Order Autoregressive Model Research Articles

Classification of EEG Signals Based on Autoregressive Model and Wavelet Packet Decomposition

Classification of electroencephalogram (EEG) signals is an important task in the brain computer interface system. This paper presents two combination strategies of feature extraction on EEG signals. In the first strategy, Autoregressive coefficients and approximate entropy are calculated respectively, and the features are obtained by assembling them. In the second strategy, the EEG signals are first decomposed into sub-bands by wavelet packet decomposition. Wavelet packet coefficients are then sent to the autoregressive model to calculate autoregressive coefficients, which are used as features extracted from the original EEG signals. These features are fed to support vector machine for classifying the EEG signals. The classification accuracy has been used for evaluating the classification performance. Experimental results in five mental tasks show that the combination strategies can effectively improve the classification performance when the order of autoregressive model is greater than 5, and the second strategy is superior to the first one in terms of the classification accuracy.

Time Series Models of Monthly Rainfall and Temperature to Detect Climate Change for Jorhat (Assam), India

<div> <p>In the present study, monthly rainfall, maximum temperature and minimum time series models were developed for Jorhat (Assam) situated in northeast India using monthly rainfall, maximum temperature and minimum temperature data from the year 1965 to 2000. A trend free time series of rainfall and temperature was obtained by eliminating the trend component in the original time series, and then was used in identifying the periodic component. Fourier series analysis was used to identify periodic component. First five harmonics explained total variance of 79.4, 72.6 and 73.7% for monthly rainfall, maximum temperature and minimum temperature respectively. In the stochastic dependent component modelling, Autoregressive (AR) models of order 12 were found suitable on the basis of minimum value of AICC and BIC statistics. Portmanteau test formulated by McLeod and Li was carried out for checking the independence of stochastic dependent component which indicated that series consist of independent and identically distributed variables. Independent stochastic components were further modelled using normal distribution function.  Nash-Sutcliffe coefficient also indicated high degree of models fitness to the observed data. Developed time series models were validated using eight years (2001-2008) data. Using the developed time series models, monthly rainfall, maximum temperature and minimum temperature were forecasted up to the year 2050. Assessment of changes in monthly rainfall, maximum temperature and minimum temperature in generated series (2009 to 2050) were predicted using linear regression which indicated no significant trend, i.e., the climate at Jorhat (Assam) in next four decades will remain more or less stable. </p> </div> <p> </p>

A simple hourly wind power simulation for the South-West region of Western Australia using MERRA data

A simple simulator capable of generating synthetic hourly values of wind power was developed for the South West region of Western Australia. The global Modern Era Retrospective Analysis for Research and Applications (MERRA) atmospheric database was used to calibrate the simulation with wind speeds 50 m above ground level. Analysis of the MERRA data indicated that the normalised residual of hourly wind speed had a double exponential distribution. A translated square-root transformation function yn=((1.96+ye)−1.4)/0.302 was used to convert this to a normal-like distribution so that autoregressive (AR) time series analysis could be used. There was a significant dependency in this time series on the last 3 h m so a third order AR model was used to generate hourly 50 m wind speed residuals. The MERRA daily average 50 m wind speed was found to have a Weibull-like distribution, so a square root conversion was used on the data to obtain a normal distribution. The time series for this distribution was found to have a significant dependency on the values for the last two days, so a second order AR model was also used in the simulation to generate synthetic time series values for the square root of the daily average wind speed. Seasonal, daily, diurnal, and hourly components were added to generate synthetic time series values of total 50 m wind speed. To scale this wind speed to turbine hub height, a time varying wind shear factor model was created and calibrated using measured data at a coastal and an inland site. Standard wind turbine power curves were modified to produce an estimate of wind farm power output from the hub-height wind speed. Comparison with measured grid supervisory control and data acquisition (SCADA) data indicated that the simulation generated conservative power output values. The simulation was compared to two other models: a Weibull distribution model, and an AR model with normally distributed residuals. The statistical fit with the SCADA data was found to be closer than these two models. Spatial correlation using only the MERRA data was found to be higher than the SCADA data, indicating that there is still a further source of variability to be accounted for. Hence the simulation spatial correlation was calibrated to previously reported findings, which were similar to the SCADA data.

Non-parametric directionality analysis – Extension for removal of a single common predictor and application to time series

BackgroundThe ability to infer network structure from multivariate neuronal signals is central to computational neuroscience. Directed network analyses typically use parametric approaches based on auto-regressive (AR) models, where networks are constructed from estimates of AR model parameters. However, the validity of using low order AR models for neurophysiological signals has been questioned. A recent article introduced a non-parametric approach to estimate directionality in bivariate data, non-parametric approaches are free from concerns over model validity. New methodWe extend the non-parametric framework to include measures of directed conditional independence, using scalar measures that decompose the overall partial correlation coefficient summatively by direction, and a set of functions that decompose the partial coherence summatively by direction. A time domain partial correlation function allows both time and frequency views of the data to be constructed. The conditional independence estimates are conditioned on a single predictor. ResultsThe framework is applied to simulated cortical neuron networks and mixtures of Gaussian time series data with known interactions. It is applied to experimental data consisting of local field potential recordings from bilateral hippocampus in anaesthetised rats. Comparison with existing method(s)The framework offers a non-parametric approach to estimation of directed interactions in multivariate neuronal recordings, and increased flexibility in dealing with both spike train and time series data. ConclusionsThe framework offers a novel alternative non-parametric approach to estimate directed interactions in multivariate neuronal recordings, and is applicable to spike train and time series data.

First difference transformation in panel VAR models: Robustness, estimation, and inference

ABSTRACTThis article considers estimation of Panel Vector Autoregressive Models of order 1 (PVAR(1)) with focus on fixed T consistent estimation methods in First Differences (FD) with additional strictly exogenous regressors. Additional results for the Panel FD ordinary least squares (OLS) estimator and the FDLS type estimator of Han and Phillips (2010) are provided. Furthermore, we simplify the analysis of Binder et al. (2005) by providing additional analytical results and extend the original model by taking into account possible cross-sectional heteroscedasticity and presence of strictly exogenous regressors. We show that in the three wave panel the log-likelihood function of the unrestricted Transformed Maximum Likelihood (TML) estimator might violate the global identification assumption. The finite-sample performance of the analyzed methods is investigated in a Monte Carlo study.

Mean lag in general error correction models

Most of the empirical literature inappropriately applies Hendry’s (1995) mean lag formula–which he derived for first order autoregressive distributed lag models under the assumption of a homogeneous long-run equilibrium–to error correction models that have complex lag structures and lack long-run homogeneity. We derive an expression for the mean lag in general error correction models without imposing the assumption of a homogeneous equilibrium. In addition, we quantify the bias due to the incorrect use of Hendry’s (1995) formula.

Modeling South African Banks closing stock prices: a Markov-Switching Approach

In this paper, we provide evidence that the five variables used in the study were nonlinear in nature, while finding a better Markov-switching model. The study used dailydata obtained from the Johannesburg Stock Exchange over the period from January 2010 to December 2012. An extension of Markov Switching with autoregressive model was used for empirical analysis. Prior to using this model, the series were tested for nonlinear unit root with modified Kapetanois-Shin-Snell nonlinear Augmented Dickey-Fuller (KSS-NADF) test which successfully provided positive results.Other preliminary tests selected the first lag as optimal and confirmed that stock prices may switch between two regimes. Further empirical findings proved that stock prices can be successfully modelled with Markov Switching Autoregressive model of order one. First National bank was found to have 99.64% longer stock price stability if adjustments regards tofinancialpolicies are made. Capitec Bank was the least favoured among the banks.

Evaluation of Phase I analysis scenarios on Phase II performance of control charts for autocorrelated observations

ABSTRACTPhase I analysis of a control chart implementation comprises parameter estimation, chart design, and outlier filtering, which are performed iteratively until reliable control limits are obtained. These control limits are then used in Phase II for online monitoring and prospective analyses of the process to detect out-of-control states. Although a Phase I study is required only when the true values of the parameters of a process are unknown, this is the case in many practical applications. In the literature, research on the effects of parameter estimation (a component of Phase I analysis) on the control chart performance has gained importance recently. However, these studies consider availability of complete and clean data sets, without outliers and missing observations, for estimation. In this article, we consider AutoRegressive models of order 1 and study the effects of two extreme cases for Phase I analysis; the case where all outliers are filtered from the data set (parameter estimation from incomplete but clean data) and the case where all outliers remain in the data set during estimation. Performance of the maximum likelihood and conditional sum of squares estimators are evaluated and effects on the Phase II use are investigated. Results indicate that the effect of not detecting outliers in Phase I can be severe on the Phase II application of a control chart. A real-world example is provided to illustrate the importance of an appropriate Phase I analysis.

Analysis of Recorded Inflow Data of Ataturk Reservoir

Since the beginning of the last century, the competition for water resources has intensified dramatically, especially between countries that have no agreements in place for water resources that they share. Such is the situation with the Euphrates River which flows through three countries (Turkey, Syria, and Iraq) and represents the main water resource for these countries. Therefore, the comprehensive hydrologic investigation needed to derive optimal operations requires reliable forecasts. This study aims to analysis and create a forecasting model for data generation from Turkey perspective by using the recorded inflow data of Ataturk reservoir for the period (Oct. 1961 - Sep. 2009). Based on 49 years of real inflow data from the Euphrates River recorded at Ataturk, a spilt-sample approach was adopted for testing homogeneity. The autoregressive model of order one [AR(1)] was found to be the best for the forecasting as it accurately reproduced the means, standard deviations, and skewness coefficients observed in the generated records forecast at the Ataturk reservoir. Ten sets of 100 years data have been forecasted.
 In Iraq, optimization of the operation of all reservoirs is necessary after operating new reservoirs in Turkey.
 

패널 1차 자기회귀과정들의 동질성 검정 통계량 비교

Abstract We can achieve the principle of parsimony and efficiency if homogeneity for panel time series model issatisfied. We suggest a Rao test statistic and a Wald test statistic for the test of homogeneity for panelAR(1) and derived the limit distribution. We performed a simulation to examine statistics with the same chi-square distribution when number of the individual is small and in common with large. We also simulated tocompare the empirical power of the statistics in a small panel. In application, we fit panel AR(1) model usingregional monthly economical active population data and test homogeneity for panel AR(1). It is satisfiedhomogeneity, so it could be fitted AR(1) using the sample mean at the time point. We also compare thepower of prediction between each individual and pooled model.Keywords: panel first order autoregressive model, test of homogeneity, Rao test statistic, Wald test statistic,regional economical active population data 1. 서론 하나의현상에 대해 여러 개의독립적인시계열로 구성된 자료는 실제 현상에서자주 나타나게 되는데 이를 패널 시계열 자료라 한다. 이때

On Least Squares Estimation in a Simple Linear Regression Model with Periodically Correlated Errors: A Cautionary Note

In this research the simple linear regression (SLR) model with autocorrelated errors is considered. Traditionally, correlated errors are assumed to follow the autoregressive model of order one (AR(1)). Beside this model we will also study the SLR model with errors following the periodic autoregressive model of order one (PAR(1)). The later model is useful for modeling periodically autocorrelated errors. In particular, it is expected to beuseful when the data are seasonal. We investigate the properties of the least squares estimators of the parameters of the simple regression model when the errors are autocorrelated and for various models. In particular, the relative efficiency of those estimates are obtained and compared for the white noise, AR(1) and PAR(1) models. Also, the generalized least squares estimates for the SLR with PAR(1) errors are derived. The relative efficiency of the intercept and slope estimates based on both methods is investigated via Monte-Carlo simulation. An application on real data set is also provided.It should be emphasized that once there are sufficient evidences that errors are autocorrelated then the type of this autocorrelation should be uncovered. Then estimates of model’s parameters should be obtained accordingly, using some method like the generalized least squares but not the ordinary least squares.

Bootstrap-based unit root tests for higher order autoregressive models with GARCH(1, 1) errors

ABSTRACTBootstrap-based unit root tests are a viable alternative to asymptotic distribution-based procedures and, in some cases, are preferable because of the serious size distortions associated with the latter tests under certain situations. While several bootstrap-based unit root tests exist for autoregressive moving average processes with homoskedastic errors, only one such test is available when the innovations are conditionally heteroskedastic. The details for the exact implementation of this procedure are currently available only for the first order autoregressive processes. Monte-Carlo results are also published only for this limited case. In this paper we demonstrate how this procedure can be extended to higher order autoregressive processes through a transformed series used in augmented Dickey–Fuller unit root tests. We also investigate the finite sample properties for higher order processes through a Monte-Carlo study. Results show that the proposed tests have reasonable power and size properties.

Time series modeling of Army Mission Command communication networks: an event-driven analysis

We examine the communication time series of a fully-networked Army coalition command and control organization. The network comprised two echelons of command, at the Division and Brigade levels, over a 2-week military scenario exercise involving a Mission Command staff communicating over email and phone. We used time series analysis to predict the communications record based on an external work variable of the number of important scenario events occurring across time. After taking into account structural features of the time series—decreasing communications over time, a network crash, and the transition between weeks—we examined the remaining variability in email and phone communication. We found that the exercise scenario events were not a significant predictor of the Divisional communications, which were best fit by an auto-regressive model of order 1, meaning that the best predictor of the volume of communications at a given time point was the volume of communications on the immediately preceding time point. The occurrence of scenario events, however, did predict the Brigade communication time series, which were well fit by a lag dependent variable model. These results demonstrate that Brigade communications responded to and could be predicted by battlefield events, whereas the Division communications were only predicted by their own past values. These results highlight the importance of modeling environmental work events to predict organizational communication time series and suggest that network communications are perhaps increasingly dependent upon battlefield events for lower echelons of command closer to the tactical edge.

Timeseries Analysis of All Shares Index of Nigerian Stock Exchange: A Box-Jenkins Approach

This study was aimed at analyzing the Nigerian Stock Exchange All Share Index. The data was extracted from the Central Bank of Nigeria’s Statistical Bulletin and it covered the period of January 1985 to September 2014. The Box and Jenkins approach of model identification, parameter estimation and diagnostic checking was adopted in the analysis with the aid of S-plus Package. From the analysis, the result revealed that Autoregressive model of order two AR (2) after differencing once gives Akaike Information Criteria (AIC) of 6682.4416 which is an optimal order for Nigeria Stock Exchange All Share Index, the model is ... . Therefore, the model generated shows that ARIMA (2, 1, 0) is adequate to define the optimal order of Nigerian Stock Exchange All Share index.

Stability and asymptotics for autoregressive processes

The paper studies infinite order autoregressive models for both temporal and spatial processes. We present sufficient conditions for the existence of stationary distributions. To understand the underlying dynamics and to capture the dependence structure, we introduce functional dependence measures and relate them with Lipschitz coefficients of the data-generating mechanisms. Our stability result allows both short- and long-range dependence. With functional dependence measures, we can establish an asymptotic theory for the underlying processes.

Simulation of non-stationary wind speed and direction time series

The simulation of synthetic wind time series is strictly necessary, among others, to assess the risk of structures and systems, to model the dynamic of morphological features like dunes, or to investigate the potential of wind energy in a certain location. For all these applications, a tool able to simulate time series of wind speed and direction is required. In this paper we propose a methodology for the simulation of bivariate non-stationary time series of wind speed and direction. This methodology takes into account the circular nature of the wind direction, as well as the mean annual cycle of both wind speed and direction. For modelling the joint distribution of the two variables, wind speed is modelled conditioned to the wind direction. For modelling short-term self- and cross-dependency among the variables a Vector Autoregressive (VAR) model of order p is used, with an innovation process at time t that depends on the value taken by the variables at time t−1, based on the use of a mixture of multivariate normal distributions. The proposed methodology is applied to a case study, simulating several synthetic series, of the same length as the original series. The simulated series satisfactorily captures the characteristics of averaging or common data (i.e. with low or moderate speed) and, under certain independence conditions, the directional extreme value distribution of the wind speed is also properly reproduced.

A sparse Bayesian learning based scheme for multi-movement recognition using sEMG.

This paper proposed a feature extraction scheme based on sparse representation considering the non-stationary property of surface electromyography (sEMG). Sparse Bayesian learning was introduced to extract the feature with optimal class separability to improve recognition accuracy of multi-movement patterns. The extracted feature, sparse representation coefficients (SRC), represented time-varying characteristics of sEMG effectively because of the compressibility (or weak sparsity) of the signal in some transformed domains. We investigated the effect of the proposed feature by comparing with other fourteen individual features in offline recognition. The results demonstrated the proposed feature revealed important dynamic information in the sEMG signals. The multi-feature sets formed by the SRC and other single feature yielded more superior performance on recognition accuracy, compared with the single features. The best average recognition accuracy of 94.33% was gained by using SVM classifier with the multi-feature set combining the feature SRC, Williston amplitude (WAMP), wavelength (WL) and the coefficients of the fourth order autoregressive model (ARC4) via multiple kernel learning framework. The proposed feature extraction scheme (known as SRC + WAMP + WL + ARC4) is a promising method for multi-movement recognition with high accuracy.

Long-term earthquake forecasting model for northeast India and surrounding region: seismicity-based model

An earthquake forecasting model has been proposed for northeast India and surrounding region in a specified time span by exploiting the temporal and the spatial variations in the Gutenberg and Richter parameters (a and b). The study region has been divided into grid with a grid interval of 0.1° in latitude and longitude and 14 zones for the seismic activity density and the seismicity parameters estimation, respectively, while the time span of the used earthquake catalog has been divided into time grids with a fixed time interval of 5 years. The seismic activity rate at a grid point has been estimated from seismic activity density at the grid point and seismic activity in zone comprising the grid. The normalized multivariate Gaussian mixture model is considered to estimate the seismic activity density, while seismicity parameters have been estimated using the Gutenberg and Richter relation and the method of maximum likelihood estimation. The seismic activity rates at each grid point in all time grids have been fitted to an autoregressive model of order three, and the inferred coefficients of the model has been used to forecast seismic activity rate in next time grid, e.g., in time grid from 2011 to 2015 including.

Statistical Inference in Autoregressive Models with Non-negative Residuals

Normal residual is one of the usual assumptions of autoregressive models but in practice sometimes we are faced with non-negative residuals case. In this paper we consider some autoregressive models with non-negative residuals as competing models and we have derived the maximum likelihood estimators of parameters based on the modified approach and EM algorithm for the competing models. Also, based on the simulation study, we have compared the ability of some model selection criteria to select the optimal autoregressive model. Then we consider a set of real data, level of lake Huron 1875-1930, as a data set generated from a first order autoregressive model with non-negative residuals and based on the model selection criteria we select the optimal model between the competing models.

The performance of the spatiotemporal Kalman filter and LORETA in seizure onset localization.

The assumption of spatial-smoothness is often used to solve the bioelectric inverse problem during electroencephalographic (EEG) source imaging, e.g., in low resolution electromagnetic tomography (LORETA). Since the EEG data show a temporal structure, the combination of the temporal-smoothness and the spatial-smoothness constraints may improve the solution of the EEG inverse problem. This study investigates the performance of the spatiotemporal Kalman filter (STKF) method, which is based on spatial and temporal smoothness, in the localization of a focal seizure's onset and compares its results to those of LORETA. The main finding of the study was that the STKF with an autoregressive model of order two significantly outperformed LORETA in the accuracy and consistency of the localization, provided that the source space consists of a whole-brain volumetric grid. In the future, these promising results will be confirmed using data from more patients and performing statistical analyses on the results. Furthermore, the effects of the temporal smoothness constraint will be studied using different types of focal seizures.