DISASTER DATA

In this paper, the Total deaths and Cost per Index (CPI) of worldwide climate disaster dataset has been modelled. The time period of the dataset is from 1900 to 2021. The Autoregressive Integrated Moving Average (ARIMA) has been applied to forecast the Total Deaths and CPI of the study area. The total of 75% of the train data is used for construction of the model and the remaining 25% dataset is used for testing the model. The ARIMA model is general provides more accurate projection especially interval forecast and is more reliable than other common statistical techniques. The best-fitted model is identified as ARIMA(2,0,1) and (2,1,2) for Cost per Index CPI and Total Deaths respectively, generated on the basis of minimum values of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) procedures. The accuracy parameter considered as Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) both parameters shows the model is accurate respectively. There is a 7% difference between the auto and manual models for the CPI feature, similarly, there is a 4% difference for Total Deaths, indicating that CPI plays a significant impact in climatic disasters. In order to identify best fitted model, we applied the model manually and automatic processing. By means of Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) plots, the most appropriate order of the ARIMA model are determine and evaluated. Accordingly the created model can help in determining future strategies related to climate disaster dataset of the world. From the forecast result it is found that the results seems to show an increasing trend in CPI values and the minimal decreasing in total death condition and economic activities of the world.

Interpretable spatial-temporal attention convolutional network for rainfall forecasting

The interpretability of rainfall forecasting models is a major challenge in the field of artificial intelligence. Its importance is equal to the evaluation of model accuracy. Owing to the uncertainty and nonlinearity of the rainfall forecasting process, existing hydrological rainfall forecasting models often have low prediction robustness, and the machine learning method ignores the influence of physical factors in the surrounding areas; thus, the physical interpretability of the model is inferior. This study proposes an interpretable spatial-temporal attention convolution network for rainfall interval forecasting (IDSTA-TCN). To analyze and mine the uncertainty of input data more effectively, we enhanced a variational mode decomposition (EBO-VMD) algorithm based on Bayesian optimization to decompose the input data. To improve the performance of the original temporal convolution network (TCN) unit in rainfall forecasting and to effectively use the spatial-temporal information of rainfall forecasting data, we improved the spatial-temporal attention mechanism, dynamically combined the geographical information of the meteorological stations in the surrounding area to assist the network unit in better mining the nonlinear impact of historical input information on current rainfall forecasting, and improved the prediction performance of the IDSTA-TCN model. Finally, we designed a more reasonable error factor adjustment interval output strategy to better quantify the impact of prediction errors on the rainfall interval prediction results. Moreover, we conducted a series of experiments to compare and analyze the accuracy of each model according to the most commonly used evaluation indicators in the field of rainfall forecasting. The results demonstrate that the proposed IDSTA-TCN model is superior to the baseline models in most cases. We preliminarily analyzed the spatial-temporal attention weights, which explained the physical rationality of our model.

Short-term forecasting of German generation-based CO2 emission factors using parametric and non-parametric time series models

This study focuses on forecasting German generation-based CO2 emission factors to develop accurate prediction models, which help to shift flexible loads in time with low emissions. While most existing research relies on point forecasts to predict CO2 emission factors, the presented methods are utilized to perform interval forecasts. In addition, compared to other studies, recent data that extends over a long period is used. The study describes the used data and discusses the concept of walk-forward validation. Further, various models are employed and tuned to forecast the emission factors, including benchmark, parametric (e.g., SARIMAX), and non-parametric (bagging, random forest, gradient boosting, CNN, LSTM, MLP) models. The study reveals that all applied parametric and non-parametric models yield better results than the benchmark models, while the gradient boosting model has the lowest mean absolute error with 40.66 gCO2/kWh, the lowest mean absolute percentage error 8.17%, and the random forest has the lowest root mean square error with 57.61 gCO2/kWh. However, the potential of the deep learning models was not fully exploited. In a live application, the implementation effort should be evaluated against the benefit of better prediction.

Reprint of: When will Arctic sea ice disappear? Projections of area, extent, thickness, and volume

Rapidly diminishing Arctic summer sea ice is a strong signal of the pace of global climate change. We provide point, interval, and density forecasts for four measures of Arctic sea ice: area, extent, thickness, and volume. Importantly, we enforce the joint constraint that these measures must simultaneously arrive at an ice-free Arctic. We apply this constrained joint forecast procedure to models relating sea ice to atmospheric carbon dioxide concentration and models relating sea ice directly to time. The resulting “carbon-trend” and “time-trend” projections are mutually consistent and predict a nearly ice-free summer Arctic Ocean by the mid-2030s with an 80% probability. Moreover, the carbon-trend projections show that global adoption of a lower carbon path would likely delay the arrival of a seasonally ice-free Arctic by only a few years.

A Novel Interval Forecast for K-Nearest Neighbor Time Series: A Case Study of Durian Export in Thailand

A Novel Interval Forecast for K-Nearest Neighbor Time Series: A Case Study of Durian Export in Thailand

Developing a concept for the economic and social management of a city with due account for the predicted industrial development

Subject. Theoretical, methodological, and practical issues related to the economic and social management of the city with due account of the predicted values of the industrial development.Objectives. Justification of scientific and methodological provisions of a conceptual nature related to urban management and solving local social problems by forecasting the level of industrial development.Methodology. The authors put forward a hypothesis: if the level of industrial development is forecasted accurately, it is possible to plan upcoming changes in the main economic and social indicators of the municipal economy. Theoretically, the hypothesis is based on the method of logical scaling and synthesis of scientific and practical knowledge. Statistical studies were conducted using the method of econometric and financial analysis based on socio-economic indicators of industrial cities in the Southern Federal District of Russia for the period from 2013 to 2022. Forecasting for the subsequent periods is based on an applied approach to constructing estimates of the quasi-maximal likelihood of the level of industrial development, which was carried out using the theory of stochastic differential equations based on methods of probabilistic forecasting.Results and discussion. As a result of the study, it was substantiated that municipal management contributes to the production of material goods and to harmonisation of socio-economic relations between local authorities, businesses, public organisations, and individuals, which are interrelated with the level of industrial development of a city. The developed applied approach to constructing estimates of the quasi-maximal likelihood of values of socio-economic parameters makes it possible to forecast the level of industrial development of cities in the Russian Federation. Point and interval forecasts lay the foundation for planning economic and other indicators. The concept of economic and social management of administrative-territorial units was proposed. The mandatory socio-economic blocks of the concept were supplemented with the functionality of prediction modelling, which requires further discussion, critical understanding, and subsequent improvement. Future changes in local industrial policy need to be analysed and evaluated in terms of their effectiveness in the context of structural modernisation of the economic and organisational mechanism for urban and social management of the city.

An FCM based weather type classification method considering photovoltaic output and meteorological characteristics and its application in power interval forecasting

AbstractWith the increasing installation of photovoltaic (PV) systems, the impact of their randomness and volatility on power system has become a significant concern. To effectively quantify the uncertainty of PV output, it is crucial to develop reliable PV power interval forecasting technology. However, the complex relationship between PV output and meteorological factors makes it challenging for a single forecasting model to meet the forecasting demand. To solve this problem, this paper proposes a weather classification method that takes into account both PV output and meteorological characteristics. Initially, the relationship between PV output and meteorological factors is analyzed, and weather types are classified using fuzzy c‐means algorithm (FCM). Then, an extreme learning machine (ELM) is employed to establish point forecasting model. By combining kernel density estimation, a PV power generation interval forecasting model is derived. The results demonstrate that the FCM‐ELM model achieves higher forecasting accuracy and narrower interval width compared to traditional ELM models, with accuracy improvement of more than 2%. Additionally, the proposed method outperforms seasonal models with an accuracy improvement of more than 1%. The contribution of this paper includes identifying the limitations of traditional weather classification methods, proposing a novel multi‐model approach for PV interval forecasting.

Novel deterministic and probabilistic forecasting methods for crude oil price employing optimized deep learning, statistical and hybrid models

In this paper, individual and hybrid methods are proposed employing optimized statistical and deep learning (DL) models for deterministic (point) and probabilistic (interval) forecasting of crude oil price time series. The statistical models are optimized using the Forecast package of R. To enhance the performance of DL models, a novel pruning DE-DL method is proposed, which employs the differential evolution (DE) algorithm to optimize architecture and continuous and discrete-valued hyper-parameters. The proposed DE-DL method is so generic that it can be applied to optimize different DL models for any supervised learning problem. Five DL models (LSTM, BiLSTM, GRU, CNN, and ConvLSTM) are optimized for forecasting monthly crude oil prices and hybridized with an optimized ARIMA model for developing optimized additive and multiplicative hybrid forecasting models. The effectiveness of the proposed methods is evaluated through deterministic and probabilistic forecasting measures, comparing the results with six optimized statistical models, thirteen machine learning models, five optimized DL models, and ten optimized hybrid models. It is observed from the simulation results that the proposed optimized Additive-ARIMA-GRU hybrid model provides statistically superior forecasts, and the t Location Scale distribution is more suitable than the Gaussian distribution for computing reliable prediction intervals with different significance levels.

Revealing patterns in the influence of variable permeability of well bottomhole zones on the operational modes of underground gas storage facilities

The object of this study is underground gas storage facilities (UGSF). The main problem being solved is to ensure effective management of the operation process of underground gas storage facilities (UGSF) at operational and forecast time intervals. One of the main factors that affect the operating modes of UGSF is significantly non-stationary filtration processes that take place in the bottomhole zones of wells. The complexity of assessing the multifactorial impact on depression/repression around the wells affects both the speed and accuracy of calculating the mode parameters of UGSF operation. Analysis of the results of well studies revealed a significant area of uncertainty in the calculation of the filtration resistance coefficients of their bottomhole zones. A satisfactory accuracy of the result in the expected time was achieved by building a model of integrated consideration of the influence of the parameters of all the bottomhole zones of the wells on the mode of UGSF operation. It turned out that the integrated consideration of the impact on the parameters of the bottomhole zones of the wells neutralized the effect of significant changes in the filtration resistance coefficients of the wells and ensured a sufficient speed of calculation of UGSF operation modes. Simultaneous simulation of ten operating UGSFs under the peak mode of withdrawal the entire available volume of active gas takes no more than six minutes. The speed of simulation of filtration processes in the bottomhole zones of wells ensured finding the best of them according to one or another criterion of operation mode quality. As a result of the research, a model was built and implemented by software, which was tested under real operating conditions and provides optimal planning of UGSF operating modes for given time intervals. Its use is an effective tool for the operational calculation of current modes and technical capacity of UGSF for a given pressure distribution in the system of main gas pipelines. The performance of the constructed mathematical methods has been confirmed by the results of numerical experiments

A novel interval-valued carbon price analysis and forecasting system based on multi-objective ensemble strategy for carbon trading market

Accurate forecasting of carbon price is crucial for the efficient management and stable operation of carbon markets. Earlier studies are limited to point and interval forecasts based on single-valued carbon price and lack analysis and forecasting based on interval-valued carbon price. Therefore, this study proposes a novel analysis and forecasting system from a new perspective of interval-valued carbon price. Specifically, a carbon price analysis sub-system is developed to investigate the directional causal relationship between the upper and lower bounds of the interval-valued carbon price series. The carbon price forecasting sub-system is developed by designing a data preprocessing module, sub-model forecasting module, and multi-objective ensemble module. The data preprocessing module adopts the decomposition algorithm to preprocess the interval-valued carbon price. Then the sub-model forecasting module utilizes multiple neural network models to predict the highest and lowest prices. Finally, the multi-objective ensemble module adopts a non-linear and multi-objective ensemble strategy to ensemble the forecasting results of the sub-models. It can be found that the consideration of both upper and lower bounds of interval-valued carbon price within the range leads to higher prediction accuracy for the highest or lowest price predictions. Additionally, the ensemble model can effectively leverage the strengths of individual sub-models, resulting in more precise and stable predictions. The average absolute percentage errors for the highest and lowest price predictions in the Hubei and Guangzhou carbon trading markets are 0.8574%, 1.2738%, 0.9774%, and 1.8217% respectively, vividly demonstrating the effectiveness of the proposed system in carbon price prediction.

Tunnel performance prediction through degradation inspection and digital twin construction

Civil infrastructures inevitably undergo a degradation process due to extended periods of operation, frequent service requests, and weathering. This paper proposes a methodology for predicting necessary interventions and presents a database of inspection information for tunnels. The model developed correlates performance loss, measured by the tunnel serviceability index (TSI), to defects detected through a 2D grid composed of classified unit cells converted into a virtual representation. To support the framework developed, intervention time estimates were compared to stochastic degradation models presented in the literature. A limit analysis was performed using inverse exponential equations, utilizing data from different sources and supported by a digital representation of the analysis structure. This was done to estimate times with unitary inspection data, deterioration mapping control, and data connection to the developed inspection model. A railway tunnel for ore transport in northern Brazil was selected as a case study to apply the forecast model, as it showed an accelerated deterioration process within a few years of service. The tunnel was divided into four sections that were analyzed using the methodology developed through inspection-sensitive analysis. The section with the lowest service level (TS 1) matched the geological-geotechnical mapping, which indicated a rock mass with high metamorphic grade and susceptibility to weathering agents. The digital model resulted in an inspection digital twin (IDT) prototype that maps the zones with the greatest problems regarding the degradation process. Metadata is assigned to control elements, and there is online connection to a visual database of the tunnel. The target intervention time was set at 16 years by the developed structure, which falls within all forecast intervals calculated by the limit analyses. The inspection DT enables digital monitoring of the structure under analysis, allowing for efficient and optimized management.

РЕТРОСПЕКТИВНИЙ АНАЛІЗ ВАРТОСТІ ПОХИБКИ ПРОГНОЗУ ДЛЯ ПОБУДОВИ БАЛАНСУЮЧИХ ГРУП ВИРОБНИКІВ З ВІДНОВЛЮВАНИХ ДЖЕРЕЛ ЕНЕРГІЇ

The significant increase in the installed capacity of power plants with renewable energy sources and the imbalance of the financial system of the wholesale electricity market of Ukraine prompted the Ministry of Energy to develop an alter-native support mechanism for RES producers. The introduction of a feed-in tariff (FIP), which compensates for the difference between the actual sale price of electricity and the "green" tariff, can help producers receive more money immediately after the electricity is released. However, studies have shown that exiting a balancing group without form-ing a new one can lead to increased costs associated with forecasting error. It is important for manufacturers to form independent balancing groups to compensate for negative consequences. The findings of the article show that there is no single optimal balancing group for all manufacturers, but some groups are often repeated. Switching to a separate balancing group can have a significant economic effect for the manufacturer, reducing the cost of forecasting error compared to being solely responsible for the imbalance. However, the balancing group determined by the method of retrospective calculation of the cost of the forecast error is not stable in the long term. Ref. 8, fig. 2, tab. 3 Key words: renewable sources, electricity market, short-term forecasting, forecast interval, deep learning neural net-works, cost estimation.

Assessment of Wave Energy Converters Based on Historical Data from a Given Point in the Sea

The assessment of wave energy converters is a key issue for planning and managing the economic feasibility wave power plants. However, obtaining reliable assessments is a difficult goal due to the strong stochastic component of wave behaviour. This paper proposes a simple and straightforward assessment method based on empirical data to estimate not only the expected values of converted power, but also their confidence limits. The method combines Gaussian mixed models with the Monte Carlo method. The proposed approach was validated by assessing five converters with data obtained from two different buoys. The daily converted power values agree with the measured wave parameter patterns. Furthermore, all the observed values of monthly generated energy in the three years after the evaluation fell within the forecast intervals, supporting the validity of the proposed approach.

Enhancing Accuracy of Groundwater Level Forecasting with Minimal Computational Complexity Using Temporal Convolutional Network

Multiscale forecasting of groundwater levels (GWLs) is essential for ensuring the sustainable management of groundwater resources, particularly considering the potential impacts of climate change. Such forecasting requires a model that is not only accurate in predicting GWLs but also computationally efficient, ensuring its suitability for practical applications. In this study, a temporal convolutional network (TCN) is implemented to forecast GWLs for 17 monitoring wells possessing diverse hydrogeological characteristics, located across South Korea. Using deep learning, the influence of meteorological variables (i.e., temperature, precipitation) on the forecasted GWLs was investigated by dividing the input features into three categories. Additionally, the models were developed for three forecast intervals (at 1-, 3-, and 6-month lead times) using each category input. When compared with state-of-the-art models, that is, long short-term memory (LSTM) and artificial neural network (ANN), the TCN model showed superior performance and required much less computational complexity. On average, the TCN model outperformed the LSTM model by 24%, 21%, and 25%, and the ANN model by 24%, 37%, and 47%, respectively, for 1-, 3-, and 6-month lead times. Based on these results, the proposed TCN model can be used for real-time GWL forecasting in hydrological applications.

On approximation of linear regression disturbance distribution

Inference on the parameters of a linear regression usually requires the assumption that the disturbances are normally distributed. But sometimes this assumption does not correspond to the residual distribution. Thus, there is a need to infer the disturbances of the regression model from its residuals. In this article, the analysis is mainly focused on estimation of moments of the disturbances based on residuals. The main goal of this article is derivation of the unbiased estimators of the third and forth central moments of the linear regression disturbances. They are applied to estimation parameters of the random component distribution based on empirical data. In addition to the normal distribution of the random component, the gamma distribution and the class of Pearson curves are considered. An example of skewness and kurtosis coefficient estimation is shown. An example of estimating the dominant of the gamma distribution is shown. Finally, different types of point and interval forecasts of the examined variable are presented.

A new perspective of wind speed forecasting: Multi-objective and model selection-based ensemble interval-valued wind speed forecasting system

Wind-speed forecasting is pivotal for optimizing resource utilization and promoting sustainable development. Previous studies have predominantly focused on point and interval forecasts derived from single-valued wind speed series, failing to capture the inherent fluctuations and uncertainties in wind speed. This study introduces a novel approach: a multi-objective and model selection-based ensemble interval-valued wind speed forecasting system. The primary objective is to empower decision-makers with enhanced decision support and improved risk management. The proposed system comprises four integral components: an interval-valued wind-speed preprocessing module, a model library module, a model selection module, and a multi-objective ensemble module. First, the preprocessing module decomposes the complex interval-valued wind speed forecasting task into multiple simpler forecasting subtasks. Subsequently, a model library is constructed for different forecasting subtasks. The model selection module utilizes a comprehensive evaluation metric to select the best-suited prediction model for each forecasting subtask. Finally, the multi-objective ensemble module integrates the subtask prediction results to yield the interval-valued wind speed forecasting outcomes. The most significant findings of this study are: (1) When faced with different forecasting subtasks, the choice of the optimal prediction model varies depending on the nature of the task. Therefore, the results of the model selection also differ with changes in the data characteristics. (2) In the ensemble stage, the importance and contribution of different subtasks may differ. The proposed ensemble module considers the interrelations and interactions between subtasks, resulting in varying weights for each subtask. For the two different datasets from the Chengde wind farm, the interval mean absolute percentage error values were 2.0862 % and 3.3632 %, and the interval standard deviation values of the error were 0.1383 and 0.3206, respectively. The experimental results clearly demonstrate the exceptional performance of the proposed system in interval-valued wind speed forecasting, which provides better decision support and risk management for wind speed forecasting.