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result(s) for
"moving average processes"
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Non‐parametric and adaptive modelling of dynamic periodicity and trend with heteroscedastic and dependent errors
Periodicity and trend are features describing an observed sequence, and extracting these features is an important issue in many scientific fields. However, it is not an easy task for existing methods to analyse simultaneously the trend and dynamics of the periodicity such as time varying frequency and amplitude, and the adaptivity of the analysis to such dynamics and robustness to heteroscedastic dependent errors are not guaranteed. These tasks become even more challenging when there are multiple periodic components. We propose a non‐parametric model to describe the dynamics of multicomponent periodicity and investigate the recently developed synchro‐squeezing transform in extracting these features in the presence of a trend and heteroscedastic dependent errors. The identifiability problem of the non‐parametric periodicity model is studied, and the adaptivity and robustness properties of the synchro‐squeezing transform are theoretically justified in both discrete and continuous time settings. Consequently we have a new technique for decoupling the trend, periodicity and heteroscedastic, dependent error process in a general non‐parametric set‐up. Results of a series of simulations are provided, and the incidence time series of varicella and herpes zoster in Taiwan and respiratory signals observed from a sleep study are analysed.
Journal Article
Complete Convergence for Moving Average Processes under m-WOD Random Variables
The m-widely orthant dependent (m-WOD) sequences are very weak dependent random variables. In the paper, the authors investigate the moving average processes, which is generated by m-WOD random variables. By using the tail cut technique and maximum moment inequality of the m-WOD random variables, moment complete convergence and complete convergence of the maximal partial sums for the moving average processes are obtained, the results generalize and improve some corresponding results of the existing literature.
Journal Article
An Advanced Quality Control Approach: Integrating Quadruple EWMA Strategy for Enhanced Sensitivity in Process Monitoring
This study proposes the Quadruple Exponentially Weighted Moving Average (QEWMA) control chart, a novel monitoring scheme designed to enhance the detection of small-to-moderate process mean shifts in the presence of autocorrelation. While traditional EWMA-based charts often struggle with dependent data, the proposed QEWMA utilizes a four-layered smoothing mechanism to effectively filter noise in Moving Average processes. The performance of the QEWMA chart was rigorously evaluated using the Numerical Integral Equation (NIE) approach to calculate the Average Run Length (ARL) and the Standard Deviation of Run Length (SDRL). Comparative results across MA(1), MA(2), and MA(3) models demonstrate that the QEWMA chart significantly outperforms the standard EWMA, DEWMA, and TEWMA charts, particularly for subtle shifts (δ≤0.10). The practical utility of the proposed chart was further validated through two real-world applications: monitoring Thailand’s daily median income (MA(3)) and gold futures prices (MA(2)). In both applications, the QEWMA chart exhibited superior sensitivity and faster detection rates, providing more reliable signals for economic and financial surveillance. These findings suggest that the QEWMA chart is a robust and highly efficient tool for quality control in complex, autocorrelated industrial and economic environments.
Journal Article
Note on the complete moment convergence of maximal partial sums for moving average process under sublinear expectations
In this paper, the complete moment convergence for the maximal partial sums of moving average processes generated by Yi,−∞
Journal Article
Stationary Reversible Processes of a Moving Average and Autorepression with Residuals as a Moving Average
In this paper, we show how to select an adequate model of a stationary reversible moving-average process of finite order, given the appropriate number of sample correlations. We find the admissibility conditions, under which, for a reversible model of a moving-average process of no higher than the fifth order, a one-to-one correspondence between the coefficients and correlations of the process is established. If the admissibility conditions for sample correlations are met, it is possible to select a reversible stationary model. For higher-order moving-average processes, a mixed autoregression and moving-average model of no higher than the fifth order preliminarily approaches the initial data. This variant also has independent significance since even at small orders of the mixed model, good agreement between the correlations of the model and the sample correlations of the process is obtained. Particular attention is paid to the reversibility of the process since the prediction formulas assume fulfillment of this condition.
Journal Article
Stochastic differential equations with a fractionally filtered delay
In this paper, we introduce a model, the stochastic fractional delay differential equation (SFDDE), which is based on the linear stochastic delay differential equation and produces stationary processes with hyperbolically decaying autocovariance functions. The model departs from the usual way of incorporating this type of long-range dependence into a short-memory model as it is obtained by applying a fractional filter to the drift term rather than to the noise term. The advantages of this approach are that the corresponding long-range dependent solutions are semimartingales and the local behavior of the sample paths is unaffected by the degree of long memory. We prove existence and uniqueness of solutions to the SFDDEs and study their spectral densities and autocovariance functions. Moreover, we define a subclass of SFDDEs which we study in detail and relate to the well-known fractionally integrated CARMA processes. Finally, we consider the task of simulating from the defining SFDDEs.
Journal Article
Quasi-experiments on process dynamics
It is often important to develop an understanding of the dynamic properties of a process. However, it is sometimes difficult if not impossible to conduct deliberate experiments on full-scale industrial plants and processes to gain such insight. Fortunately, intentional or inadvertent process changes that occur in the course of normal operation sometimes offer an opportunity to identify and estimate aspects of the dynamic behaviour. We review the theory of dynamic process modelling based on time series intervention analysis and show how this body of theory can be used for an assessment of the dynamic properties of a process. The ideas are accompanied by a detailed example of the study of a large-scale ceramic plant that was exposed to an intentional but unplanned structural change.
Journal Article
Exact Average Run Length Evaluation for an ARMAX(p,q,r) Process Running on a Modified EWMA Control Chart
In this study, we apply the Fredholm-type integral equation method to derive the explicit formulas of the average run length (ARL) for an autoregressive moving average process with explanatory variables (ARMAX(p,q,r)) with exponential white noise running on a modified exponentially weighted moving average (EWMA) control chart. As a performance measure, we compared the computational times of calculating the ARL based on explicit formulas and the classical numerical integral equation (NIE) method. We found that although the ARLs using both methods were very close with an absolute percentage difference of less than 0.00001%, their calculational times were less than 0.01 and 10 seconds, respectively. Furthermore, the comparison of the performances of the ARL methods for ARMAX(p,q,r) processes with exponential white noise by practical application for time series data comprising exchange rates and the price of energy running on modified and standard EWMA and cumulative sum (CUSUM) control charts using the relative mean index (RMI) criteria. The results show that the explicit formulas method for the ARL of the process on the modified EWMA control chart is more powerful than the CUSUM and standard EWMA control charts.
Journal Article
Enhancement of electric arc furnace reactive power compensation using Grey–Markov prediction method
The time varying nature of electric arc furnace (EAF) gives rise to voltage fluctuations, which produces the effect known as flicker. Employing reactive power compensation devices such as static VAr compensator (SVC) is one of the main approaches to mitigate this phenomenon. By utilising prediction methods to forecast EAFs reactive power consumption for a half-cycle ahead, performance of SVC can be enhanced substantially. This study proposes a rolling Grey model and a Grey–Markov method to predict the actual reactive power of Mobarakeh Steel Company, Isfahan/Iran. To investigate the efficiency of the proposed methods the results are compared with the results of EAFs reactive power compensation when no prediction method is employed. Furthermore, autoregressive moving average (ARMA) models with updating coefficients, which are studied in the literature are used to predict EAF reactive power. Various methods for updating ARMA coefficients including normalised least mean square, recursive least square method and an online genetic algorithm are used. By comparing the indices which are defined using the concept of flicker frequency and power spectral density, the superiority of Grey–Markov and rolling Grey model over the aforementioned prediction methods is investigated.
Journal Article
Complete moment convergence of moving average processes for m-WOD sequence
In this paper, the complete moment convergence for the partial sum of moving average processes Xn=∑i=−∞∞aiYi+n,n≥1 is established under some mild conditions, where Yi,−∞
Journal Article