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The purpose of this study is to propose the time series decomposition approach to analyze and predict the failure data of the repairable systems.

This study employs NHPP to model the failure data. Initially, Nelson's graph method is employed to estimate the mean number of repairs and the MCRF value for the repairable system. Second, the time series decomposition approach is employed to predict the mean number of repairs and MCRF values.

The proposed method can analyze and predict the reliability for repairable systems. It can analyze the combined effect of trend‐cycle components and the seasonal component of the failure data.

This study only adopts simulated data to verify the proposed method. Future research may use other real products' failure data to verify the proposed method. The proposed method is superior to ARIMA and neural network model prediction techniques in the reliability of repairable systems.

Results in this study can provide a valuable reference for engineers when constructing quality feedback systems for assessing current quality conditions, providing logistical support, correcting product design, facilitating optimal component‐replacement and maintenance strategies, and ensuring that products meet quality requirements.

The time series decomposition approach was used to model and analyze software aging and software failure in 2007. However, the time series decomposition approach was rarely used for modeling and analyzing the failure data for repairable systems. This study proposes the time series decomposition approach to analyze and predict the failure data of the repairable systems and the proposed method is better than the ARIMA model and neural networks in predictive accuracy.

Repairable system reliability analysis is very important to industry and, for complex systems, replacing a failed component is the most commonly used corrective maintenance action as it is an inexpensive way to restore the system to its functional state. However, failure data analysis for repairable system is not an easy task and usually a number of assumptions which are difficult to validate have to be made. Despite the fact that time series models have the advantage of few such assumptions and they have been successfully applied in areas such as chemical processes, manufacturing and economics forecasting, its use in the field of reliability prediction has not been that widespread. In this paper, we examine the usefulness of this powerful technique in predicting system failures. Time series models are statistically and theoretically sound in their foundation and no postulation of models is required when analysing failure data. Illustrative examples using actual data are presented. Comparison with the traditional Duane model, which is commonly used for repairable system, is also discussed. The time series method gives satisfactory results in terms of its predictive performance and hence can be a viable alternative to the Duane model.

Purpose – Time-series regression models are applied to analyse transport safety data for three purposes: (1) to develop a relationship between transport accidents (or incidents) and various time-varying factors, with the aim of identifying the most important factors; (2) to develop a time-series accident model in forecasting future accidents for the given values of future time-varying factors and (3) to evaluate the impact of a system-wide policy, education or engineering intervention on accident counts. Regression models for analysing transport safety data are well established, especially in analysing cross-sectional and panel datasets. There is, however, a dearth of research relating to time-series regression models in the transport safety literature. The purpose of this chapter is to examine existing literature with the aim of identifying time-series regression models that have been employed in safety analysis in relation to wider applications. The aim is to identify time-series regression models that are applicable in analysing disaggregated accident counts.

Methodology/Approach – There are two main issues in modelling time-series accident counts: (1) a flexible approach in addressing serial autocorrelation inherent in time-series processes of accident counts and (2) the fact that the conditional distribution (conditioned on past observations and covariates) of accident counts follow a Poisson-type distribution. Various time-series regression models are explored to identify the models most suitable for analysing disaggregated time-series accident datasets. A recently developed time-series regression model – the generalised linear autoregressive and moving average (GLARMA) – has been identified as the best model to analyse safety data.

Findings – The GLARMA model was applied to a time-series dataset of airproxes (aircraft proximity) that indicate airspace safety in the United Kingdom. The aim was to evaluate the impact of an airspace intervention (i.e., the introduction of reduced vertical separation minima, RVSM) on airspace safety while controlling for other factors, such as air transport movements (ATMs) and seasonality. The results indicate that the GLARMA model is more appropriate than a generalised linear model (e.g., Poisson or Poisson-Gamma), and it has been found that the introduction of RVSM has reduced the airprox events by 15%. In addition, it was found that a 1% increase in ATMs within UK airspace would lead to a 1.83% increase in monthly airproxes in UK airspace.

Practical applications – The methodology developed in this chapter is applicable to many time-series processes of accident counts. The models recommended in this chapter could be used to identify different time-varying factors and to evaluate the effectiveness of various policy and engineering interventions on transport safety or similar data (e.g., crimes).

Originality/value of paper – The GLARMA model has not been properly explored in modelling time-series safety data. This new class of model has been applied to a dataset in evaluating the effectiveness of an intervention. The model recommended in this chapter would greatly benefit researchers and analysts working with time-series data.

The purpose of this paper is to present a new quantum‐inspired evolutionary hybrid intelligent (QIEHI) approach, in order to overcome the random walk dilemma for stock market prediction.

The proposed QIEHI method is inspired by the Takens' theorem and performs a quantum‐inspired evolutionary search for the minimum necessary dimension (time lags) embedded in the problem for determining the characteristic phase space that generates the financial time series phenomenon. The approach presented in this paper consists of a quantum‐inspired intelligent model composed of an artificial neural network (ANN) with a modified quantum‐inspired evolutionary algorithm (MQIEA), which is able to evolve the complete ANN architecture and parameters (pruning process), the ANN training algorithm (used to further improve the ANN parameters supplied by the MQIEA), and the most suitable time lags, to better describe the time series phenomenon.

This paper finds that, initially, the proposed QIEHI method chooses the better prediction model, then it performs a behavioral statistical test to adjust time phase distortions that appear in financial time series. Also, an experimental analysis is conducted with the proposed approach using six real‐word stock market times series, and the obtained results are discussed and compared, according to a group of relevant performance metrics, to results found with multilayer perceptron networks and the previously introduced time‐delay added evolutionary forecasting method.

The paper usefully demonstrates how the proposed QIEHI method chooses the best prediction model for the times series representation and performs a behavioral statistical test to adjust time phase distortions that frequently appear in financial time series.

Study conditions of empirical publications on time series modeling and forecasting of electricity prices vary widely, making it difficult to generalize results. The key purpose of the present study is to offer a comparison of different model types and modeling conditions regarding their forecasting performance.

The authors analyze the forecasting performance of AR (autoregressive), MA (moving average), ARMA (autoregressive moving average) and GARCH (generalized autoregressive moving average) models with and without the explanatory variables, that is, power consumption and power generation from wind and solar. Additionally, the authors vary the detailed model specifications (choice of lag-terms) and transformations (using differenced time series or log-prices) of data and, thereby, obtain individual results from various perspectives. All analyses are conducted on rolling calibrating and testing time horizons between 2010 and 2014 on the German/Austrian electricity spot market.

The main result is that the best forecasts are generated by ARMAX models after spike preprocessing and differencing the data.

The present study extends the existing literature on electricity price forecasting by conducting a comprehensive analysis of the forecasting performance of different time series models under varying market conditions. The results of this study, in general, support the decision-making of electricity spot price modelers or forecasting tools regarding the choice of data transformation, segmentation and the specific model selection.

This study analyses the prevalent coronavirus disease (COVID-19) epidemic using machine learning algorithms. The data set used is an API data provided by the John Hopkins University resource centre and used the Web crawler to gather all the data features such as confirmed, recovered and death cases. Because of the unavailability of any COVID-19 drug at the moment, the unvarnished truth is that this outbreak is not expected to end in the near future, so the number of cases of this study would be very date specific. The analysis demonstrated in this paper focuses on the monthly analysis of confirmed, recovered and death cases, which assists to identify the trend and seasonality in the data. The purpose of this study is to explore the essential concepts of time series algorithms and use those concepts to perform time series analysis on the infected cases worldwide and forecast the spread of the virus in the next two weeks and thus aid in health-care services. Lower obtained mean absolute percentage error results of the forecasting time interval validate the model’s credibility.

In this study, the time series analysis of this outbreak forecast was done using the auto-regressive integrated moving average (ARIMA) model and also seasonal auto-regressive integrated moving averages with exogenous regressor (SARIMAX) and optimized to achieve better results.

The inferences of time series forecasting models ARIMA and SARIMAX were efficient to produce exact approximate results. The forecasting results indicate that an increasing trend is observed and there is a high rise in COVID-19 cases in many regions and countries that might face one of its worst days unless and until measures are taken to curb the spread of this disease quickly. The pattern of the rise of the spread of the virus in such countries is exactly mimicking some of the countries of early COVID-19 adoption such as Italy and the USA. Further, the obtained numbers of the models are date specific so the most recent execution of the model would return more recent results. The future scope of the study involves analysis with other models such as long short-term memory and then comparison with time series models.

A time series is a time-stamped data set in which each data point corresponds to a set of observations made at a particular time instance. This work is novel and addresses the COVID-19 with the help of time series analysis. The inferences of time series forecasting models ARIMA and SARIMAX were efficient to produce exact approximate results.

This study constructs time series model, artificial neural networks (ANNs) and statistical topologies to examine the volatility and forecast foreign exchange rates. The Mauritian forex market has been utilized as a case study, and daily data for nominal spot rate (during a time period of five years spanning from 2014 to 2018) for EUR/MUR, GBP/MUR, CAD/MUR and AUD/MUR have been applied for the predictions.

Autoregressive integrated moving average (ARIMA) and generalized autoregressive conditional heteroskedasticity (GARCH) models are used as a basis for time series modelling for the analysis, along with the non-linear autoregressive network with exogenous inputs (NARX) neural network backpropagation algorithm utilizing different training functions, namely, Levenberg–Marquardt (LM), Bayesian regularization and scaled conjugate gradient (SCG) algorithms. The study also features a hybrid kernel principal component analysis (KPCA) using the support vector regression (SVR) algorithm as an additional statistical tool to conduct financial market forecasting modelling. Mean squared error (MSE) and root mean square error (RMSE) are employed as indicators for the performance of the models.

The results demonstrated that the GARCH model performed better in terms of volatility clustering and prediction compared to the ARIMA model. On the other hand, the NARX model indicated that LM and Bayesian regularization training algorithms are the most appropriate method of forecasting the different currency exchange rates as the MSE and RMSE seemed to be the lowest error compared to the other training functions. Meanwhile, the results reported that NARX and KPCA–SVR topologies outperformed the linear time series models due to the theory based on the structural risk minimization principle. Finally, the comparison between the NARX model and KPCA–SVR illustrated that the NARX model outperformed the statistical prediction model. Overall, the study deduced that the NARX topology achieves better prediction performance results compared to time series and statistical parameters.

The foreign exchange market is considered to be instable owing to uncertainties in the economic environment of any country and thus, accurate forecasting of foreign exchange rates is crucial for any foreign exchange activity. The study has an important economic implication as it will help researchers, investors, traders, speculators and financial analysts, users of financial news in banking and financial institutions, money changers, non-banking financial companies and stock exchange institutions in Mauritius to take investment decisions in terms of international portfolios. Moreover, currency rates instability might raise transaction costs and diminish the returns in terms of international trade. Exchange rate volatility raises the need to implement a highly organized risk management measures so as to disclose future trend and movement of the foreign currencies which could act as an essential guidance for foreign exchange participants. By this way, they will be more alert before conducting any forex transactions including hedging, asset pricing or any speculation activity, take corrective actions, thus preventing them from making any potential losses in the future and gain more profit.

This is one of the first studies applying artificial intelligence (AI) while making use of time series modelling, the NARX neural network backpropagation algorithm and hybrid KPCA–SVR to predict forex using multiple currencies in the foreign exchange market in Mauritius.

The purpose of this paper is to describe a real‐world system developed for a large food distribution company which requires forecasting demand for thousands of products across multiple warehouses. The number of different time series that the system must model and predict is on the order of 10⁵. The study details the system's forecasting algorithm which efficiently handles several difficult requirements including the prediction of multiple time series, the need for a continuously self‐updating model, and the desire to automatically identify and analyze various time series characteristics such as seasonal spikes and unprecedented events.

The forecasting algorithm makes use of a hybrid model consisting of both statistical and heuristic techniques to fulfill these requirements and to satisfy a variety of business constraints/rules related to over‐ and under‐stocking.

The robustness of the system has been proven by its heavy and sustained use since being adopted in November 2009 by a company that serves 91 percent of the combined populations of Australia and New Zealand.

This paper provides a case study of a real‐world system that employs a novel hybrid model to forecast multiple time series in a non‐static environment. The value of the model lies in its ability to accurately capture and forecast a very large and constantly changing portfolio of time series efficiently and without human intervention.