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The similarity measurement of time series is an important research in time series detection, which is a basic work of time series clustering, anomaly discovery, prediction and many other data mining problems. The purpose of this paper is to design a new similarity measurement algorithm to improve the performance of the original similarity measurement algorithm. The subsequence morphological information is taken into account by the proposed algorithm, and time series is represented by a pattern, so the similarity measurement algorithm is more accurate.

Following some previous researches on similarity measurement, an improved method is presented. This new method combines morphological representation and dynamic time warping (DTW) technique to measure the similarities of time series. After the segmentation of time series data into segments, three parameter values of median, point number and slope are introduced into the improved distance measurement formula. The effectiveness of the morphological weighted DTW algorithm (MW-DTW) is demonstrated by the example of momentum wheel data of an aircraft attitude control system.

The improved method is insensitive to the distortion and expansion of time axis and can be used to detect the morphological changes of time series data. Simulation results confirm that this method proposed in this paper has a high accuracy of similarity measurement.

This improved method has been used to solve the problem of similarity measurement in time series, which is widely emerged in different fields of science and engineering, such as the field of control, measurement, monitoring, process signal processing and economic analysis.

In the similarity measurement of time series, the distance between sequences is often used as the only detection index. The results of similarity measurement should not be affected by the longitudinal or transverse stretching and translation changes of the sequence, so it is necessary to incorporate the morphological changes of the sequence into similarity measurement. The MW-DTW is more suitable for the actual situation. At the same time, the MW-DTW algorithm reduces the computational complexity by transforming the computational object to subsequences.

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.

Given the recent explosion of interest in streaming data and online algorithms, clustering of time series subsequences has received much attention. In this work we make a surprising claim. Clustering of time series subsequences is completely meaningless. More concretely, clusters extracted from these time series are forced to obey a certain constraint that is pathologically unlikely to be satisfied by any dataset, and because of this, the clusters extracted by any clustering algorithm are essentially random. While this constraint can be intuitively demonstrated with a simple illustration and is simple to prove, it has never appeared in the literature. We can justify calling our claim surprising, since it invalidates the contribution of dozens of previously published papers. We will justify our claim with a theorem, illustrative examples, and a comprehensive set of experiments on reimplementations of previous work.

This research study aims to design a novel risk-managed time-series momentum approach. The present study also examines the time-series momentum effect in the Indian equity market. Apart from this, the study also proposes a novel risk-managed time-series momentum approach.

The study considers the adjusted monthly closing prices of the stocks listed on the Bombay Stock Exchange from January 1996 to December 2020 to formulate long-short portfolios. Newey–West t statistics were used to test the significance of momentum returns. The present research has considered standard risk factors, i.e. market, size and value, to evaluate the risk-adjusted performance of time-series momentum portfolios.

The present research reports a substantial absolute momentum effect in the Indian equity market. However, absolute momentum strategies are exposed to occasional severe losses. The proposed time-series momentum approach not only yields 2.5 times higher return than the standard time-series momentum approach but also causes substantial enhancement in downside risks and higher-order moments.

The study's outcomes offer valuable insights for professional investors, capital market regulators and asset management companies.

This study is one of the pioneers attempting to test the time-series momentum effect in emerging economies. Besides, current research contributes to the escalating literature on risk-managed momentum by suggesting a novel revised time-series momentum approach.

The common methods for clustering time series are the use of specific distance criteria or the use of standard clustering algorithms. Ensemble clustering is one of the common techniques used in data mining to increase the accuracy of clustering. In this study, based on segmentation, selecting the best segments, and using ensemble clustering for selected segments, a multistep approach has been developed for the whole clustering of time series data.

First, this approach divides the time series dataset into equal segments. In the next step, using one or more internal clustering criteria, the best segments are selected, and then the selected segments are combined for final clustering. By using a loop and how to select the best segments for the final clustering (using one criterion or several criteria simultaneously), two algorithms have been developed in different settings. A logarithmic relationship limits the number of segments created in the loop.

According to Rand's external criteria and statistical tests, at first, the best setting of the two developed algorithms has been selected. Then this setting has been compared to different algorithms in the literature on clustering accuracy and execution time. The obtained results indicate more accuracy and less execution time for the proposed approach.

This paper proposed a fast and accurate approach for time series clustering in three main steps. This is the first work that uses a combination of segmentation and ensemble clustering. More accuracy and less execution time are the remarkable achievements of this study.

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.

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.

The paper aims to estimate the segment size and alphabet size of Symbolic Aggregate approXimation (SAX). In SAX, time series data are divided into a set of equal-sized segments. Each segment is represented by its mean value and mapped with an alphabet, where the number of adopted symbols is called alphabet size. Both parameters control data compression ratio and accuracy of time series mining tasks. Besides, optimal parameters selection highly depends on different application and data sets. In fact, these parameters are iteratively selected by analyzing entire data sets, which limits handling of the huge amount of time series and reduces the applicability of SAX.

The segment size is estimated based on Shannon sampling theorem (autoSAXSD_S) and adaptive hierarchical segmentation (autoSAXSD_M). As for the alphabet size, it is focused on how mean values of all the segments are distributed. The small number of alphabet size is set for large distribution to easily distinguish the difference among segments.

Experimental evaluation using University of California Riverside (UCR) data sets shows that the proposed schemes are able to select the parameters well with high classification accuracy and show comparable efficiency in comparison with state-of-the-art methods, SAX and auto_iSAX.

The originality of this paper is the way to find out the optimal parameters of SAX using the proposed estimation schemes. The first parameter segment size is automatically estimated on two approaches and the second parameter alphabet size is estimated on the most frequent average (mean) value among segments.

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.