DR-AR Model

This paper presents the possibility of early detection and localization of epileptogenic focus in the iEEG (intracranial Electroencephalography) signal using a method based on multidimensional autoregressive models. The work provides the first results of the method in the iEEG signal, and discusses technical aspects in terms of the suitability of the sampling frequency, AR model order and segmentation step.

This paper presents an optimum combination of two robust statistical techniques that can be used to improve the skill of long-range weather forecasts. The first method uses decomposition and analysis based on EEOF (Extended Empirical Orthogonal Functions), with a 3-month data window, for temperature and precipitation fields in Romania. Using Rule N to select the significant components led to 3 modes for temperature and to 9 modes for precipitation. In linear extrapolation, an AR model is used to produce forecast the time series of the EEOF components. The parameters of this model are determined by a method consistent with the maximum entropy method, which is why this model is named AR-MEM. In order to select model order, 7 criteria are tested, some of which are efficient, while the others are consistent. Model parameters are determined from observational data over the period 1950 -1990. The Heidke skill score is computed using independent data (1991)(1992)(1993)(1994)(1995)(1996)(1997). The best results have been obtained for the temperature field filtered by the first 3 EEOF modes, for the meteorological stations situated in the central part of Romania. For precipitation, the forecast based on the EEOF 1 component with one-step ahead, led to skill scores worse than those obtained using persistence in all cases.

This correspondence discusses the application of random autoregressive (AR) models to signal processing problems: specifically, to adaptive line enhancement (ALE). The advantage of this approach is that random AR models may reflect more accurately the uncertainty in the stochastic process that generates the received signal. It is shown, through Monte Carlo simulations, that by using random AR models one obtains better results than by using the conventional deterministic AR models under the same conditions.

To have a continuous navigation solution that does not suffer from interruption, GPS is integrated with relative positioning techniques such as odometry and inertial navigation. Targeting a low-cost navigation solution for land vehicles, this paper uses a reduced multisensor system consisting of one microelectromechanical-system (MEMS)-based single-axis gyroscope used together with the vehicle's odometer, and the whole system is integrated with GPS. This system provides a 2-D navigation solution, which is adequate for land vehicles. The traditional technique for this multisensor integration problem is Kalman filtering (KF). Due to the inherent errors of MEMS inertial sensors and their stochastic nature, which is difficult to model, the KF with its linearized models has limited capabilities in providing accurate positioning. Particle filtering (PF) has recently been suggested as a nonlinear filtering technique to accommodate arbitrary inertial sensor characteristics, motion dynamics, and noise distributions. An enhanced version of PF is utilized in this paper and is called the Mixture PF. Since PF can accommodate nonlinear models, this paper uses total-state nonlinear system and measurement models. In addition, sophisticated models are used to model the stochastic drift of the MEMS-based gyroscope. A nonlinear system identification technique based on parallel cascade identification (PCI) is used to model this stochastic gyroscope drift. In this paper, the performance of the PCI model is compared with that of higher order autoregressive (AR) stochastic models. Such higher order models are difficult to use with KF since the size of the dynamic matrix and the error-covariance matrix becomes very large and complicates the KF operation. The performance of the proposed 2-D navigation solution using Mixture PF with both PCI and higher Manuscript order AR models is examined by road-test trajectories in a land vehicle. The two proposed combinations are compared with four other 2-D solutions: a Mixture PF with the Gauss-Markov (GM) model for the gyro drift, a Mixture PF with only white Gaussian noise (WGN) for stochastic gyro errors, and two different KF solutions with GM model for the gyro drift. The experimental results show that the two proposed solutions outperform all the compared counterparts. He has published extensively in the areas of nonlinear system identification and time-series analysis.

This paper deals with the joint signal and parameter estimation for linear state-space models. An efficient solution to this problem can be obtained by using a recursive instrumental variable technique based on two dual Kalman filters. In that case, the driving process and the observation noise in the state-space representation for each filter must be white with known variances. These conditions, however, are too strong to be always satisfied in real cases. To relax them, we propose a new approach based on two dual filters. Once a new observation of the disturbed signal is available, the first algorithm uses the latest estimated parameters to estimate the signal, while the second algorithm uses the estimated signal to update the parameters. In addition, as the filter behavior depends on the choice of various weights, we present a way to recursively tune them. This approach is then studied in the following cases: 1) consistent estimation of the AR parameters from noisy observations and 2) speech enhancement, where no a priori model of the additive noise is required for the proposed approach. In each case, a comparative study with existing methods is carried out to analyze the relevance of our solution.

This paper addresses the prediction of epileptic seizures from the online analysis of EEG data. This problem is of paramount importance for the realization of monitoring/control units to be implanted on drug-resistant epileptic patients. The proposed solution relies in a novel way on autoregressive modeling of the EEG time series and combines a least-squares parameter estimator for EEG feature extraction along with a support vector machine (SVM) for binary classification between preictal/ictal and interictal states. This choice is characterized by low computational requirements compatible with a real-time implementation of the overall system. Moreover, experimental results on the Freiburg dataset exhibited correct prediction of all seizures (100% sensitivity) and, due to a novel regularization of the SVM classifier based on the Kalman filter, also a low false alarm rate.

The wrist pulse signals can be used to analyze a person's health status in that they reflect the pathologic changes of the person's body condition. This paper aims to present a novel time series analysis approach to analyze wrist pulse signals. First, a data normalization procedure is proposed. This procedure selects a reference signal that is 'closest' to a newly obtained signal from an ensemble of signals recorded from the healthy persons. Second, an autoregressive (AR) model is constructed from the selected reference signal. Then, the residual error, which is the difference between the actual measurement for the new signal and the prediction obtained from the AR model established by reference signal, is defined as the diseasesensitive feature. This approach is based on the premise that if the signal is from a patient, the prediction model previously identified using the healthy persons would not be able to reproduce the time series measured from the patients. The applicability of this approach is demonstrated using a wrist pulse signal database collected using a Doppler Ultrasound device. The classification accuracy is over 82% in distinguishing healthy persons from patients with acute appendicitis, and over 90% for other diseases. These results indicate a great promise of the proposed method in telling healthy subjects from patients of specific diseases.

In this paper we present some results on detection and classification of low metal content anti personnel (AP) landmines using a modified version of the Auto Regressive (AR) modeling algorithm presented in. A statistical distance is computed between the AR coefficients of the measured GPR time signal and the AR coefficients of a reference database (containing the AR models of the mines of interest) and a detection is declared if this distance is below a given threshold.

This paper proposes the use of the minimum entropy deconvolution (MED) technique to enhance the ability of the existing autoregressive (AR) model based filtering technique to detect localised faults in gears. The AR filter technique has been proven superior for detecting localised gear tooth faults than the traditionally used residual analysis technique. The AR filter technique is based on subtracting a regular gearmesh signal, as represented by the toothmesh harmonics and immediately adjacent sidebands, from the spectrum of a signal from one gear obtained by the synchronous signal averaging technique (SSAT). The existing AR filter technique performs well but is based on autocorrelation measurements and is thus insensitive to phase relationships which can be used to differentiate noise from impulses. The MED technique can make a use of the phase information by means of the higher-order statistical (HOS) characteristics of the signal, in particular the kurtosis, to enhance the ability to detect emerging gear tooth faults. The experimental results presented in this paper validate the superior performance of the combined AR and MED filtering techniques in detecting spalls and tooth fillet cracks in gears. r

Autoregressive (AR) spectral estimation is a popular method for modeling the electroencephalogram (EEG), and therefore the frequency domain EEG phenomena that are used for control of a brain-computer interface (BCI). Several studies have been conducted to evaluate the optimal AR model order for EEG, but the criteria used in these studies does not necessarily equate to the optimal AR model order for sensorimotor rhythm (SMR)-based BCI control applications. The present study confirms this by evaluating the EEG spectra of data obtained during control of SMR-BCI using different AR model orders and model evaluation criteria. The results indicate that the AR model order that optimizes SMR-BCI control performance is generally higher than the model orders that are frequently used in SMR-BCI studies.

Electroencephalogram (EEG) analysis remains problematic due to limited understanding of the signal origin, which leads to the difficulty of designing evaluation methods. In spite of these shortcomings, the EEG is a valuable tool in the evaluation of some neurological disorders as well as in the evaluation of overall cerebral activity. In most studies, which use quantitative EEG analysis, the properties of measured EEG are computed by applying power spectral density (PSD) estimation for selected representative EEG samples. The sample for which the PSD is calculated is assumed to be stationary. This work deals with a comparative study of the PSD obtained from normal, epileptic and alcoholic EEG signals. The power density spectra were calculated using fast Fourier transform (FFT) by Welch's method, auto regressive (AR) method by Yule-Walker and Burg's method. The results are tabulated for these different classes of EEG signals.

R. Koenker a G. Basset (1978) proposed the regression quantiles as any generalization of usual quantiles to linear regression model. They characterized the regression quantile as the solution of the linear program. called the componenents of the optimal solution of dual problem as the regression rank scores. They showed that many aspects of the duality of order statistics and ranks in the location model generalize naturally to the linear model. proposed some tests based on regression rank scores generated by truncated score functions. A general class of tests based on regression rank scores, parallel to classical rank tests as the Wilcoxon, normal scores and median, was constructed in . The tests of the Kolmogorov-Smirnov type were proposed by Jurečková (1992) and the tests of homoscedasticity in the linear model based regression rank scores were proposed by Gutenbrunner (1994). The concept of regression rank scores was extended in , as autoregression rank scores, to the autoregressive (AR) model. The tests of the linear hypothesis on the AR parameter based on the autoregression rank scores were constructed in and in Hallin and el. (1997). A nonparametric test of independence of two autoregressive time series was considered Hallin and el. (2001). Goodness-of-fit tests in the model with nuisance regression and scale parameters were constructed by Jurečková, .

This paper presents a robust model-based technique for the detection and diagnosis of gear faults under varying load conditions using the gear motion residual signal. Since the majority of energy in the healthy state of the gear of interest is concentrated at the meshing fundamental and its harmonics, the gear motion residual signal, obtained by the removal of the regular gear meshing fundamental and its harmonics from the time-synchronous average (TSA) signal, will be much less sensitive to the varying load conditions than the TSA signal. Also, the gear motion residual signal usually shows evidence of faults earlier and more clearly than the TSA signal. Therefore, less load dependence and an earlier indication of incipient faults can be obtained simultaneously. A noise-adaptive Kalman filter-based auto-regressive (AR) model is fitted to the gear motion residual signals in the healthy state of the gear of interest. By the selection of a proper model order which provides a compromised model for the healthy gear under various load conditions with the aid of a specific AR model order selection method proposed in this study, further enhancement in load independence can be obtained in the AR model residuals. Consequently, a robust statistical measure, which takes the percentage of outliers exceeding the three standard deviation limits of the baseline AR model residuals, is applied to evaluate the state of the gear of interest. The proposed diagnostic model is validated using full lifetime vibration signals of gearbox operating from new to breakdown under a variety of failure modes and demonstrates remarkable advantages over other newly proposed techniques.

This paper investigates regression quantiles (RQ) for unstable autoregressive models. The uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit circle. Unlike the results already available for the regression and stationary autoregression quantiles, the joint asymptotic distribution involves stochastic integrals in terms of a series of independent and identically distributed multivariate Brownian motions with correlated components. The related L−estimator is also discussed. As an auxiliary theorem, a weak convergence of a randomly weighted residual empirical process to the stochastic integral of a Kiefer process is established. The results obtained in this paper provide an asymptotic theory for nonstationary time series processes, which can be used to construct robust unit root tests. * The authors would like to acknowledge the financial support of the Australian Research Council. This paper was revised while the second author was visiting the Institute of Social and Economic Research at Osaka University.

In this paper, EEG signals of 20 schizophrenic patients and 20 age-matched control participants are analyzed with the objective of determining the more informative channels and finally distinguishing the two groups. For each case, 22 channels of EEG were recorded. A two-stage feature selection algorithm is designed, such that, the more informative channels are first selected to enhance the discriminative information. Two methods, bidirectional search and plus-L minus-R (LRS) techniques are employed to select these informative channels. The interesting point is that most of selected channels are located in the temporal lobes (containing the limbic system) that confirm the neuro-phychological differences in these areas between the schizophrenic and normal participants. After channel selection, genetic algorithm (GA) is employed to select the best features from the selected channels. In this case, in addition to elimination of the less informative channels, the redundant and less discriminant features are also eliminated. A computationally fast algorithm with excellent classification results is obtained. Implementation of this efficient approach involves several features including autoregressive (AR) model parameters, band power, fractal dimension and wavelet energy. To test the performance of the final subset of features, classifiers including linear discriminant analysis (LDA) and support vector machine (SVM) are employed to classify the reduced feature set of the two groups. Using the bidirectional search for channel selection, a classification accuracy of 84.62% and 99.38% is obtained for LDA and SVM, respectively. Using the LRS technique for channel selection, a classification accuracy of 88.23% and 99.54% is also obtained for LDA and SVM, respectively. Finally, the results are compared and contrasted with two well-known methods namely, the single-stage feature selection (evolutionary feature selection) and principal component analysis (PCA)-based feature selection. The results show improved accuracy of classification in relatively low computational time with the two-stage feature selection. #

A multivariate autoregressive (AR) model for rain attenuation on a network of radio links is presented. Underlying assumptions are discussed, including the stationarity of rainfall rate in space and time within the region enclosing the links. Formulation of the model is described, together with some considerations for its application in assessing performance of a network of radio links. An example of use of the model for simulation of rain attenuation on two short converging links operating at 30 GHz is given.

Continuous glucose monitors (CGMs) present a problem of lack of accuracy, especially in the lower range, sometimes leading to missed or false hypoglycemia. A new algorithm is presented here aimed at improving the measurement accuracy and hypoglycemia detection. Its core is the estimation of blood glucose (BG) in real time (RT) from CGM intensity readings using autoregressive (AR) models.

Since EEG is one of the most important sources of information in therapy of epilepsy, several researchers tried to address the issue of decision support for such a data. In this paper, we introduce two fundamentally different approaches for designing classification models (classifiers); the traditional statistical method based on logistic regression and the emerging computationally powerful techniques based on artificial neural networks (ANNs). Logistic regression as well as feedforward error backpropagation artificial neural networks (FEBANN) and wavelet neural networks (WNN) based classifiers were developed and compared in relation to their accuracy in classification of EEG signals. In these methods we used FFT and autoregressive (AR) model by using maximum likelihood estimation (MLE) of EEG signals as an input to classification system with two discrete outputs: epileptic seizure or nonepileptic seizure. By identifying features in the signal we want to provide an automatic system that will support a physician in the diagnosing process. By applying AR with MLE in connection with WNN, we obtained novel and reliable classifier architecture. The network is constructed by the error backpropagation neural network using Morlet mother wavelet basic function as node activation function. The comparisons between the developed classifiers were primarily based on analysis of the receiver operating characteristic (ROC) curves as well as a number of scalar performance measures pertaining to the classification. The WNN-based classifier outperformed the FEBANN and logistic regression based counterpart. Within the same group, the WNN-based classifier was more accurate than the FEBANN-based classifier, and the logistic regression-based classifier. q (LR); Feedforward error backpropagation artificial neural network (FEBANN); Wavelet neural network (WNN) Neural Networks 18 985-997 www.elsevier.com/locate/neunet 0893-6080/$ -see front matter q

lower bound (CRLB) Fisher information matrix (FIM) Nonsymmetric half-plane (NSHP) Two-dimensional (2-D) Autoregressive (AR) model Moving average (MA) model Autoregressive moving average (ARMA) model Parameter estimation Homogeneous random fields The Cramer-Rao lower bound (CRLB) that gives the minimal achievable variance/standard deviation for any unbiased estimator offers a useful tool for an assessment of the consistency of parameter estimation techniques. In this paper, a closed-form expression for the computation of the exact CRLB on unbiased estimates of the parameters of a twodimensional (2-D) autoregressive moving average (ARMA) model with a nonsymmetric half-plane (NSHP) region of support is developed. The proposed formulation is mainly based on a matrix representation of 2-D real-valued discrete and homogeneous random field characterized by the NSHP ARMA model. Assuming that the random field is Gaussian, the covariance matrix of the NSHP ARMA random field is first expressed in terms of the model parameters. Then, using this matrix structure, a closed-form expression of the exact Fisher information matrix required for the CRLB computation of the NSHP ARMA model parameters is developed. Finally, the main formulas derived for the NSHP ARMA model are rearranged for its autoregressive and moving average counterparts, separately. Numerical simulations are included to demonstrate the behavior of the derived CRLB formulas.

This paper deals with the case of a high speed mobile receiver operating in an orthogonal-frequency-divisionmultiplexing (OFDM) communication system. Assuming the knowledge of delay-related information, we propose an iterative algorithm for joint multi-path Rayleigh channel complex gains and data recovery in fast fading environments. Each complex gain time-variation, within one OFDM symbol, is approximated by a polynomial representation. Based on the Jakes process, an autoregressive (AR) model of the polynomial coefficients dynamics is built, making it possible to employ the Kalman filter estimator for the polynomial coefficients. Hence, the channel matrix is easily computed, and the data symbol is estimated with free inter-sub-carrier-interference (ICI) thanks to the use of a QRdecomposition of the channel matrix. Our claims are supported by theoretical analysis and simulation results, which are obtained considering Jakes' channels with high Doppler spreads.

 Statistical (or technical analysis) approaches, which either are direct applications of the statistical techniques of load forecasting or power market implementations of econometric models. While the efficiency and usefulness of technical analysis in financial markets is often questioned, in power markets these methods do stand a better change. The reason for this is the seasonality prevailing in electricity price processes during normal, non-spiky periods. It makes the electricity prices more predictable than those of "very randomly" fluctuating financial assets. Moreover, to enhance their efficiency many of the statistical approaches considered in the literature often incorporate one or two fundamental factors, like loads or fuel prices. Examples of statistical models are further discussed in Section 1.3.  Artificial intelligence-based (or non-parametric) techniques, which model price processes via non-parametric tools such as neural networks, fuzzy logic, etc. AI-based models tend to be flexible and can handle complexity and non-linearity. This makes them promising for short-term predictions and a number of authors have reported their excellent performance in STPF. Like in load forecasting, artificial neural networks (ANNs) have probably received the most attention [30] . Other non-parametric techniques have been also applied, however, typically in hybrid constructions .

In system identification and parametric spectral estimation by two-dimensional (2-D) autoregressive (AR) and 2-D autoregressive moving average (ARMA) models, the order selection problem is often required. In this correspondence, we show that the information of 2-D AR model order is implicitly contained in a correlation matrix. An algorithm for 2-D quarter-plane AR model order determination is proposed. Numerical simulations are presented to show the efficiency of the proposed singular value decomposition (SVD) based algorithm.

Neural networks are trained to classify half-second segments of six-channel, EEG data into one of five classes corresponding to five cognitive tasks performed by four subjects. Two and three-layer feedforward neural networks are trained using 10-fold cross-validation and early stopping to control over-fitting. EEG signals were represented as autoregressive (AR) models. The average percentage of test segments correctly classified ranged from 71% for one subject to 38% for another subject. Cluster analysis of the resulting neural networks' hidden-unit weight vectors identifies which EEG channels are most relevant to this discrimination problem.

This paper deals with the on-line estimation of time-varying frequency-flat Rayleigh fading channels based on training sequences and using H ∞ filtering. When the fading channel is approximated by an autoregressive (AR) process, the AR model parameters must be estimated. As their direct estimations from the available noisy observations at the receiver may yield biased values, the joint estimation of both the channel and its AR parameters must be addressed. Among the existing solutions to this joint estimation issue, Expectation Maximization (EM) algorithm or crosscoupled filter based approaches can be considered. They usually require Kalman filtering which is optimal in the H 2 sense provided that the initial state, the driving process and measurement noise are independent, white and Gaussian. However, in real cases, these assumptions may not be satisfied. In addition, the state-space matrices and the noise variances are not necessarily accurately estimated. To take into account the above problem, we propose to use two crosscoupled H ∞ filters. This method makes it possible to provide A. Jamoos (B) robust estimation of the fading channel and its AR parameters.

This paper presents an inflow-forecasting model and a Piecewise Stochastic Dynamic Programming model (PSDP) to investigate the value of the Quantitative Precipitation Forecasts (QPFs) comprehensively. Recently medium-range quantitative precipitation forecasts are addressed to improve inflow forecasts accuracy. Revising the Ertan operation, a simple hydrological model is proposed to predict 10-day average inflow into the Ertan dam using GFS-QPFs of 10-day total precipitation during wet season firstly. Results show that the reduction of average absolute errors (ABE) is of the order of 15% and the improvement in other statistics is similar, compared with those from the currently used AR model. Then an improved PSDP is proposed to generate monthly or 10-day operating policies to incorporate forecasts with various lead-times as hydrologic state variables. Finally performance of the PSDP is compared with alternative SDP models to evaluate the value of the GFS-QPFs in hydropower generation. The simulation results demonstrate that including the GFS-QPFs is beneficial to the Ertan reservoir inflow forecasting and hydropower generation dispatch.

This paper tries to show how System Dynamics (SD) models may easily incorporate fundamental elements of AR models. We first review the different elements of AR models with increasing complexity: a single variable AR model; vector autoregressive models (VAR) considering a vector with several variables; and structural vector autoregressive (SVAR) models, where several economy theory elements can be considered. As

An adaptive on-line procedure is presented for autoregressive (AR) modeling of nonstationary multivariate time series by means of Kalman filtering. The parameters of the estimated time-varying model can be used to calculate instantaneous measures of linear dependence. The usefulness of the procedures in the analysis of physiological signals is discussed in two examples: First, in the analysis of respiratory movement, heart rate fluctuation, and blood pressure, and second, in the analysis of multichannel electroencephalogram (EEG) signals. It was shown for the first time that in intact animals the transition from a normoxic to a hypoxic state requires tremendous short-term readjustment of the autonomic cardiac-respiratory control. An application with experimental EEG data supported observations that the development of coherences among cell assemblies of the brain is a basic element of associative learning or conditioning.

A complete signal processing strategy is presented to detect and precisely recognize tongue movement by monitoring changes in airflow that occur in the ear canal. Tongue movements within the human oral cavity create unique, subtle pressure signals in the ear that can be processed to produce commands signals in response to that movement. Once recognized, said movements can in turn be used in humanmachine interface applications such as communicating with a computer and controlling mechanical devices. The processing strategy includes pressure signal acquisition using a microphone inserted into the ear-canal, PSD analysis to design bandpass filters to reject pressure changes due to sources other than tongue movements, start-and end-point detection in the waveforms through crosscorrelation, signal estimation, and the design and evaluation of parametric and non-parametric signal classifiers. The non-parametric signal classifiers include non-linear alignment classifiers and matched filters, while the parametric classification involves a multivariate Gaussian classifier using AR model parameters. The complete strategy is tested on 4 tongue actions: touching the tongue to the left and right corners of the mouth, and to the top and bottom center of the mouth. Through extensive experiments, it is shown that the pressure signals due to tongue movements are distinct and can be detected with over 97% accuracy. It is thus concluded that the unique strategy will make hands-free control of devices using tongue movements a practical reality.

We investigate the forecasting power of different time series models for electricity spot prices. The models include different specifications of linear autoregressive time series with heteroscedastic noise and/or additional fundamental variables and non-linear regime-switching TAR-type models. The models are tested on a time series of hourly system prices and loads from the California power market. Data from the period July 5, 1999 - April 2, 2000 are used for calibration and from the period April 3 - December 3, 2000 for out-of-sample testing.

This paper compares the performance of four approaches for the detection of transient episodes in the heart rate variability (HRV) records. These are based on autoregressive (AR) modeling, Discrete wavelet transforms (DWT), wavelet packet transforms, and hidden Markov Modeling 0. A competitive neural network has been applied for classification and the results of the four techniques have been compared. It has been concluded that the autoregressive model is the most efficient technique for detecting the essential features describing the transient episodes in HRV.

To forecast future values of a time series is one of the main goals in times series analysis. Many forecasting methods have been developed and its performance evaluated. In order to make a selection among an avalanche of such emerging methods they have to be compared in a kind of forecasting competition. One of these competitions is the M3 competition with its 3003 time series. The competition results in paper are frequently used as a benchmark in comparative studies. The Boot.EXPOS approach developed by the authors, combines the use of exponential smoothing methods with the bootstrap methodology to forecast time series. The idea is to join these two approaches (bootstrap and exponential smoothing) and to construct a computational algorithm to obtain forecasts. It works in an automatic way and can be summarized as follows: (i) choose an exponential smoothing model, among several proposed using the mean squared error, and obtain the model components; (ii) fit an AR to the residuals of the adjusted model; the order of the AR is selected by AIC criterion; (iii) center the new residuals obtained in previous step and resample; (iv) obtain a bootstrapped replica of the time series according to the AR model and exponential smoothing components found in first step; (v) forecast future values according to model in (i); (vi) compute the point forecast as the mean or as the median of the predicted values. The performance of the procedure here proposed is evaluated by comparing it with other procedures presented in the M3 competition. Some accuracy measures are used for that comparison. All computational work is done using the R2.8.1 software (R Development Core Team, 2008).

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 is explained, from an econometric perspective, by our theoretical and simulation results.

A computationally efficient procedure was developed for the fitting of many multivariate locally stationary autoregressive models. The details of the Householder method for fitting multivariate autoregressive model and multivariate locally stationary autoregressive model (MLSAR model) are shown. The proposed procedure is quite efficient in both accuracy and computation. The amount of computation is bounded by a multiple of Nm 2 with N being the data length and m the highest model order, and does not depend on the number of models checked. This facilitates the precise estimation of the change point of the AR model. Based on the AICs' of the fitted MLSAR models and Akalke's definition of the likelihood of the models, a method of evaluating the posterior distribution of the change point of the AR model is also presented. The proposed procedure is, in particular, useful for the estimation of the arrival time of the S wave of a microearthquake. To illustrate the usefulness of the proposed procedure, the seismograms of the foreshocks of the 1982 Urakawa-Oki Earthquake were analyzed. These data sets have been registered to AISM Data Library and the readers of this Journal can access to them by the method described in this issue.

Staging and detection of various states of sleep derived from EEG and other biomedical signals have proven to be very helpful in diagnosis, prognosis and remedy of various sleep related disorders. The time consuming and costly process of visual scoring of sleep stages by a specialist has always motivated researchers to develop an automatic sleep scoring system and the first step toward achieving this task is finding discriminating characteristics (or features) for each stage. A vast variety of these features and methods have been investigated in the sleep literature with different degrees of success. In this study, we investigated the performance of a newly introduced measure: the Itakura Distance (ID), as a similarity measure between EEG and EOG signals. This work demonstrated and further confirmed the outcomes of our previous research that the Itakura Distance serves as a valuable similarity measure to differentiate between different sleep stages.

A channel estimation algorithm for MIMO-OFDM systems in Fast Time-Varying Environments is proposed. The channel estimation function is based on the equivalent discretetime channel taps or on the physical propagation channel parameters. To handle rapid variations of channels within a transmission block, we approximate the channel by a basis expansion model (BEM). Based on the Jakes process, an auto-regressive (AR) model of the BEM coefficients dynamics is built, making it possible to estimate and track the BEM coefficients using Kalman filter . Hence, the channel matrix is easily computed, and the data symbol is detected with free ICI . Our claims are supported by theoretical analysis and simulation results, which are obtained considering Jakes' channels with high Doppler spreads.

This paper tests whether housing prices in the five segments of the South African housing market, namely large–middle, medium–middle, small–middle, luxury and affordable, exhibit non-linearity based on smooth transition autoregressive (STAR) models estimated using quarterly data from 1970:Q2 to 2009:Q3. Findings point to an overwhelming evidence of non-linearity in these five segments based on in-sample evaluation of the linear and non-linear models. We next provide further support for non-linearity by comparing one- to four-quarters-ahead out-of-sample forecasts of the non-linear time series model with those of the classical and Bayesian versions of the linear autoregressive (AR) models for each of these segments, for the out-of-sample horizon 2001:Q1 to 2009:Q3, using the in-sample period 1970:Q2 to 2000:Q4. Our results indicate that barring the one-, two and four-step(s)-ahead forecasts of the small segment, the non-linear model always outperforms the linear models. In addition, given the existence of strong causal relationship amongst the house prices of the five segments, the multivariate versions of the linear (classical and Bayesian) and STAR (MSTAR) models were also estimated. The MSTAR always outperformed the best performing univariate and multivariate linear models. Thus, our results highlight the importance of accounting for non-linearity, as well as the possible interrelationship amongst the variables under consideration, especially for forecasting.► This paper finds overwhelming evidence of non-linearity in five segments of the South African housing market, covering the period of 1970:Q2 to 2009:Q3. ► The five segments are: large–middle, medium–middle, small–middle, luxury and affordable. ► Further support for non-linearity is provided by comparing forecasts of the non-linear time series model with those of the classical and Bayesian versions of the linear autoregressive (AR).

We present a new method that uses the pulse oximeter signal to estimate the respiratory rate. The method uses a recently developed time-frequency spectral estimation method, variablefrequency complex demodulation (VFCDM), to identify frequency modulation (FM) of the photoplethysmogram waveform. This FM has a measurable periodicity, which provides an estimate of the respiration period. We compared the performance of VFCDM to the continuous wavelet transform (CWT) and autoregressive (AR) model approaches. The CWT method also utilizes the respiratory sinus arrhythmia effect as represented by either FM or AM to estimate respiratory rates. Both CWT and AR model methods have been previously shown to provide reasonably good estimates of breathing rates that are in the normal range (12-26 breaths/min). However, to our knowledge, breathing rates higher than 26 breaths/min and the real-time performance of these algorithms are yet to be tested. Our analysis based on 15 healthy subjects reveals that the VFCDM method provides the best results in terms of accuracy (smaller median error), consistency (smaller interquartile range of the median value), and computational efficiency (less than 0.3 s on 1 min of data using a MATLAB implementation) to extract breathing rates that varied from 12-36 breaths/min. Index Terms-FM, pulse oximeter, respiratory sinus arrhythmia, time-frequency analysis.

The main purpose of this paper is to propose a new fault feature extraction approach based on empirical mode decomposition (EMD) method and autoregressive (AR) model for roller bearings. AR model is an effective approach to extract the fault feature of the vibration signals and the fault pattern can be identified directly by the extracted fault features without establishing the mathematical model and studying the fault mechanism of the system. However, AR model can only be applied to stationary signals, while the fault vibration signals of a roller bearing are non-stationary. Aiming at this problem, in this paper, the EMD method is used as a pretreatment to decompose the non-stationary vibration signal of a roller bearing into a number of intrinsic mode function (IMF) components which are stationary, then the AR model of each IMF component can be established. The AR parameters and the remnant's variance of the AR models of each IMF components are regarded as the feature vectors. The Mahalanobis distance criterion function is used to identify the condition and fault pattern of a roller bearing. Experimental analysis results show that the roller bearing fault features can be extracted by the proposed approach effectively. r

Abstracf-The quasiperiodicity of regularly spaced scatterers results in characteristic patterns in the spectra of backscattered ultrasonic signals from which the mean scatterer spacing can be estimated. The mean spacing has been considered for classifying certain biological tissue. This paper addresses the problem of estimating the mean scatterer spacing from backscattered ultrasound signals using the frequency-smoothed spectral autocorrelation (SAC) function. The SAC function exploits characteristic differences between the phase spectrum of the resolvable quasiperiodic scatterers and the unresolvable uniformly distributed (diffuse) scatterers to improve estimator performance over other estimators that operate directly on the magnitude spectrum. Mean scatterer spacing estimates are compared for the frequencysmoothed SAC function and a cepstral technique using an AR model. Simulation results indicate that SAC-based estimates converge more reliably over smaller amounts of data than cepstrumbased estimates. An example of computing an estimate from liver tissue scans is also presented for the SAC function and the AR cepstrum.