Exponentially Weighted Moving Average Model Research Articles

Early Detection of SARS-CoV-2 Epidemic Waves: Lessons from the Syndromic Surveillance in Lombardy, Italy.

We evaluated the performance of the exponentially weighted moving average (EWMA) model for comparing two families of predictors (i.e., structured and unstructured data from visits to the emergency department (ED)) for the early detection of SARS-CoV-2 epidemic waves. The study included data from 1,282,100 ED visits between 1 January 2011 and 9 December 2021 to a local health unit in Lombardy, Italy. A regression model with an autoregressive integrated moving average (ARIMA) error term was fitted. EWMA residual charts were then plotted to detect outliers in the frequency of the daily ED visits made due to the presence of a respiratory syndrome (based on coded diagnoses) or respiratory symptoms (based on free text data). Alarm signals were compared with the number of confirmed SARS-CoV-2 infections. Overall, 150,300 ED visits were encoded as relating to respiratory syndromes and 87,696 to respiratory symptoms. Four strong alarm signals were detected in March and November 2020 and 2021, coinciding with the onset of the pandemic waves. Alarm signals generated for the respiratory symptoms preceded the occurrence of the first and last pandemic waves. We concluded that the EWMA model is a promising tool for predicting pandemic wave onset.

Performance evaluation of internal quality control rules, EWMA, CUSUM, and the novel machine learning model

Abstract Objectives The present study set out to build a machine learning model to incorporate conventional quality control (QC) rules, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) with random forest (RF) algorithm to achieve better performance and to evaluate the performances the models using computer simulation to aid laboratory professionals in QC procedure planning. Methods Conventional QC rules, EWMA, CUSUM, and RF models were implemented on the simulation data using an in-house algorithm. The models’ performances were evaluated on 170,000 simulated QC results using outcome metrics, including the probability of error detection (Ped), probability of false rejection (Pfr), average run length (ARL), and power graph. Results The highest Pfr (0.0404) belonged to the 1–2s rule. The 1–3s rule could not detect errors with a 0.9 Ped up to 4 SD of systematic error. The random forest model had the highest Ped for systematic errors lower than 1 SD. However, ARLs of the model require the combined utility of the RF model with conventional QC rules having lower ARLs or more than one QC measurement is required. Conclusions The RF model presented in this study showed acceptable Ped for most degrees of systematic error. The outcome metrics established in this study will help laboratory professionals planning internal QC.

Feedback adjustment using exponentially weighted moving average schemes

In this study, we discuss the use of exponentially weighted moving average (EWMA) schemes in feedback adjustment for process improvement. By application the different measures of dispersion yield different optimal values. In particular it is suggested that a robust statistic based on the median is more appropriate than the usual mean of square error (MSE).We also consider an autoregressive time series model for modeling the deviations from target and this model is compared with the usual EWMA model. The problem of applying feedback adjustment to a controllable process is discussed and it is shown via a simulation that correlation structure of the data of interest play a critical role on whether the MSE after adjustment is lower than the MSE before adjustment.

Conditional covariance matrix forecast using the hybrid exponentially weighted moving average approach

AbstractThis paper extends the hybrid multivariate exponentially weighted moving average (EWMA) approach to incorporate realized variance for conditional covariance matrix forecast. The proposed estimator employs a realized variance‐based EWMA specification to estimate the conditional variance of returns and a standard return‐based EWMA specification to estimate the correlation between each pair of returns. This hybrid realized variance‐based EWMA estimator produces forecasts of the conditional covariance matrix that are statistically more accurate and informative and economically more useful than those produced by the standard EWMA and the multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models using only daily returns. The evidence of incremental forecast accuracy and the economic value over the intraday range‐based hybrid EWMA estimator is, however, insignificant. Moreover, the hybrid EWMA estimators are less sensitive to the choice of decay factors than the standard EWMA model and thus provide a robust framework to accommodate intradaily information for estimates of daily return volatility while achieving a simplicity and ease of implementation.

Unsupervised online detection and prediction of outliers in streams of sensor data

Outliers are unexpected observations, which deviate from the majority of observations. Outlier detection and prediction are challenging tasks, because outliers are rare by definition. A stream is an unbounded source of data, which has to be processed promptly. This article proposes novel methods for outlier detection and outlier prediction in streams of sensor data. The outlier detection is an independent, unsupervised process, which is implemented using an autoencoder. The outlier detection continuously evaluates if the latest data point mathbf {x}_i from a stream is an inlier or an outlier. This distinction is based on the reconstruction cost accompanied with Chebyshev’s inequality and the EWMA (exponentially weighted moving average) model. The outlier prediction uses the results of the outlier detection to form the required training data. The outlier prediction utilizes LR (logistic regression), SGD (stochastic gradient descent) and the hidden representation provided by the autoencoder to predict outliers in streams. The results of the experiments show that the proposed methods (1) provide accurate results, (2) are calculated in reduced computation time and (3) use a low amount of memory. Our proposed methods are suitable for analyzing streams of sensor data and providing results with low latency. The experiments also indicated that the outlier prediction is able to anticipate the occurrence of outliers in streams of sensor data.

Inference for asymmetric exponentially weighted moving average models

The exponentially weighted moving average (EWMA) model in ‘Risk‐Metrics’ has been a benchmark for controlling and forecasting risks in financial operations. However, it is incapable of capturing the asymmetric volatility effect and the heavy‐tailed innovation, which are two important stylized features of financial returns. We propose a new asymmetric EWMA model driven by the Student's t‐distributed innovations to take these two stylized features into account and study its maximum likelihood estimation and model diagnostic checking. The finite‐sample performance of the estimation and diagnostic test statistic is examined by the simulated data.

Acceptance sampling plans based on EWMA yield index for the first order autoregressive process

Acceptance-sampling plan plays an important role in quality control. Four new sampling plans based on the yield index are proposed to deal with lot sentencing for a first-order autoregressive process. The first plan is based on exponentially weighted moving average (EWMA) model. The other three plans are based on resubmitted, repetitive group sampling (RGS), and multiple dependent state repetitive (MDSR), respectively. The EWMA and MDSR models use the quality information of the current lot and previous lots. The resubmitted and repetitive group sampling plans are allowed resampling under a certain condition. We found that the sample size required for lot sentencing is the most economical for the EWMA model. Moreover, the RGS and MDSR plans are much more efficient than the traditional single sampling plan. The resubmitted scheme has the least efficiency. Considering the acceptable quality level at the producer’s risk and the lot tolerance percent defective at the consumer’s risk, a nonlinear optimisation models are proposed to determine the plan parameters. Two examples are provided to show the applicability of the proposed sampling plans.

Recursive estimation of the exponentially weighted moving average model

The exponentially weighted moving average (EWMA) model is a particular modeling scheme, supported by RiskMetrics, that is capable of forecasting the current level of volatility of financial time series. It is designed to track changes in the conditional variance of financial returns by assigning exponentially decreasing weights to observed past squared measurements. The aim of this paper is twofold. First, it introduces two recursive estimation algorithms that are appropriate for the EWMA model. Both are derived by employing the general recursive prediction error scheme. Moreover, they represent a computationally effective alternative to already established nonrecursive estimation strategies since they are effective in terms of memory storage, computational complexity and detecting structural changes. Second, this paper investigates the prediction ability of the proposed recursive estimation schemes when compared with other common (nonrecursive) estimation methods. The priorities of the suggested recursive estimators are demonstrated by means of a simulation study and an extensive empirical case study of eighteen key world stock indexes. Combinations of recursive predictions are also studied. Such a strategy can be recommended due to its advantageous properties when predicting volatility.

Modelling and predicting the Bitcoin volatility using GARCH models

This paper is the first to forecast the volatility of the Bitcoin/USD exchange rate. It assesses and compares the predictive ability of the generalised autoregressive conditional heteroscedasticity (GARCH) (1,1), the exponentially weighted moving average (EWMA), and the exponential generalised autoregressive conditional heteroscedasticity (EGARCH) (1,1). Models' parameters are first estimated from the in sample Bitcoin/USD exchange rate returns and in sample volatility is calculated. Out of sample volatility is forecasted afterward. Estimated volatilities are then compared to realised volatilities relying on error statistics, after which the models are ranked. The EGARCH (1,1) model outperforms the GARCH (1,1) and EWMA models in both in sample and out of sample contexts with increased accuracy in the out of sample period. Results show an original reflection concern with regard to the nature of the Bitcoin, which behaves differently than traditional currencies. Given the early-stage behaviour of the Bitcoin, results might change in the future.

Stochastic Correlation in Risk Analytics: A Financial Perspective

Risk analytics has been popularized by some of the today’s most successful companies through new theories such as enterprise risk management. Maximizing the benefit from investments on projects can be more based on the correlation structure dynamically from various different sources. It becomes very important to assess the forecasting performance of the stochastic correlation models to achieve higher predictive power for risk analytics. We conduct evaluations of stochastic correlation modeling in risk analytics from a financial perspective in this paper. We compare the out-of-sample forecasting performance of exponentially weighted moving average (EWMA) model of RiskMetrics, the dynamic conditional correlation (DCC) multivariate GARCH, the orthogonal GARCH (OGARCH), and the generalized orthogonal GARCH (GOGARCH) using the data from various markets. We find that OGARCH has the best performance and all the multivariate GARCH models outperform EWMA model in risk measurement.

Macroeconomic Determinants of Volatility for the Gold Price in Ethiopia: The Application of GARCH and EWMA Volatility Models

Modelling and forecasting of commodity price volatility has important applications for asset management, portfolio analysis and risk assessment due to the simple fact that volatility has informational content and contains signals of the market information flow. This article models and forecasts the gold price volatility using the exponentially weighted moving average (EWMA) and the generalized autoregressive conditional heteroscedasticity (GARCH) models for the period from 1998 to 2014. The gold series shows the classical characteristics of financial time series, such as leptokurtic distributions, data dependence and strong serial correlation in squared returns. Hence, the series can be modelled using both EWMA and GARCH-type models. Among the GARCH-type models, GARCH-M(2,2) with Student’s t distribution for the residuals was found to be the best-fit model. Moreover, the manuscript finds that interest rates, exchange rates and crude oil prices have a significant impact on gold volatility. The risk premium effect is found to be positive and statistically significant, suggesting increased volatility is followed by a higher mean. Finally, a comparison is made between the GARCH and the EWMA models. Using the relative mean squared error and mean absolute error measures, the empirical result suggests that GARCH models with explanatory variables are superior for volatility forecasting.

Modeling volatility on the Karachi Stock Exchange, Pakistan

Purpose The current paper aims to fill a gap in the literature by analyzing the nature of volatility on the Karachi Stock Exchange (KSE) 100 index of the KSE, and develop an understanding as to which model is most suitable for measuring volatility among those used. The study contributes significantly to the literature as, compared with the limited previous studies of Pakistan undertaken in the past, it covers three types of data (i.e. daily, weekly and monthly) for the whole period from the introduction of the KSE 100 index on November 2, 1991 to December 31, 2013. In addition, to analyze the impact of global financial crises upon volatility, the data have been divided into pre-crisis (1991-2007) and post-crisis (2008-2013) periods. Design/methodology/approach This study has used an advanced set of volatility models such as autoregressive conditional heteroskedasticity [ARCH (1)], generalized autoregressive conditional heteroskedasticity [GARCH (1, 1)], GARCH in mean [GARCH-M (1, 1)], exponential GARCH [E-GARCH (1, 1)], threshold GARCH [T-GARCH (1, 1)], power GARCH [P-GARCH (1, 1)] and also a simple exponentially weighted moving average (EWMA) model. Findings The results reveal that daily, weekly and monthly return series show non-normal distribution, stationarity and volatility clustering. However, the heteroskedasticity is absent only in the monthly returns making only the EWMA model usable to measure the volatility level in the monthly series. The P-GARCH (1, 1) model proved to be a better model for modeling volatility in the case of daily returns, while the GARCH (1, 1) model proved to be the most appropriate for weekly data based on the Schwarz information criterion (SIC) and log likelihood (LL) functionality. The study shows high persistence of volatility, a mean reverting process and an absence of a risk premium in the KSE market with an insignificant leverage effect only in the case of weekly returns. However, a significant leverage effect is reported regarding the daily series of the KSE 100 index. In addition, to analyze the impact of global financial crises upon volatility, the findings show that the subperiods demonstrated a slightly low volatility and the global economic crisis did not cause a rise in volatility levels. Originality/value Previously, the literature about volatility modeling in Pakistan’s markets has been limited to a few models of relatively small sample size. The current thesis has attempted to overcome these limitations and used diverse models for three types of data series (daily, weekly and monthly). In addition, the Pakistani economy has been beset by turmoil throughout its history, experiencing a range of shocks from the mild to the extreme. This paper has measured the impact of those shocks upon the volatility levels of the KSE.

Implementing EWMA Yield Index for Simple Linear Profiles with One-sided Specifications in Product Acceptance Determination

In this paper, we propose a new acceptance sampling plan based on the exponentially weighted moving average (EWMA) with the yield index for simple linear profiles with one-sided specifications. The EWMA model provides information about current lots' and preceding lots' quality characteristics. The plan parameters are determined according to the smoothing constant of the EWMA statistic and various risks between the producer and the customer. As the smoothing constant equals one, the proposed plan becomes the traditional single sampling plan. The number of profiles required for lot sentencing using the proposed method is more economical than the traditional single sampling plan. The smaller the value of the smoothing constant, the lower the number of profiles required. A practical example from wind turbine manufacturing is applied to illustrate the performance of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

A refrigerant charge fault detection method for variable refrigerant flow (VRF) air-conditioning systems

Degradation occurs in a VRF system after years of operation due to refrigerant leakage, mechanical failure or improper maintenance. VRF systems require approaches to detect faults and sustain its normal operation. This paper proposes a creative statistical method to detect the refrigerant charge faults in VRF systems, which is based on principal component analysis (PCA) and exponentially-weighted moving average (EWMA) control charts. The EWMA model is built with the residual vector of the PCA model. Data of the experimental VRF system is used to validate the advantages of the PCA–EWMA method. Results show that the combined use of PCA and EWMA methods can achieve better fault detection efficiency than PCA based T2-statistic and Q-statistic methods at low fault severity levels. The robustness of the PCA–EWMA method in online fault detection is verified using the data from different type of VRF systems.

A Single Sampling Plan Based on Exponentially Weighted Moving Average Model for Linear Profiles

The exponentially weighted moving average (EWMA) model has been successfully used in acceptance sampling plans. The EWMA model provides the quality information of the current lot and the preceding lots. In addition, a multiple dependent state (MDS) sampling plan considers the quality information of the preceding lots. In this study, we present two new sampling plans for linear profiles. One is based on EWMA model with yield index using the single sampling plan, and the other is based on EWMA model with yield index using the MDS sampling plans. The plan parameters are determined by a nonlinear optimization approach. As the smoothing parameter value equals to one, the first proposed plan becomes the traditional single sampling plan. In addition, we compare the proposed plans with the traditional single sampling plan. The results indicate that the MDS sampling plan based on EWMA model with yield index with smaller value of smoothing parameter performs better than the traditional single sampling plan and the single sampling plan based on EWMA model with yield index in terms of the sample size required. One real example is used to illustrate the proposed plan. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamic margin setting with EWMA volatilities

The optimal clearing margin levels are crucial for default risk management system of a clearing house. The margin levels must be conservatively high enough to provide financial protection in the default loss event, but not too high to cause market liquidity problem. A static margin setting can result in a margin level which is too high. This paper proposes a dynamic margin setting model and methodology based on value-at-risk with simulated exponentially weighted moving average (EWMA) volatilities. The EWMA model gives the largest weight to the most recent innovation, which makes the dynamic setting of the margin levels more plausible. Based on the worst-case-scenario approach, the optimal margin levels can be set by choosing the model parameters as their maximum values from across different historical periods. The back test shows that the margin setting model is not sensitive to any chosen sample period. Both optimal margin level and back test can be run on a daily basis.

What should the value of lambda be in the exponentially weighted moving average volatility model?

Forecasting volatility is fundamental to forecasting parametric models of value-at-risk. The exponentially weighted moving average (EWMA) volatility model is the recommended model for forecasting volatility by the Riskmetrics group. For monthly data, the lambda parameter of the EWMA model is recommended to be set to 0.97. In this study, we empirically investigate if this is the optimal value of lambda in terms of forecasting volatility. Employing monthly realized volatility as the benchmark for testing the value of lambda, it is found that a value of lambda of 0.97 is far from optimal. The tests are robust to a variety of test statistics. It is further found that the optimal value of lambda is time varying and should be based upon recent historical data. The article offers a practical method to increase the reliability and accuracy of value-at-risk forecasts that can be easily implemented within an Excel spreadsheet.

EWMA model based shift-detection methods for detecting covariate shifts in non-stationary environments

Dataset shift is a very common issue wherein the input data distribution shifts over time in non-stationary environments. A broad range of real-world systems face the challenge of dataset shift. In such systems, continuous monitoring of the process behavior and tracking the state of shift are required in order to decide about initiating adaptive corrections in a timely manner. This paper presents novel methods for covariate shift-detection tests based on a two-stage structure for both univariate and multivariate time-series. The first stage works in an online mode and it uses an exponentially weighted moving average (EWMA) model based control chart to detect the covariate shift-point in non-stationary time-series. The second stage validates the shift-detected by first stage using the Kolmogorov–Smirnov statistical hypothesis test (K–S test) in the case of univariate time-series and the Hotelling T-Squared multivariate statistical hypothesis test in the case of multivariate time-series. Additionally, several orthogonal transformations and blind source separation algorithms are investigated to counteract the adverse effect of cross-correlation in multivariate time-series on shift-detection performance. The proposed methods are suitable to be run in real-time. Their performance is evaluated through experiments using several synthetic and real-world datasets. Results show that all the covariate shifts are detected with much reduced false-alarms compared to other methods.

Exponentially weighted moving average chart as a suitable tool for nuchal translucency quality review

This study aimed to design an exponentially weighted moving average (EWMA) chart for the quality review of nuchal translucency (NT) and to assess its performance compared with the methods currently in use: retrospective distribution-based methods and the cumulative sum (CUSUM) chart. The EWMA model was designed for NT quality review using simulation. The NT measurements obtained during routine first-trimester screening in our centre over a two-and-a-half-year period were retrieved from the database. The NT distribution parameters, EWMA and CUSUM chart were established, and the methods were compared. On the basis of the results from the simulation, the optimal EWMA settings were established. A set of 9338 NT measurements obtained from nine sonographers was used to construct the EWMA and CUSUM charts and to calculate the distribution parameters. Distribution-based methods were unable to reveal the temporal periods of poor performance. The EWMA model agreed closely with the CUSUM but had the advantage promptly indicating when the process returned to an in-control state, thus extending its use to long-term prospective and retrospective quality assessments. The EWMA provides a universal, easy and efficient tool for NT quality review when the prompt and effective detection of suboptimal performance is desired.

Dynamic hedge fund portfolio construction

In this paper, we provide further evidence on the use of multivariate conditional volatility models in hedge fund risk measurement and portfolio allocation, using monthly hedge fund index return data for the period 1990 to 2009. Building on Giamouridis and Vrontos (2007), we consider a broad set of multivariate GARCH models as well as the simpler exponentially weighted moving average (EWMA) estimator of RiskMetrics (1996). We find that while multivariate GARCH models provide some improvement in portfolio performance over static models, they are generally dominated by the EWMA model. In particular, in addition to providing better risk-adjusted performance, the EWMA model leads to dynamic allocation strategies that have substantially lower turnover and could therefore be expected to involve lower transaction costs. Moreover, we show that these results are robust across low-volatility and high-volatility sub-periods.