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Accurately predicting the price of carbon is an effective way of ensuring the stability of the carbon trading market and reducing carbon emissions. Aiming at the non-smooth and non-linear characteristics of carbon price, this paper proposes a novel hybrid prediction model based on improved feature extraction and non-linear integration, which is built on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), fuzzy entropy (FuzzyEn), improved random forest using particle swarm optimisation (PSORF), extreme learning machine (ELM), long short-term memory (LSTM), non-linear integration based on multiple linear regression (MLR) and random forest (MLRRF), and error correction with the autoregressive integrated moving average model (ARIMA), named CEEMDAN-FuzzyEn-PSORF-ELM-LSTM-MLRRF-ARIMA. Firstly, CEEMDAN is combined with FuzzyEn in the feature selection process to improve extraction efficiency and reliability. Secondly, at the critical prediction stage, PSORF, ELM, and LSTM are selected to predict high, medium, and low complexity sequences, respectively. Thirdly, the reconstructed sequences are assembled by applying MLRRF, which can effectively improve the prediction accuracy and generalisation ability. Finally, error correction is conducted using ARIMA to obtain the final forecasting results, and the Diebold–Mariano test (DM test) is introduced for a comprehensive evaluation of the models. With respect to carbon prices in the pilot regions of Shenzhen and Hubei, the results indicate that the proposed model has higher prediction accuracy and robustness. The main contributions of this paper are the improved feature extraction and the innovative combination of multiple linear regression and random forests into a non-linear integrated framework for carbon price forecasting. However, further optimisation is still a work in progress. [ABSTRACT FROM AUTHOR]

With developments in global economic integration and the increase in future economic uncertainty, it is imperative to have the ability to predict future capital in relation to financial capital inflow and outflow predictions to ensure capital optimization is within a controllable range within the current macroeconomic environment and situation. This paper proposes an automated capital prediction strategy for the capital supply chain using time series analysis artificial intelligence methods. Firstly, to analyze the fluctuation and tail risk of the financial characteristics, the paper explores the financial characteristics for measuring the dynamic VaR from the perspectives of volatility, tail, and peak with the Bayesian peaks over threshold (POT) model. Following this, in order to make the modeling more refined, the forecast targets are split before modeling with seasonal Autoregressive Integrated Moving Average (ARIMA) models and Prophet models. Finally, the time series modeling of the wavelet Long Short-Term Memory (LSTM) model is carried out using a two-part analysis method to determine the linear separated wavelet and non-linear embedded wavelet parts to predict strong volatility in financial capital. Taking the user capital flow of the Yu'e Bao platform, the results prove the feasibility and prediction accuracy of the innovative model proposed. [ABSTRACT FROM AUTHOR]

The issue of climate change holds immense significance, affecting various aspects of life, including the environment, the interaction between soil conditions and the atmosphere, and agriculture. Over the past few decades, a range of spatio-temporal and Deep Neural Network (DNN) techniques had been proposed within the field of Machine Learning (ML) for climate forecasting, using spatial and temporal data. The forecasting model in this paper is highly complex, particularly due to the presence of nonlinear data in the residual modeling of General Space-Time Autoregressive Integrated Moving Average (GSTARIMA), which represented nonstationary data with time and location dependencies. This model effectively captured trends and seasonal data with time and location dependencies. On the other hand, DNNs proved reliable for modeling nonlinear data that posed challenges for spatio-temporal approaches. This research presented a comprehensive overview of the integrated approach between the GSTARIMA model and DNNs, following the six-stage Data Analytics Lifecycle methodology. The focus was primarily on previous works conducted between 2013 and 2022. The review showed that the GSTARIMA–DNN integration model was a promising tool for forecasting climate in a specific region in the future. Although spatio-temporal and DNN approaches have been widely employed for predicting the climate and its impact on human life due to their computational efficiency and ability to handle complex problems, the proposed method is expected to be universally accepted for integrating these models, which encompass location and time dependencies. Furthermore, it was found that the GSTARIMA–DNN method, incorporating multivariate variables, locations, and multiple hidden layers, was suitable for short-term climate forecasting. Finally, this paper presented several future directions and recommendations for further research. [ABSTRACT FROM AUTHOR]

Urban rail transit offers advantages such as high safety, energy efficiency, and environmental friendliness. With cities rapidly expanding, travelers are increasingly using rail systems, heightening demands for passenger capacity and efficiency while also pressuring these networks. Passenger flow forecasting is an essential part of transportation systems. Short-term passenger flow forecasting for rail transit can estimate future station volumes, providing valuable data to guide operations management and mitigate congestion. This paper investigates short-term forecasting for Suzhou's Shantang Street station. Shantang Street's high commercial presence and distinct weekday versus weekend ridership patterns make it an interesting test case, making it a representative subway station. Wavelet denoising and Long Short Term Memory (LSTM) were combined to predict short-term flows, comparing the results to those of standalone LSTM, Support Vector Regression (SVR), Artificial Neural Network (ANN), and Autoregressive Integrated Moving Average Model (ARIMA). This study illustrates that the algorithms adopted exhibit good performance for passenger prediction. The LSTM model with wavelet denoising proved most accurate, demonstrating applicability for short-term rail transit forecasting and practical significance. The research findings can provide fundamental recommendations for implementing appropriate passenger flow control measures at stations and offer effective references for predicting passenger flow and mitigating traffic pressure in various cities. [ABSTRACT FROM AUTHOR]

Technical and technological developments in recent decades have stimulated the rapid development of methods and tools in the field of statistical process quality control, which also includes control charts. The principle of control charts defined by Dr. W. Shewhart has been known for more than 100 years. Since then, they have been used in many industries to monitor and control processes. This paper aims to assess the possibilities of use and the selection of the most suitable type of control chart for monitoring the quality of a process depending on its nature. This tool should help operators in monitoring coking time, which is one of the important control variables affecting the quality of coke production. The autoregressive nature of the variable being monitored was considered when selecting a suitable control chart from the group of options considered. In addition to the three traditional types of control charts (Shewhart's, CUSUM, and EWMA), which were applied to the residuals of individual values of different types of ARIMA models, various statistical tests, and plots, a dynamic EWMA control chart was also used. Its advantage over traditional control charts applied to residuals is that it works with directly measured coking time data. This chart is intended to serve as a method to monitor the process. Its role is only to alert the process operator to the occurrence of problems with the length of the coking time. [ABSTRACT FROM AUTHOR]

In commerce, economics, engineering and the sciences, quantitative methods based on statistical models for forecasting are very useful tools for prediction and decision. There is an abundance of papers on forecasting for continuous-time series but relatively fewer papers for time series of counts which require special consideration due to the integer nature of the data. A popular method for modelling is the method of mixtures which is known for its flexibility and thus improved prediction capability. This paper studies the coherent forecasting for a flexible stationary mixture of Pegram and thinning (MPT) process, and develops the likelihood-based asymptotic distribution. Score functions and the Fisher information matrix are presented. Numerical studies are used to assess the performance of the forecasting methods. Also, a comparison is made with existing discrete-valued time series models. Finally, the practical application is illustrated with two sets of real data. It is shown that the mixture model provides good forecasting performance. [ABSTRACT FROM AUTHOR]

The seasonal autoregressive integrated moving average with exogenous factors (SARIMAX) has shown promising results in modeling small and sparse observed time-series data by capturing linear features using independent and dependent variables. Long short-term memory (LSTM) is a promising neural network for learning nonlinear dependence features from data. With the increase in wildlife roadkill patterns, the SARIMAX-only and LSTM-only models would likely fail to learn the precise endogenous and/or exogenous variables driven by this wildlife roadkill data. In this paper, we design and implement an error correction mathematical framework based on LSTM-only. The framework extracts features from the residual error generated by a SARIMAX-only model. The learned residual features correct the output time-series prediction of the SARIMAX-only model. The process combines SARIMAX-only predictions and LSTM-only residual predictions to obtain a hybrid SARIMAX-LSTM. The models are evaluated using South African wildlife–vehicle collision datasets, and the experiments show that compared to single models, SARIMAX-LSTM increases the accuracy of a taxon whose linear components outweigh the nonlinear ones. In addition, the hybrid model fails to outperform LSTM-only when a taxon contains more nonlinear components rather than linear components. Our assumption of the results is that the collected exogenous and endogenous data are insufficient, which limits the hybrid model's performance since it cannot accurately detect seasonality on residuals from SARIMAX-only and minimize the SARIMAX-LSTM error. We conclude that the error correction framework should be preferred over single models in wildlife time-series modeling and predictions when a dataset contains more linear components. Adding more related data may improve the prediction performance of SARIMAX-LSTM. [ABSTRACT FROM AUTHOR]

Forecasting future values of Colombian companies traded on the New York Stock Exchange is a daily challenge for investors, due to these stocks' high volatility. There are several forecasting models for forecasting time series data, such as the autoregressive integrated moving average (ARIMA) model, which has been considered the most-used regression model in time series prediction for the last four decades, although the ARIMA model cannot estimate non-linear regression behavior caused by high volatility in the time series. In addition, the support vector regression (SVR) model is a pioneering machine learning approach for solving nonlinear regression estimation procedures. For this reason, this paper proposes using a hybrid model benefiting from ARIMA and support vector regression (SVR) models to forecast daily and cumulative returns of selected Colombian companies. For testing purposes, close prices of Bancolombia, Ecopetrol, Tecnoglass, and Grupo Aval were used; these are relevant Colombian organizations quoted on the New York Stock Exchange (NYSE). [ABSTRACT FROM AUTHOR]

The research paper is devoted to developing a mathematical approach for dealing with time-varying parameters in rolling window logit models for credit risk assessment. Forecasting coefficients yields a better model accuracy than a trivial approach of using computed past statistics parameters for the next time period. In this paper, a new method of dealing with time-varying parameters of scoring models is proposed, which is aimed at computing the default probability of a borrower. It was empirically shown that in a continuously changing economic environment factors' influence on a target variable is also changing. Therefore, forecasting coefficients yields a better financial result than simply applying parameters obtained by accumulated statistics over past time periods. The paper develops a new theoretical approach, incorporating a combination of the ARIMA class model, the DCC-GARCH model and the state–space model, which is more accurate, than using only the ARIMA model. Rigorous simulation testing is provided to confirm the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The peaks-over-threshold (POT) method has a long tradition in modelling extremes in environmental variables. However, it has originally been introduced under the assumption of independently and identically distributed (iid) data. Since environmental data often exhibits a time series structure, this assumption is likely to be violated due to short- and long-term dependencies in practical settings, leading to clustering of high-threshold exceedances. In this paper, we first review popular approaches that either focus on modelling short- or long-range dynamics explicitly. In particular, we consider conditional POT variants and the Mittag–Leffler distribution modelling waiting times between exceedances. Further, we propose a new two-step approach capturing both short- and long-range correlations simultaneously. We suggest the autoregressive fractionally integrated moving average peaks-over-threshold (ARFIMA-POT) approach, which in a first step fits an ARFIMA model to the original series and then in a second step utilises a classical POT model for the residuals. Applying these models to an oceanographic time series of significant wave heights measured on the Sefton coast (UK), we find that neither solely modelling short- nor long-range dependencies satisfactorily explains the clustering of extremes. The ARFIMA-POT approach, however, provides a significant improvement in terms of model fit, underlining the need for models that jointly incorporate short- and long-range dependence to address extremal clustering, and their theoretical justification. [ABSTRACT FROM AUTHOR]

Forecasting has become essential in different economic sectors for decision making in local and regional policies. Therefore, the aim of this paper is to use and compare performance of two linear models to predict future values of a measure of real profit for a group of companies in the fashion sector, as a financial strategy to determine the economic behavior of this industry. With forecasting purposes, Exponential Smoothing (ES) and autoregressive integrated moving averages (ARIMA) models were used for yearly data. ES and ARIMA models are widely used in statistical methods for time series forecasting. Accuracy metrics were used to select the model with best performance and ES parameters. For the real profit measure of the financial performance of the fashion sector in Colombia EBITDA (Earnings Before Interest, Taxes, Depreciation, and Amortization) was used and was calculated using multiple SQL queries. [ABSTRACT FROM AUTHOR]

This study implements various, maximum overlap, discrete wavelet transform filters to model and forecast the time-dependent mortality index of the Lee-Carter model. The choice of appropriate wavelet filters is essential in effectively capturing the dynamics in a period. This cannot be accomplished by using the ARIMA model alone. In this paper, the ARIMA model is enhanced with the integration of various maximal overlap discrete wavelet transform filters such as the least asymmetric, best-localized, and Coiflet filters. These models are then applied to the mortality data of Australia, England, France, Japan, and USA. The accuracy of the projecting log of death rates of the MODWT-ARIMA model with the aforementioned wavelet filters are assessed using mean absolute error, mean absolute percentage error, and mean absolute scaled error. The MODWT-ARIMA (5,1,0) model with the BL14 filter gives the best fit to the log of death rates data for males, females, and total population, for all five countries studied. Implementing the MODWT leads towards improvement in the performance of the standard framework of the LC model in forecasting mortality rates. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of predicting time series data using the autoregressive integrated moving average (ARIMA) model in an online manner. Existing algorithms require model selection, which is time consuming and unsuitable for the setting of online learning. Using adaptive online learning techniques, we develop algorithms for fitting ARIMA models without hyperparameters. The regret analysis and experiments on both synthetic and real-world datasets show that the performance of the proposed algorithms can be guaranteed in both theory and practice. [ABSTRACT FROM AUTHOR]

Real-time monitoring of the economy is based on activity indicators that show regular patterns such as trends, seasonality and business cycles. However, parametric and non-parametric methods for signal extraction produce revisions at the end of the sample, and the arrival of new data makes it difficult to assess the state of the economy. In this paper, we compare two signal extraction procedures: Circulant Singular Spectral Analysis, CiSSA, a non-parametric technique in which we can extract components associated with desired frequencies, and a parametric method based on ARIMA modelling. Through a set of simulations, we show that the magnitude of the revisions produced by CiSSA converges to zero quicker, and it is smaller than that of the alternative procedure. [ABSTRACT FROM AUTHOR]

A hybrid model for the time series of complex structure (HMTS) was proposed. It is based on the combination of function expansions in a wavelet series with ARIMA models. HMTS has regular and anomalous components. The time series components, obtained after expansion, have a simpler structure that makes it possible to identify the ARIMA model if the components are stationary. This allows us to obtain a more accurate ARIMA model for a time series of complicated structure and to extend the area for application. To identify the HMTS anomalous component, threshold functions are applied. This paper describes a technique to identify HMTS and proposes operations to detect anomalies. With the example of an ionospheric parameter time series, we show the HMTS efficiency, describe the results and their application in detecting ionospheric anomalies. The HMTS was compared with the nonlinear autoregression neural network NARX, which confirmed HMTS efficiency. [ABSTRACT FROM AUTHOR]

Autoregressive models have played an important role in time series. In this paper, an autoregressive model based on the skew-normal distribution is considered. The estimation of its parameters is carried out by using the expectation–maximization algorithm, whereas the diagnostic analytics are conducted by means of the local influence method. Normal curvatures for the model under four perturbation schemes are established. Simulation studies are conducted to evaluate the performance of the proposed procedure. In addition, an empirical example involving weekly financial return data are analyzed using the procedure with the proposed diagnostic analytics, which has improved the model fit. [ABSTRACT FROM AUTHOR]

This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]