Order Autoregressive Model Research Articles

A new sampling strategy to reduce the effect of autocorrelation on a control chart

On-line monitoring of quality characteristics is essential to limit scrap and rework costs due to bad quality in a manufacturing process. In several manufacturing environments, during production process data can be massively collected with high sampling rates and tight sampling frequencies. As a consequence, natural autocorrelation may arise among consecutive measures within a sample. Autocorrelation significantly inflates the average run length of a control chart and deteriorates its sensitivity to the occurrence of assignable causes. In this paper, we propose a new mixed sampling strategy for the Shewhart chart monitoring the sample mean in a process where temporal autocorrelation between two consecutive observations can be represented by means of a first order autoregressive model AR(1). With this strategy, the sample mean at each inspection time is computed by merging measures of a generic quality characteristic from two consecutive samples taken h hours apart. The statistical properties of a Shewhart control chart implementing the proposed strategy are compared to those implementing a skipping strategy recently proposed in literature. A numerical analysis shows that the mixed sampling outperforms the skipping sampling strategy for high levels of autocorrelation.

The evaluation of evidence relating to traces of cocaine on banknotes

Banknotes can be seized from crime scenes as evidence for suspected association with illicit drug dealing. Tandem mass spectrometry data are available from banknotes seized in criminal investigations, as well as from banknotes from general circulation. The aim of the research is to evaluate the support provided by the data gathered in a criminal investigation for the proposition that the banknotes from which the data were obtained are associated with a person who is associated with a criminal activity related to cocaine in contrast to the proposition that the banknotes are associated with a person who is not associated with a criminal activity involving cocaine. The data considered are the peak area for the ion count for cocaine product ion m/z 105. Previous methods for assessment of the relative support for these propositions were concerned with the percentage of banknotes contaminated or assume independence of measurements of quantities between adjacent banknotes. Methods which account for an association of the quantity of drug on a banknote with that on adjacent banknotes are described. The methods are based on an autoregressive model of order one and on two versions of a nonparametric approach. The results are compared with a standard model which assumes measurements on individual banknotes are independent; there is no autocorrelation. Performance is assessed using rates of misleading evidence and a recommendation made as to which method to use.

Stability Analysis of Anonlinear Autoregressive Model of First Order

In this paper, we study the moment of a non linear – autoregressive polynomial model of first order, also we analysis the stability of this model and find the singular point as well as the limit cycle by using the linear approximation technique.

PATH INTEGRAL METHOD FOR LIMITING DISTRIBUTION OF AN ESTIMATOR ARISING FROM AN AR(1)-PROCESS WITH A UNIT ROOT

We propose the path-integral technique to derive the characteristic function of the limiting distribution of the unit root test in a first order autoregressive model. Our results provide a new and useful approach to obtain the closed form of the characteristic function of a random variable associated with the limiting distribution, which is realized as a ratio of Brownian functionals on the classical Wiener space.

On a class of bivariate exponential distributions

A class of absolutely continuous bivariate exponential distributions is constructed using the product form of a first order autoregressive model. Inference methods are proposed for parameter estimation and diagnosis. Data analysis is carried out to illustrate the applications.

Objective priors for causal AR(p) with partial autocorrelations

We consider the problem of deriving formal objective priors for the causal/stationary autoregressive model of order p. We compare the frequentist behaviour of the most common default priors, namely the uniform (over the stationarity region) prior, the Jeffreys’ prior and the reference prior.

A conditionally heteroskedastic global inflation model

PurposeThe purpose of this paper is to propose and test empirically an inflation model containing permanent and transitory heteroskedastic components for the G7 countries. More specifically, recent evidences from the literature are gathered to construct a model with a heteroskedastic global component capturing comovements amongst G7 economies. Moreover, evidence of asymmetric generalized autoregressive conditionally heteroskedastic effects both in the transitory and in the permanent components are taken into account, and the time‐varying variance of each component allows their influence over the observable inflation to change over time. Out‐of‐sample forecasting exercises are used to test the model validity.Design/methodology/approachThe model is written in state‐space form and estimation is carried out in one step via quasi‐maximum likelihood using the augmented Kalman filter, which allows us to compute smoothed estimates of permanent and of transitory components of inflation rates. Out‐of‐sample forecasts are compared against a random walk (RW) and an autoregressive (AR) model of order one. The significance of the differences in forecast accuracy is tested using the Diebold‐Marino test, the forecast encompassing test, and the Pesaran and Timmermann test.FindingsThe proposed model fits the data quite well and has good forecasting capabilities when compared to RW and to AR models of order one. The volatility of the global inflation trend extracted from the model captures the international effects of the “Great Moderation” and of the “Great Recession”. An increase in correlation of inflation for certain country pairs since the start of the “Great Recession” is observed. Moreover, there is evidence of asymmetry in inflation volatility, which is consistent with the idea that higher inflation levels lead to greater uncertainty about future inflation.Originality/valueThis article introduces a new global inflation model with permanent and transitory heteroskedastic components incorporating many recent findings of the literature, and proposes a one step estimation procedure for it. The model fits very well the data and produces good out‐of‐sample forecasts.

Study of vibration microaccelerations onboard the International Space Station

The results of studying vibration microaccelerations aboard the International Space Station are presented. The study was performed using the measurement data of the MAMS low-frequency and the SAMS high-frequency accelerometers. For the study, six intervals of measurements were selected, performed in 2005. During these intervals the station was flying in the standard orbital orientation, attitude control engines were not switched on, and the crew rested. Discrete and continuous spectra were analyzed on selected intervals. The most significant disturbances with the discrete spectrum (cyclic trends) have been found. Using the second order autoregression model, parameters of the most significant disturbances with the continuous spectrum were determined. This study was carried out as a part of the technical experiment “The ISS environment”.

Optimizing the performance of Kalman filter based statistical time-varying air quality models

In this study, the Bayesian approach is proposed to estimate the noise variances of Kalman filter based statistical models for predicting the daily averaged PM10 concentrations of a typical coastal city, Macau, with Latitude 22°10’N and Longitude 113°34’E. By using the measurements in 2001 and 2002, the Bayesian approach is capable to estimate the most probable values of the noise variances in the Kalman filter based prediction models. It turns out that the estimated process noise variance of the time-varying autoregressive model with exogenous inputs, TVAREX, is significantly (~76%) less than that of the time-varying autoregressive model of order 1, TVAR(1), since the TVAREX model incorporates important mechanisms which govern the daily averaged PM10 concentrations in Macau. By further using data between 2003 and 2005, the choice of the noise variances is shown to affect the model performance, measured by the root-mean-squared error, of the TVAR(p) model and the TVAREX model. In addition, the optimal estimates of noise variances obtained by Bayesian approach for both models are located in the region where the model performance is insensitive to the choice of noise variances. Furthermore, the Bayesian approach will be demonstrated to provide more reasonable estimates of noise variances compared to the noise variances found by simply minimizing the root-mean-squared prediction error of the model. By comparing the optimized TVAREX model and the TVAR(p) models in predicting the daily averaged PM10 concentrations between 2003 and 2005, it is found that the TVAREX model outperforms the TVAR(p) models in terms of the general performance and the episode capturing capability.

Towards a data assimilation system for morphodynamic modeling: bathymetric data assimilation for wave property estimation

Data assimilation is mainly concerned with the proper management of uncertainties. The main objective of the present work is to implement and analyze a data assimilation technique capable of assimilating bathymetric data into a coupled flow, wave, and morphodynamic model. For the case presented here, wave significant height, wave direction of incidence, and wave peak period are being optimized based on bathymetric data taken from a twin experiment. An adjoint-free variational scheme is used. In this approach, a linear reduced order model (ROM) is constructed as an approximation of the full model. The ROM is an autoregressive model of order 1 (AR1) that preserves the parametrization. Since the ROM is linear, the construction of its adjoint is straightforward, making the implementation of 4D variational data assimilation effortless. The scheme is able to update the morphodynamic model satisfactorily despite the fact that the model shows nonlinear behavior even for very small perturbations of all three parameters. The size and direction of the perturbations necessary for constructing the ROM have a significant impact on the performance of the technique.

Forecasting a long memory process subject to structural breaks

We develop an easy-to-implement method for forecasting a stationary autoregressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an autoregressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids the issue of estimation inaccuracy of the long memory parameter and the issue of spurious breaks in finite sample. Insights from our theoretical analysis are confirmed by Monte Carlo experiments, through which we also find that our method provides a substantial improvement over existing prediction methods. An empirical application to the realized volatility of three exchange rates illustrates the usefulness of our forecasting procedure. The empirical success of the HAR-RV model can be explained, from an econometric perspective, by our theoretical and simulation results.

Forecasting a Long Memory Process Subject to Structural Breaks

We develop an easy-to-implement method for forecasting a stationary auto-regressive fractionally integrated moving average (ARFIMA) process subject to structural breaks with unknown break dates. We show that an ARFIMA process subject to a mean shift and a change in the long memory parameter can be well approximated by an auto-regressive (AR) model and suggest using an information criterion (AIC or Mallows’ Cp) to choose the order of the approximate AR model. Our method avoids the issue of estimation inaccuracy of the long memory parameter and the issue of spurious breaks in finite sample. Insights from our theoretical analysis are confirmed by Monte Carlo experiments, through which we also find that our method provides a substantial improvement over existing prediction methods. An empirical application to the realized volatility of three exchange rates illustrates the usefulness of our forecasting procedure. The empirical success of the HAR-RV model is explained, from an econometric perspective, by our theoretical and simulation results.

LONGITUDINAL INTENSITY NORMALIZATION IN THE PRESENCE OF MULTIPLE SCLEROSIS LESIONS.

This paper proposes a longitudinal intensity normalization algorithm for T1-weighted magnetic resonance images of human brains in the presence of multiple sclerosis lesions, aiming towards stable and consistent longitudinal segmentations. Unlike previous longitudinal segmentation methods, we propose a 4D intensity normalization that can be used as a preprocessing step to any segmentation method. The variability in intensities arising from the relapsing and remitting nature of the multiple sclerosis lesions is modeled into an otherwise smooth intensity transform based on first order autoregressive models, resulting in smooth changes in segmentation statistics of normal tissues, while keeping the lesion information unaffected. We validated our method on both simulated and real longitudinal normal subjects and on multiple sclerosis subjects.

Two Notes On Wiener System Identification

This paper is concerned with system identification problem. We consider a Wiener system and we first let the output of linear part of system be a linear process and then we consider a first order autoregressive model with a GARCH series as input process. A conclusion section is also given.

An improved autoregressive model by particle swarm optimization for prognostics of lithium-ion batteries

A novel data-driven approach for remaining useful life (RUL) prognostics for lithium-ion batteries using an improved autoregressive (AR) model by particle swarm optimization (PSO) is proposed. First, the AR model based on the capacity fade trends of lithium-ion batteries is presented. Second, the shortcomings of the traditional criteria for AR model order determination are analyzed. Third, the root mean square error (RMSE) is proposed as the new method for AR model order determination. Then, we use PSO algorithm to search the optimal AR model order. In addition, at the prediction stage, the information contained in the data is updated through metabolism which makes the AR model order change adaptively. Finally, the experimental data are used to validate the proposed prognostic approach. The experimental results show the following: (1) the proposed prognostic approach can predict the RUL of batteries with small error; (2) the proposed prognostic approach can be employed in on-board applications.

Supervised learning algorithm with bivariate AR(p) model

Time series classification is one of the most predominant factors for efficient data analysis in finance, image processing, signal processing, medical imaging, speech recognition etc. Much work has been reported in literature regarding supervised learning algorithm in time series data. In all these algorithms, it is customary to consider each variate separately for mining bivariate time series (Xiong and Yeung, Pattern Recogn 37:1675–1689, 2004). However, in many practical situations, one variable is highly influenced by other variable and hence analyzing each variable isolately may not provide accurate results. Very little work has been reported in supervised learning algorithm with bivariate auto regressive model of order P. Hence, in this paper, we introduce a new and novel supervised learning algorithm with bivariate auto regressive model of order P to mine the bivariate time series data. It is assumed that the whole data set is characterized by the M-component mixture of Bivariate AR (p) model. The number of components is known and fixed by defining the query under consideration. The model parameters are estimated using EM algorithm. The supervised learning algorithm is developed by utilizing component maximum likelihood and Bayesian information criteria. The performance of the developed algorithm is studied through data collected from opening price stock of a portfolio and closing price stock of a portfolio. A comparative study of the developed algorithm is made with the data mining algorithm with univariate AR(2) model. The Comparative study of developed algorithm reveal that its performance is better than existing algorithms. This algorithm also includes Univariate supervised learning algorithm as a particular case.

Postprandial performance of Dexcom® SEVEN® PLUS and Medtronic® Paradigm® Veo™: Modeling and statistical analysis

BackgroundMinimizing excessive postprandial glucose excursion is still an unmet need in treating diabetes. This work addresses the analysis and modeling in the postprandial state of two commercial CGM devices. MethodsTwelve patients with type 1 diabetes were studied in the postprandial state on four different occasions under controlled conditions. Each time, we performed simultaneous glucose monitoring using the Dexcom SEVEN® PLUS (47 datasets) and the Medtronic Paradigm® Veo™ (42 datasets). The following statistical properties of the error signal were analyzed and modeled sequentially for the two devices: the lag time, the error stationarity, the error probability distribution and the time correlation. Finally, models were built for sensor simulation in silico studies. ResultsLag time followed an exponential probability distribution for both monitors (μsevenplus=108, μveo=1.69). Standard deviation and mean of the error signal, calculated as time-dependent signals across the population of sensors, were time-varying and correlated with the reference value and its rate of change, respectively. In both cases, a high variability of postprandial behaviors was observed. After non-stationarity compensation, a logistic distribution was obtained for the SEVEN® PLUS error (close to normal distribution). Regarding the Paradigm® Veo™, a multimodal distribution was obtained, which turned into normal after elimination of five “unstable” sensors. Finally, a first order autoregressive model fitted the SEVEN® PLUS error time-series while a third-order filter was necessary for the Paradigm® Veo™. ConclusionsThe Paradigm® Veo™ device exhibited greater delay variability with higher delay time and higher probability of abnormal sensor behaviors as compared to the SEVEN® PLUS device. In both cases, the observed variability may have important clinical implications in postprandial performance. Therefore, further improvements are needed in calibration algorithms to reduce this variability.

Are There Spatial and Temporal Correlations in the Incidence Distribution of Scrub Typhus in Korea?

ObjectivesA hierarchical generalized linear model (HGLM) was applied to estimate the transmission pattern of scrub typhus from 2001 to 2011 in the Republic of Korea, based on spatial and temporal correlation. MethodsBased on the descriptive statistics of scrub typhus incidence from 2001 to 2011 reported to the Korean Centers for Disease Control and Prevention, the spatial and temporal correlations were estimated by HGLM. Incidences according to age, sex, and year were also estimated by the best-fit model out of nine HGLMs. A disease map was drawn to view the annual regional spread of the disease. ResultsThe total number of scrub typhus cases reported from 2001 to 2011 was 51,136: male, 18,628 (36.4%); female, 32,508 (63.6%). The best-fi;t model selected was a combination of the spatial model (Markov random-field model) and temporal model (first order autoregressive model) of scrub typhus transmission. The peak incidence was 28.80 per 100,000 persons in early October and the peak incidence was 40.17 per 100,000 persons in those aged 63.3 years old by the best-fit HGLM. The disease map showed the spread of disease from the southern central area to a nationwide area, excepting Gangwon-do (province), Gyeongsangbuk-do (province), and Seoul. ConclusionIn the transmission of scrub typhus in Korea, there was a correlation to the incidence of adjacent areas, as well as that of the previous year. According to the disease map, we are unlikely to see any decrease in the incidence in the near future, unless ongoing aggressive measures to prevent the exposure to the vector, chigger mites, in rural areas, are put into place.

Detection of precursory signals in front of impulsive P-waves

The precursory signals, which are preceding the impulsive P-waves, are analyzed in this study. These signals cause an error in automatic P-wave detectors which motivated us to propose an algorithm to identify these signals automatically. The first detail of multi-resolution analysis (MRA) of discrete wavelet transform (DWT) is used to detect these precursory signals. The proposed algorithm is built based on the parameters of the second order autoregressive (AR) model. 34 impulsive P-wave segments with precursory signals are used to test the ability of the proposed algorithm to detect these signals. Length of each precursory signal is calculated manually and using the proposed algorithm, where the difference between the two calculations is the error of the automatic detection. The proposed algorithm used both Haar and Daubechies wavelet filters of order 2 (abbreviated as Dau(2)) for comparison. It is found that the Dau(2) wavelet filter gave better results than Haar wavelet filter as will be discussed later. The mean and standard deviation of the error, when using Dau(2) wavelet, are -1 and 4 samples, respectively.

Analysis of chromite processing plant data by first order autoregressive model

Many mineral processing data can be monitored by a time series model. This research presents results of analysis and simulations of a chromite processing plant data determined by time series model. The plant data obtained by shift to shift include feed grade, concentrate grade, tailing grade, Cr/Fe ratio in concentrate. All the chromite processing data were found stationary over time. The autocorrelation was high for feed grade and Cr/Fe ratio. Weaker autocorrelation was observed for concentrate grade and tailing grade. Autoregressive integrated moving average (ARIMA, 1,0,0) or first order autoregressive (AR, 1) model, was found to fit all data very well. The models obtained have been also shown to be used for the near future estimation of these data. The time constant which is an indicator of sampling frequency of the data sets were determined. It was found that sampling frequency was enough for concentrate and tailing grade and their original values can be used in process control charts for monitoring. On the other hand, the sampling frequency should be reduced for feeding grade and Cr/Fe ratio for the same aims hence ARIMA residual charts were more suitable to monitor their values.