Autocorrelation In Data Research Articles

How Hotelling’s T<sup>2</sup> Control Chart Performed with the Autocorrelation Imposed when Controlled Correlation is Used

Control charts are made to identify assignable causes of difference that could exist in production processes. It is usually believed the probability distribution which represents the actual observations includes a known functional form and it is constant as time passes. However, in reality, observations obtained through continuous and discrete procedures in many cases are serially correlated. Autocorrelation not just breaks the actual independence assumption of conventional control charts, but also can impact the efficiency associated with control charts negatively. In this article, we are going to investigate the impact of autocorrelation to the performance of Hotelling T2 control chart in which autocorrelated data were utilized to construct the Hotelling’s T2 chart with induced autocorrelation from various levels of correlation at different sample sizes. Simulations had been done to generate the data set used to construct the Hotelling’s T2 control chart and the outcomes implies that all of the control charts constructed had their points outside the designed control limits, that confirmed the effect of autocorrelation to the performance of the Hotelling’s T2 control chart. Suggestions on how to tackle the problem was proposed.

A Robust Control Chart for Monitoring the Mean of an Autocorrelated Process

Residual control charts are frequently used for monitoring autocorrelated processes. In the design of a residual control chart, values of the true process parameters are often estimated from a reference sample of in-control observations by using least squares (LS) estimators. We propose a robust control chart for autocorrelated data by using Modified Maximum Likelihood (MML) estimators in constructing a residual control chart. Average run length (ARL) is simulated for the proposed chart when the underlying process is AR(1). The results show the superiority of the new chart under several situations. Moreover, the chart is robust to plausible deviations from assumed distribution of errors.

Uncertainty, priors, autocorrelation and disparate data in downscaling of species distributions

AbstractAimWe provide a step‐by‐step demonstration of how a map of species' detections at continental extent can be downscaled to a fine‐grain map of occurrence probabilities using a two‐scale hierarchical Bayesian modelling (HBM). The method requires fine‐grain environmental data, but it does not require fine‐grain data on species detections. We demonstrate how it can incorporate spatial autocorrelation (SAC) and informative priors based on known habitat preferences, and how it can provide maps of uncertainty about the downscaled predictions.LocationUSA.MethodsWe used range map and point record data on the distribution of American three‐toed woodpecker (Picoides dorsalis, Baird 1858) to produce a reliable coarse‐grain (160 km × 160 km) map of the species' presences and absences. We developed an HBM combining coarse‐grain information with fine‐grain (20 km × 20 km) environmental data to predict probabilities of occurrence at the fine grain together with 95% prediction intervals. The model incorporated SAC in the form of conditional autoregressive (CAR) random effects. It also incorporated prior knowledge on habitat preferences in the form of prior distribution of parameters. We evaluated the predictions using 751 well‐surveyed fine‐grain cells.ResultsOur HBM produced reliable fine‐grain probabilities of occurrence that matched the detections and non‐detections in the 751 validation cells well (Nagelkerke's R2 = 0.69, AUC = 0.93). By mapping the uncertainty in the downscaled predictions, we identified areas of low uncertainty and high occurrence probability, as well as large areas of high prediction uncertainty. Mapping the autocorrelation term enabled to identify areas of likely spurious observations.Main conclusionsWe demonstrate how hierarchical downscaling enables estimation of species distributions at grains finer than the grain of the original data. The approach can integrate various types of information on distribution and biology in a single statistical framework, and it enables propagating and mapping prediction uncertainty. Yet there are also computational challenges for large datasets.

Simulation modelling analysis for small sets of single-subject data collected over time

The behavioural data yielded by single subjects in naturalistic and controlled settings likely contain valuable information to scientists and practitioners alike. Although some of the properties unique to this data complicate statistical analysis, progress has been made in developing specialised techniques for rigorous data evaluation. There are no perfect tests currently available to analyse short autocorrelated data streams, but there are some promising approaches that warrant further development. Although many approaches have been proposed, and some appear better than others, they all have some limitations. When data sets are large enough (∼30 data points per phase), the researcher has a reasonably rich pallet of statistical tools from which to choose. However, when the data set is sparse, the analytical options dwindle. Simulation modelling analysis (SMA; described in this article) is a relatively new technique that appears to offer acceptable Type-I and Type-II error rate control with short streams of autocorrelated data. However, at this point, it is probably too early to endorse any specific statistical approaches for short, autocorrelated time-series data streams. While SMA shows promise, more work is needed to verify that it is capable of reliable Type-I and Type-II error performance with short serially dependent streams of data.

Chaotic substitution for highly autocorrelated data in encryption algorithm

This paper addresses the major drawback of substitution-box in highly auto-correlated data and proposes a novel chaotic substitution technique for encryption algorithm to sort the problem. Simulation results reveal that the overall strength of the proposed technique for encryption is much stronger than most of the existing encryption techniques. Furthermore, few statistical security analyses have also been done to show the strength of anticipated algorithm.

Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies

On-line monitoring of process variability is strategic to achieve high standards of quality and maintain at acceptable levels the number of nonconforming items. Shewhart control charts are the simplest Statistical Process Control (SPC) procedure to achieve this goal. An efficient implementation of a control chart requires the optimal selection of its design parameters. They can be selected according to an economic-statistical objective: an expected total cost per unit of time incurred during production is minimized subject to a statistical constraint limiting the number of false alarms issued by the control chart. This paper investigates the economic-statistical design of Shewhart control charts implementing skip sampling strategies for constructing subgroups and monitoring autocorrelated AR(1) processes. Implementing skip sampling strategies within a rational subgroup reduces the negative effects of autocorrelation on the statistical performance of the Shewhart control chart. A wide benchmark of examples has been generated as a screening experimental design to study the process and cost factors influencing the selection of the sampling strategy. Regression models have been fitted to the results to help practitioners in the selection of the most convenient sampling strategy. Finally, a sensitivity analysis has been performed to evaluate how the parameters misspecification biases the evaluation of the optimal cost per unit of time.

Detection of long-term trends in monthly hydro-climatic series of Colombia through Empirical Mode Decomposition

We test for the existence of long-term trends in 25- to 50-year long series of monthly rainfall, average river discharges, and minimum air temperatures in Colombia. The Empirical Mode Decomposition method is used as a mathematical filter to decompose a given time series into a finite number of intrinsic mode functions, assuming the coexistence of different frequency oscillatory modes in the series, and that the residual captures the likely existing long-term trends. The Mann-Kendall test for autocorrelated data is used to assess the statistical significance of the identified trends, and the Sen test is used to quantify their magnitudes. Results show that 62 % of river discharge series exhibit significant decreasing trends between 0.01-1.92 m 3 s −1 per year, which are highly consistent downstream albeit with different ratios between the trend magnitudes and mean discharges. Most minimum temperature series (87 %) exhibit increasing trends (0.01-0.08 °Cyr −1). Results for precipitation series are inconclusive owing to the mixing between increasing trends (41 %, between 0.1-7.0 mm yr −1) and decreasing trends (44 %, between 0.1-7.4 mm yr −1), with no clear-cut geographical pattern, except for the increasing trend identified along the Pacific region, consistent with the increasing trend identified in the strength of the Choco low-level wind jet off the Pacific coast of Colombia, an important moisture source of continental precipitation. Our results contribute to discerning between signals of climate change and climate variability in tropical South America.

Some Current Directions in the Theory and Application of Statistical Process Monitoring

The purpose of this paper is to provide an overview and our perspective of recent research and applications of statistical process monitoring. The focus is on work done over the past decade or so. We review briefly a number of important areas, including health-related monitoring, spatiotemporal surveillance, profile monitoring, use of autocorrelated data, the effect of estimation error, and high-dimensional monitoring, among others. We briefly discuss the choice of performance metrics. We provide references and offer some directions for further research.

A modified range (R) chart to monitor process dispersion of autocorrelated data

The range (R) charts are widely used in industries to monitor the process dispersion. Monitoring process dispersion is as important as monitoring the process mean. In actual practice, some process outputs are correlated, the performance of R chart may have adverse effect on it. The performance of the chart is measured in terms of the average run length (ARL), which is the average number of samples before an out-of-control signal is obtained. Ultimately, the performance of these charts may be suspected due to autocorrelation. In this paper, an attempt is made to counter the autocorrelation by designing the new R chart named modified R chart, based on sum of chi-squares. The performance of this modified R chart is computed for sample sizes of 3 and 5. It is observed that when the level of correlation (Φ) increases, the performance of the modified R chart deteriorates. Moreover, the modified R chart for sample size of three and five is compared with adaptive R charts, suggested by Lee (2011) at zero level of correlation (Φ). It is found that modified R chart performs better than adaptive R charts for most of the cases.

Developing New Multivariate Process Capability Indices for Autocorrelated Data

Traditionally, the process capability index is developed assuming that the process output data are independent and follow normal distribution. However, in most environmental cases, the process data have more than one quality characteristic and exhibit property of autocorrelation. We propose two novel multivariate process capability indices for autocorrelated data, NMACp and NMACpm, for the nominal-the-best case. For the smaller-the-better case, Γ(0) is used to modify the ND index and a new multivariate autocorrelated process capability index NMACpu is derived. Furthermore, a simulation study is conducted to compare the performance of the various multivariate autocorrelated indices. The simulation results show that the actual nonconforming rates can be correctly reflected by our proposed indices, which outperform the previous Cpm, MCp, MCpm, NMCp, NMCpm, and ND indices under different time series models. Thus, our proposed capability indices can be used in evaluating the performance of multivariate autocorrelated processes. Finally, a realistic example in hydrological application further demonstrates the usefulness of our proposed capability indices. Copyright © 2013 John Wiley & Sons, Ltd.

<b>The Mann-Kendall test: the need to consider the interaction between serial correlation and trend</b> - doi: 10.4025/actasciagron.v35i4.16006

Pre-whitening approaches have been widely used to remove the influence of serial correlations on the Mann-Kendall trend test (MK_prew). However, previous studies indicate that this procedure may lead to a false reduction of the significance of a trend. An alternative approach (MK_interact) has been proposed to improve the assessment of the significance of a trend in auto-correlated data. Therefore, the present study compared the performance of the MK_prew and MK_interact for detecting trends in auto-correlated series. Sets of Monte Carlo experiments were carried out to evaluate the occurrence of type I and II errors obtained from both approaches. The analyses were also based on 10-day values of the difference between precipitation and potential evapotranspiration (P-EP) obtained from the location of Campinas, State of São Paulo, Brazil. The results found in this study allow us to conclude that the MK_interac outperformed the MK_prew in correctly identifying the significance of trends and that, concerning agricultural interests, the decreasing trend described by the MK_interac during the beginning of the crop growing seasons may reveal an unfavorable temporal distribution of the P-EP values.

Semiempirical and process‐based global sea level projections

AbstractWe review the two main approaches to estimating sea level rise over the coming century: physically plausible models of reduced complexity that exploit statistical relationships between sea level and climate forcing, and more complex physics‐based models of the separate elements of the sea level budget. Previously, estimates of future sea level rise from semiempirical models were considerably larger than those from process‐based models. However, we show that the most recent estimates of sea level rise by 2100 using both methods have converged, but largely through increased contributions and uncertainties in process‐based model estimates of ice sheets mass loss. Hence, we focus in this paper on ice sheet flow as this has the largest potential to contribute to sea level rise. Progress has been made in ice dynamics, ice stream flow, grounding line migration, and integration of ice sheet models with high‐resolution climate models. Calving physics remains an important and difficult modeling issue. Mountain glaciers, numbering hundreds of thousands, must be modeled by extensive statistical extrapolation from a much smaller calibration data set. Rugged topography creates problems in process‐based mass balance simulations forced by regional climate models with resolutions 10–100 times larger than the glaciers. Semiempirical models balance increasing numbers of parameters with the choice of noise model for the observations to avoid overfitting the highly autocorrelated sea level data. All models face difficulty in separating out non‐climate‐driven sea level rise (e.g., groundwater extraction) and long‐term disequilibria in the present‐day cryosphere‐sea level system.

추세 시계열 자료의 부트스트랩 적용

In the simulation output analysis, bootstrap method is an applicable resampling technique to insufficient data which are not significant statistically. The moving block bootstrap, the stationary bootstrap, and the threshold bootstrap are typical bootstrap methods to be used for autocorrelated time series data. They are nonparametric methods for stationary time series data, which correctly describe the original data. In the simulation output analysis, however, we may not use them because of the non-stationarity in the data set caused by the trend such as increasing or decreasing. In these cases, we can get rid of the trend by differencing the data, which guarantees the stationarity. We can get the bootstrapped data from the differenced stationary data. Taking a reverse transform to the bootstrapped data, finally, we get the pseudo-samples for the original data. In this paper, we introduce the applicability of bootstrap methods to the time series data having trend, and then verify it through the statistical analyses.

Estimating animal resource selection from telemetry data using point process models

1. Analyses of animal resource selection functions (RSF) using data collected from relocations of individuals via remote telemetry devices have become commonplace. Increasing technological advances, however, have produced statistical challenges in analysing such highly autocorrelated data. Weighted distribution methods have been proposed for analysing RSFs with telemetry data. However, they can be computationally challenging due to an intractable normalizing constant and cannot be aggregated (i.e. collapsed) over time to make space-only inference. 2. In this study, we take a conceptually different approach to modelling animal telemetry data for making RSF inference. We consider the telemetry data to be a realization of a space-time point process. Under the point process paradigm, the times of the relocations are also considered to be random rather than fixed. 3. We show the point process models we propose are a generalization of the weighted distribution telemetry models. By generalizing the weighted model, we can access several numerical techniques for evaluating point process likelihoods that make use of common statistical software. Thus, the analysis methods can be readily implemented by animal ecologists. 4. In addition to ease of computation, the point process models can be aggregated over time by marginalizing over the temporal component of the model. This allows a full range of models to be constructed for RSF analysis at the individual movement level up to the study area level. 5. To demonstrate the analysis of telemetry data with the point process approach, we analysed a data set of telemetry locations from northern fur seals (Callorhinus ursinus) in the Pribilof Islands, Alaska. Both a space-time and an aggregated space-only model were fitted. At the individual level, the space-time analysis showed little selection relative to the habitat covariates. However, at the study area level, the space-only model showed strong selection relative to the covariates.

Scaling range of power laws that originate from fluctuation analysis

We extend our previous study of scaling range properties performed for detrended fluctuation analysis (DFA) [Physica A 392, 2384 (2013)] to other techniques of fluctuation analysis (FA). The new technique, called modified detrended moving average analysis (MDMA), is introduced, and its scaling range properties are examined and compared with those of detrended moving average analysis (DMA) and DFA. It is shown that contrary to DFA, DMA and MDMA techniques exhibit power law dependence of the scaling range with respect to the length of the searched signal and with respect to the accuracy R^{2} of the fit to the considered scaling law imposed by DMA or MDMA methods. This power law dependence is satisfied for both uncorrelated and autocorrelated data. We find also a simple generalization of this power law relation for series with a different level of autocorrelations measured in terms of the Hurst exponent. Basic relations between scaling ranges for different techniques are also discussed. Our findings should be particularly useful for local FA in, e.g., econophysics, finances, or physiology, where the huge number of short time series has to be examined at once and wherever the preliminary check of the scaling range regime for each of the series separately is neither effective nor possible.

Binary classification with pFDR‐pFNR losses

Connecting multiple testing with binary classification, we derive a false discovery rate-based classification approach for two-class mixture models, where the available data (represented as feature vectors) for each individual comparison take values in Rd for some d≥1 and may exhibit certain forms of autocorrelation. This generalizes previous findings for the independent case in dimension d=1. Two resulting classification procedures are described which allow for incorporating prior knowledge about class probabilities and for user-supplied weighting of the severity of misclassifying a member of the "0"-class as "1" and vice versa. The key mathematical tools to be employed are multivariate estimation methods for probability density functions or density ratios. We compare the two algorithms with respect to their theoretical properties and with respect to their performance in practice. Computer simulations indicate that they can both successfully be applied to autocorrelated time series data with moving average structure. Our approach was inspired and its practicability will be demonstrated by applications from the field of brain-computer interfacing and the processing of electroencephalography data.

Performance of CUSUM and EWMA charts for serial correlation

PurposeThe purpose of this paper is to study the effect of correlation on the performance of CUSUM and EWMA charts. The performance of the CUSUM and EWMA charts is measured in terms of average run lengths (ARLs) for the positively correlated data. The ARLs at various set of parameters of the CUSUM and EWMA charts are computed, using MATLAB. The behavior of the CUSUM and EWMA chart at the various shifts in the process mean is studied, analyzed and compared at different levels of correlation (Φ). The optimum schemes for both the charts are suggested for various levels of correlation (Φ).Design/methodology/approachPositively correlated observations having normal distribution are generated with the help of the MATLAB. Performance of both the charts in terms of ARLs is measured and compared at various levels of correlation (Φ). The optimal schemes of charts which give the desired in‐control ARLs are suggested for various levels of correlation (Φ).FindingsFor each level of correlation (Φ) various schemes of both the charts are suggested. Moreover those suggested schemes which give quick response to the shifts in the process mean is termed as optimal scheme. It is concluded that CUSUM schemes are preferred as compared to the EWMA schemes for quicker response. The optimal schemes of CUSUM and EWMA chart are also compared with the EWMAST chart suggested by Winkel and Zhang (2004).Research limitations/implicationsBoth the schemes are optimized by assuming the autocorrelated numbers to be normally distributed. But this assumption may also be relaxed to design these schemes for autocorrelated data. Moreover sample size of four is taken while developing these schemes; various other schemes can also be developed for different sample sizes. Control charts for attribute type of data can also be developed for different level of correlation (Φ).Practical implicationsFor a specific control chart, if the in‐control ARL of the process outputs of any industry is in accordance with the simulated in‐control ARL. It means the process outputs must have same level of correlation (Φ) corresponding to the simulated in‐control ARL and the suggested optimal schemes, corresponding to that level of correlation (Φ), must be adopted to avoid the false alarm rate. The correlation among the process outputs of any industry can be find out and corresponding to that level of correlation the suggested control chart parameters can be applied. Thus false alarms generated, will be minimum for the suggested schemes at different level of correlation (Φ).Social implicationsIf the optimal CUSUM schemes are employed in process/service industry, there will be a considerable amount of saving in time and money expended in search of causes behind frequent false alarms. The rejection level of products in the industries can be reduced by designing the better control chart schemes which will also reduce the loss to the society, as suggested by Taguchi.Originality/valueThe research findings could be applied to various manufacturing industries as well as service industries where the data is positively correlated and normally distributed.

Polarization-maintaining property of tapered polarization-maintaining fibers

Distributed group birefringence of tapered polarization-maintaining fibers (PMFs) is measured by employing a high-resolution optical frequency-domain reflectometry system. Autocorrelation data processing reveals distributed mode coupling between the fast and slow modes and higher-order modes excited by the tapering process along the taper region. The polarization-maintaining property of a tapered PMF is examined by distributed group birefringence along the tapered PMF with a spatial resolution of ~1.25 cm and a polarization-extinction ratio at the fiber taper output over the wavelength range of 1510-1570 nm. With a waist diameter of 80 μm, the polarization state of the launched light is maintained and the birefringence of the tapered PMF is slightly reduced from 3.28×10(-4) to 2.89×10(-4) at the taper waist. For both the waist diameters of 60 and 40 μm, mode coupling is observed in the form of significantly decreased birefringence by a factor of ~10 at the taper waists.

BAYESIAN MODELS FOR TIME SERIES WITH COVARIATES, TREND, SEASONALITY, AUTOREGRESSION AND OUTLIERS

Bayesian methods furnish an attractive approach to time series data analysis. This article proposes the forecasting models that can detect trend, seasonality, auto regression and outliers in time series data related to some covariates. Cumulative Weibull distribution functions for trend, dummy variables for seasonality, binary selections for outliers and latent autoregression for autocorrelated time series data are used for the data analysis. The Gibbs sampling, a Markov Chain Monte Carlo (MCMC) algorithm, is used for the parameter estimation. The proposed models are applied to vegetable price time series data in Thailand. According to the RMSE, MAPE and MAE criteria for model comparisons, the proposed models provide the best results compared to the exponential smoothing models, SARIMA models and the Bayesian models with trend, auto regression and outliers.

Implementation of the statistical process control with autocorrelated data in an automotive manufacturer

The continuous improvement on quality of products and processes is a constant concern at organisations, as a response to growing competition and demands of the market. The implementation of statistical techniques adjusted to different situations is one way to achieve this goal. The application of traditional control charts requires that collected data are independent and identically distributed. However, this is not always assured, reflecting a drastic increase of false alarms. This paper presents a methodology for the traditional univariate control charts application, when data exhibit significant autocorrelation. To obtain the residuals and predictive errors, the suggestion is to use the ARIMA methodology of Box and Jenkins. Implementation took place in the painting process from an automotive company, providing continuous adjustment of the same and statistically grounded, enabling the organisation to produce vehicles with greater quality assurance, lower costs and an advantageous position against their competitors.