Order Autoregressive Model Research Articles

EEMD Domain AR Spectral Method for Mean Scatterer Spacing Estimation of Breast Tumors From Ultrasound Backscattered RF Data

We present a novel method for estimating the mean scatterer spacing (MSS) of breast tumors using ensemble empirical mode decomposition (EEMD) domain analysis of deconvolved backscattered radio frequency (RF) data. The autoregressive (AR) spectrum from which the MSS is estimated is obtained from the intrinsic mode functions (IMFs) due to regular scatterers embedded in RF data corrupted by the diffuse scatterers. The IMFs are chosen by giving priority to the presence of an enhanced fundamental harmonic and the presence of a greater number of higher harmonics in the AR spectrum estimated from the IMFs. The AR model order is chosen by minimizing the mean absolute percentage error (MAPE) criterion. In order to ensure that the backscattered data is indeed from a source of coherent scattering, we begin by performing a non-parametric Kolmogorov-Smirnov (K-S) classification test on the backscattered RF data. Deconvolution of the backscattered RF data, which have been classified by the K-S test as sources of significant coherent scattering, is done to reduce the system effect. EEMD domain analysis is then performed on the deconvolved data. The proposed method is able to recover the harmonics associated with the regular scatterers and overcomes many problems encountered while estimating the MSS from the AR spectrum of raw RF data. Using our technique, a mean absolute percentage error (MAPE) of 5.78% is obtained while estimating the MSS from simulated data, which is lower than that of the existing techniques. Our proposed method is shown to outperform the state of the art techniques, namely, singular spectrum analysis, generalized spectrum (GS), spectral autocorrelation (SAC), and modified SAC for different simulation conditions. The MSS for in vivo normal breast tissue is found to be 0.69 ± 0.04 mm; for benign and malignant tumors it is found to be 0.73 ± 0.03 and 0.79 ± 0.04 mm, respectively. The separation between the MSS values of normal and benign tissues for our proposed method is similar to the separations obtained for the conventional methods, but the separation between the MSS values for benign and malignant tissues for our proposed method is slightly higher than that for the conventional methods. When the MSS is used to classify breast tumors into benign and malignant, for a threshold-based classifier, the increase in specificity, accuracy, and area under curve are 18%, 19%, and 22%, respectively, and that for statistical classifiers are 9%, 13%, and 19%, respectively, from that of the next best existing technique.

Rank based cointegration testing for dynamic panels with fixed T

In this paper, we show that the cointegration testing procedure of Binder et al. (Econom Theory 21:795–837, 2005) for Panel Vector Autoregressive model of order 1, PVAR(1) is not valid due to the singularity of the hessian matrix. As an alternative we propose a method of moments based procedure using the rank test of Kleibergen and Paap (J Econom 133:97–126, 2006) for a fixed number of time series observations. The test is shown to be applicable in situations with time-series heteroscedasticity and unbalanced data. The novelty of our approach is that in the construction of the test we exploit the “weakness” of the Anderson and Hsiao (J Econom 18:47–82, 1982) moment conditions. The finite-sample performance of the proposed test statistic is investigated using simulated data. The results indicate that for most scenarios the method has good statistical properties. The proposed test provides little statistical evidence of cointegration in the employment data of Alonso-Borrego and Arellano (J Bus Econ Stat 17:36–49, 1999).

Box-Tiao Interrupted Time Series Analysis of Bureau de Change USD/NGN Exchange Rates

This work concerns itself with the interrupted time series or intervention modelling of monthly Bureau de Change (BDC) US Dollar-Nigerian Naira exchange rates. The realization of the time series covers the period from January 2004 to February 2017. This work is necessitated by an observation of an abrupt astronomical rise in the amount of Naira per Dollar as from February 2015 which is therefore taken as an intervention point. Pre-intervention data are adjudged non-stationary. Their first differences are stationary and fitted to them is an adequate autoregressive model of order 6, on which basis post-intervention forecasts are obtained. The difference between these forecasts and their corresponding actual observations are modelled for the intervention transfer function. The parameters of this function are statistically significant signifying model adequacy. Nigerian intervention in this situation may be done on the basis of this model.

PERFORMANCE OF MULTIPLE LINEAR REGRESSION AND AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODELS IN PREDICTING ANNUAL TEMPERATURES OF OGUN STATE, NIGERIA

The performance of Autoregressive Moving Average and Multiple Linear Regression Models in predicting minimum and maximum temperatures of Ogun State is herein reported. Maximum and Minimum temperatures data covering a period of 29 years (1982 -2009) obtained from the Nigerian Meteorological Agency (NiMet), Abeokuta office, Nigeria, were used for the analyses. The data were first processed and aggregated into annual time series. Mann-Kendal non-parametric test and spectral analysis were carried out to detect whether there is trend, seasonal pattern, and either short or long memory in the time series. Mann-Kendal Z-values obtained are –0.47 and –2.03 for minimum and maximum temperatures respectively, indicating no trend, though the plot shows a slight change. The Lo’s R/S Q(N,q) values for minimum and maximum temperatures are 3.67 and 4.43, which are not within the range 0.809 and 1.862, thus signifying presence of long memory. The data was divided into two and the first 20 years data was used for model development, while the remaining was used for validation. Autoregressive Moving Average (ARMA) model of order (5, 3) and Autoregressive (AR) model of order 2 are found best for predicting minimum and maximum temperatures respectively. Multiple Linear Regression (MLR) model with 4 features (moving average, exponential moving average, rate of change and oscillator) were fitted for both temperatures. The ARMA and AR models were found to perform better with Mean Absolute Percentage Error (MAPE) values of -2.89 and -1.37 for minimum and maximum temperatures, compared with the Multiple Linear Regression Models with MAPE values of 141 and 876 respectively. Results of ARMA model can be relied on in generating forecast of temperature of the study area because of their minimal error values. However, it is recommended other climatic elements that were not captured in this paper due to unavailability of information be considered too in order to see which model is best for them.

Subject‐level reliability analysis of fast fMRI with application to epilepsy

PurposeRecent studies have applied the new magnetic resonance encephalography (MREG) sequence to the study of interictal epileptic discharges (IEDs) in the electroencephalogram (EEG) of epileptic patients. However, there are no criteria to quantitatively evaluate different processing methods, to properly use the new sequence.MethodsWe evaluated different processing steps of this new sequence under the common generalized linear model (GLM) framework by assessing the reliability of results. A bootstrap sampling technique was first used to generate multiple replicated data sets; a GLM with different processing steps was then applied to obtain activation maps, and the reliability of these maps was assessed.ResultsWe applied our analysis in an event‐related GLM related to IEDs. A higher reliability was achieved by using a GLM with head motion confound regressor with 24 components rather than the usual 6, with an autoregressive model of order 5 and with a canonical hemodynamic response function (HRF) rather than variable latency or patient‐specific HRFs. Comparison of activation with IED field also favored the canonical HRF, consistent with the reliability analysis.ConclusionThe reliability analysis helps to optimize the processing methods for this fast fMRI sequence, in a context in which we do not know the ground truth of activation areas. Magn Reson Med 78:1–1, 2017. © 2016 International Society for Magnetic Resonance in Medicine

Heartbeats classification using QRS and T waves autoregressive features and RR interval features

AbstractThis paper describes a method for the classification of heartbeats based on electrocardiogram QRS complex and T wave autoregressive (AR) features and interbeat distance (RR interval) features. The QRS complex (length n samples) is modelled using AR model of order P. A second AR model of order P1 is applied to the electrocardiogram segment including ST segment and T wave (ST/T segment) with a length of n1 samples. In addition, RR interval features such as the distance between one heartbeat and its preceding (pre‐RR) and following (post‐RR) heartbeats are extracted. The use of AR modelling is motivated by the fact that QRS complex and ST/T segment corresponding to normal beats present different patterns (in shapes and amplitudes) than those corresponding to ventricular ectopic beats. Lengths and AR model orders that minimize the number of misclassifications are determined. Obtained features are used to train and test support vector machine classifier. The proposed method is tested on MIT/BIH Arrhythmia Database and it is compared to state of the art methods. Overall classification accuracy reached 97.02%, whereas it reached 98.86% in the case of subject‐specific scheme. Results are better or comparable to those obtained by state of the art methods.

House Price Shocks and Individual Divorce Risk in the United States

Households in the United States hold a significant portion of their total wealth in owner-occupied housing. Thus, changes in housing prices may have an important impact on the marital surplus the household enjoys. What happens to marriages of homeowners when there is a shock to housing prices? This question was addressed using household data from the panel study of income dynamics (PSID) and a quarterly MSA level house price index from the Federal Housing Finance Agency, controlling for local labor market conditions. House price shocks were calculated as the cumulative sum of residuals of a second order autoregressive model from the previous four years. Results showed that positive house price shocks stabilized marriage for all couples. A one standard deviation increase in the house price shock decreased the risk of divorce in the following year by about 13–18%. The results were driven by the younger cohort of households in the PSID, those with lower educational attainment, and those with relatively low family income. The findings are discussed in the context of theories on changes in marital surplus, and changes in the transaction costs surrounding divorce.

MANAGEMENT PROCEDURE OF SUPPLIES OF UNITS, MATERIALS AND CONSTITUENT PARTS FOR REPAIR AND MAINTENANCE SUPPORT OF TRANSPORT AND PRODUCTION MACHINES

This article considers a question of creation of schemes and sequence of passing of the main stages of process of execution of repair and maintenance works order taking into account formation of stocks of necessary spare parts, materials and constituent parts. Models of an input stream are offered for inventory control system, which are rather adequately described by autoregressive models of order two.

The effects of normal mixtures and autocorrelation on the fraction non-conforming

ABSTRACTIn this article, the effects of mixtures of two normal distributions on the fraction non-conforming are studied in the context of capability analysis. When the output from several processes is mixed, the quality characteristic variables of the resulting mix may result in a normal mixture distribution. This can happen in cases such as monitoring an output from several suppliers, several machines, or several workers. This study considered the independence case and autocorrelated processes for a mixture of two normal distributions, using an autoregressive model of order one, AR(1). It is shown that the true attained process fraction non-conforming (corresponding to specific values for some capability index) can be very different from what is expected when the data are independent normal random variables.

Time Series Cross-Validation Techniques for determining the order of the Autoregressive models

In the present research paper, we introduced some techniques of cross-validation for time series data. Six different types of time series cross-validation techniques are presented and also discussed various problems in selecting the initial training sample size and the size of training folds. In this paper, all cross-validation techniques, most appropriate techniques for model selection in time series analysis and advantages of the each technique are discussed with empirical study. Keywords: Time series cross-validation, Prediction error, Order of AR model, Training sample, Test sample.

FMRI hemodynamic response function estimation in autoregressive noise by avoiding the drift

The measured functional magnetic resonance imaging (fMRI) time series is typically corrupted by instrumental drift and physiological noise due to respiration and heartbeat giving rise to temporal correlation in the signals. Most methods proposed so far for nonparametric hemodynamic response function (HRF) estimation in fMRI data do not account for these confounding effects, and thus produce biased and inefficient estimates. The aim of this paper is to address this issue by modeling the noise in fMRI time series using an autoregressive model of order p (AR(p)). Making use of a semiparametric model to characterize the fMRI time series and the AR(p) to model the temporally correlated noise, a generalized least squares (GLS) estimator for voxelwise consistent nonparametric HRF estimation is derived. The proposed estimation method is a three-stage procedure that relies on first-order differencing to remove drift and a novel structured covariance estimator for the AR noise based on Cholesky decomposition to derive the best linear unbiased estimator (BLUE) of the HRF. We also establish the asymptotic consistency of the proposed estimator. Simulation results show that the proposed method generates more accurate HRF estimates compared to existing methods. When applied to real fMRI data, it demonstrates the effectiveness in uncovering the brain response temporal dynamics for both event-related and block-design paradigms. Our approach removes the two types of noise in fMRI data simultaneously, thus providing efficient estimation of brain hemodynamic responses, while allowing for flexible characterization of the shape and timing of the voxelwise HRF.

Prediction of silver hake distribution on the Northeast U.S. shelf based on the Gulf Stream path index

Over the past ~40 years, the distribution of silver hake on the Northeast U.S. shelf is found to be significantly correlated with changes in the latitude of Gulf Stream path. The correlation coefficient between the fall Gulf Stream position and the center of biomass of spring silver hake reaches 0.75 when the Gulf Stream leads the silver hake for 6 months. Based on this lead-lag relationship and low-frequency variability of Gulf Stream position with a dominant periodicity of ~9–10 years, the Gulf Stream position is used as a predictor for the center of biomass of silver hake in linear autoregressive (AR) models. The goal of this study is then to optimize the AR model for the prediction of silver hake based on the observed changes in Gulf Stream position. Fall Gulf Stream position is first predicted out to 5 years using a 5th order AR model and the observed Gulf Stream position in preceding years. An optimization process is proposed to choose best AR coefficients based on a newly proposed combined skill parameter. Furthermore, the robustness of our Gulf Stream prediction is verified by comparing the observed Gulf Stream path index data from 2009 to 2012, which are not used for optimizing the AR model, and the predicted Gulf Stream path values for the same time period. We then use this predicted Gulf Stream position to further predict the center of biomass of silver hake in the subsequent spring. Three different methods are used and compared for the silver hake prediction. The predicted silver hake time series can explain as much as 69% of the variance of the observation for the 1st year prediction and 41% for the 5th year prediction. Our results indicate that including Gulf Stream as a predictor produces better prediction skills of silver hake center of biomass than the AR model prediction solely based on the observed silver hake time series.

Statistical Analysis of Electricity Generation in Nigeria Using Multiple Linear Regression Model and Box-Jenkins’ Autoregressive Model of Order 1

This study presents statistical analysis of electricity generation in Nigeria using two different statistical models, namely; multiple linear regression model and box-Jenkins’ autoregressive model of order 1. Two climatic variables (rainfall and temperature) were used as the explanatory variables. Data on electricity generation in Nigeria between 2002 and 2014 were obtained from the Central Bank of Nigeria Statistical Bulletin while Data on rainfall and temperature between 2002 and 2014 were extracted from the National Bureau of Statistics (NBS) abstract. Test of model fitness and forecasting accuracy were done using generic statistical approach which include coefficient of determination and root mean square error. The prediction accuracy of the two statistical models was compared and the best model was selected. Furthermore, correlation between power generation and the two climatic variables (rainfall and temperature), were carried out and the result reveals that the amount of rainfall has significant and positive relationship with power generation in Nigeria. Specifically, rainfall has correlation value of r = 0.927 with the power generation at probability, p = 0.000 and the relationship was significant at 1% (p 0.05) and the relationship was significant at 5% (p<0.05). Among the two statistical models, multiple linear regression model was selected as the best model as it gave the highest value of coefficient of determination (r2=99.77%) and the least Root Mean Square Error (60.27%).

Generalized information criterion for the AR model

This paper studies the generalized information criterion (GIC) for the problem of subset selection in the autoregressive (AR) model under the condition that some of the parameters are irrelevant to the AR model. We prove that the resulting estimator obtained by minimizing the GIC is consistent in subset selection under the mild conditions. Here, the consistency means that the probability of obtaining true sub-model increases to one asymptotically. The results hold when the numbers of the relevant and irrelevant parameters increase to infinity and when the minimum of the absolute values of nonzero parameters decreases toward zero as the sample size increases. A practical method to reduce the computation time is introduced by applying the penalized estimation, which is useful when the order of AR model is very large. Simulation studies are presented to confirm the theoretical results for finite samples. As a real life example, we apply the GIC to annual total sunspot numbers.

A Combined Analysis in Complementary Progeny Tests: Effects on breeding value accuracies

Abstract Complementary progeny tests allow for simultaneously ranking parents for their general combining ability (GCA) and within-family forward selection. To do this, progeny tests are established with different types of genetic entries (i.e., half-sib and full-sib seedlings, respectively), and different experimental designs. This study proposes a combined analysis of the GCA and full-sib (FS) tests using the mixed model approach to predict simultaneously the breeding values of grandparents, parents, full-sib families and offspring on the same scale. Moreover, a first order autoregressive spatial mixed model for the GCA tests was also implemented in the combined analysis. Our empirical study in coastal Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) shows that additional information provided from relatives and the overlap genetic entry among GCA and FS tests via the proposed combined analysis, improves the accuracies of breeding values compared to the non-combined analysis. The improvements in the accuracies of breeding values for backward and forward selections were generally modest. Spatial and combined analyses gave slightly better results than the non-spatial combined model.

Introducing REITs (Real Estate Investment Trusts) to Enhance the Risk Adjusted Returns of the Risky Direct Real Estate Portfolio

&lt;p&gt;&lt;strong&gt;&lt;em&gt;Purpose&lt;/em&gt;&lt;/strong&gt;&lt;strong&gt;&lt;em&gt;:&lt;/em&gt;&lt;/strong&gt;&lt;em&gt; &lt;/em&gt;&lt;em&gt;The paper has several objectives in mind: to examine whether or not &lt;/em&gt;&lt;em&gt;a dynamic, ex ante AHP-SAA model and a dynamic Markowitz QP TAA model that utilizes de-smoothed data, produces an investment strategy, which further optimizes the risk-adjusted return of the pan-Asian real estate portfolio. It examines the required de-smoothing and Modern Portfolio Theory (MPT) for the TAA. &lt;/em&gt;&lt;em&gt;&lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Design/Methodology/Approach&lt;/em&gt;&lt;/strong&gt;&lt;strong&gt;&lt;em&gt;:&lt;/em&gt;&lt;/strong&gt;&lt;em&gt; &lt;/em&gt;&lt;em&gt;This paper reveals that the efficient frontier of risk-adjusted returns for direct real estate portfolio is enhanced by introducing REITS. The portfolio comprises the Pan-Asian office and industrial real estate markets for 13 major Asian cities, to which Asian REITS are added. Direct real estate total return data is in its &lt;/em&gt;&lt;em&gt;“&lt;/em&gt;&lt;em&gt;smooth&lt;/em&gt;&lt;em&gt;”&lt;/em&gt;&lt;em&gt; form while the REIT data is &lt;/em&gt;&lt;em&gt;“&lt;/em&gt;&lt;em&gt;de-smoothed&lt;/em&gt;&lt;em&gt;”&lt;/em&gt;&lt;em&gt; under the 1&lt;sup&gt;st&lt;/sup&gt; and 4&lt;sup&gt;th&lt;/sup&gt; order autoregressive model. The efficient frontier is constructed under a dynamic Strategic Asset Allocation (SAA) model, incorporating the Analytic Hierarchy Process (AHP) approach. Secondly, the dynamic Markowitz quadratic-programming Tactical Asset Allocation (TAA) model is adopted to obtain a geographically and real estate sector diversified portfolio.&lt;/em&gt;&lt;em&gt;&lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Findings&lt;/em&gt;&lt;/strong&gt;&lt;strong&gt;&lt;em&gt;:&lt;/em&gt;&lt;/strong&gt;&lt;em&gt; &lt;/em&gt;&lt;em&gt;The resulting efficient frontier with the de-smoothed data reveals a higher overall TR for every corresponding standard deviation as compared to the smoothed data. TAA for the de-smoothed returns would lie on the efficient frontier at the maximum Sharpe ratio of 1.44 with a TR on 15.30% and a standard deviation of 7.31%. Conversely, TAA for the smoothed returns would lie on the efficient frontier at the maximum Sharpe ratio of 1.31 with a lower TR of 14.2% and a standard deviation of 7.18%.&lt;/em&gt;&lt;em&gt;&lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Practical implications&lt;/em&gt;&lt;/strong&gt;&lt;strong&gt;&lt;em&gt;: &lt;/em&gt;&lt;/strong&gt;&lt;em&gt;This paper should serve as a meaningful guide to look at &lt;/em&gt;&lt;em&gt;an alternative asset allocation process that can be effectively adopted and refined by practitioners and researchers. It enables asset managers/or investors to deploy expert opinions on an ex ante basis for a longer term dynamic SAA model and a short term dynamic Markowitz QP TAA model. &lt;/em&gt;&lt;em&gt;&lt;/em&gt;&lt;/p&gt;&lt;p&gt;&lt;strong&gt;&lt;em&gt;Originality/Value&lt;/em&gt;&lt;/strong&gt;&lt;strong&gt;&lt;em&gt;:&lt;/em&gt;&lt;/strong&gt;&lt;em&gt; The paper offers insightful information for &lt;/em&gt;&lt;em&gt;in adopting the AHP to develop a dynamic SAA and the dynamic Markowitz QP TAA model in utilizing de-smoothed direct real estate TR data. This paper is specific to a Pan Asian direct real estate portfolio of 13 Asian cities together with the introduction of Asian REITS, to provide greater diversification and risk-return benefits.&lt;/em&gt;&lt;em&gt;&lt;/em&gt;&lt;/p&gt;

Fractional order models for system identification of thermal dynamics of buildings

This study presents a class of fractional order models for system identification of thermal dynamics of buildings. Fractional order dynamics has been found to be inherent in the nature of heat transfer problems. It is thus instinctive to use fractional order models to describe the overall thermal dynamics of a building. Besides, fractional time series modeling is known by its long memory effect and capability of representing high-order complicated models in lower-order and compact forms. The reduction of model parameters can then relieve the computational overhead in the system identification procedure. This is of particular significance in model-based predictive control for building energy efficiency. In particular, a fractional order autoregressive model with exogenous input (FARX) is formulated and a corresponding parameter estimation using least squares technique is also provided. Furthermore, the FARX model is validated using simulation data from a detailed model built via IES<VE> software and compared with the prediction using traditional ARX model. It is found that the FARX model can reduce the computational time largely while retaining the prediction accuracy.

Subject-level reliability analysis of fast fMRI with application to epilepsy.

Recent studies have applied the new magnetic resonance encephalography (MREG) sequence to the study of interictal epileptic discharges (IEDs) in the electroencephalogram (EEG) of epileptic patients. However, there are no criteria to quantitatively evaluate different processing methods, to properly use the new sequence. We evaluated different processing steps of this new sequence under the common generalized linear model (GLM) framework by assessing the reliability of results. A bootstrap sampling technique was first used to generate multiple replicated data sets; a GLM with different processing steps was then applied to obtain activation maps, and the reliability of these maps was assessed. We applied our analysis in an event-related GLM related to IEDs. A higher reliability was achieved by using a GLM with head motion confound regressor with 24 components rather than the usual 6, with an autoregressive model of order 5 and with a canonical hemodynamic response function (HRF) rather than variable latency or patient-specific HRFs. Comparison of activation with IED field also favored the canonical HRF, consistent with the reliability analysis. The reliability analysis helps to optimize the processing methods for this fast fMRI sequence, in a context in which we do not know the ground truth of activation areas. Magn Reson Med 78:370-382, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Estimation of inverse autocovariance matrices for long memory processes

This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this goal. The spectral norm consistency of the proposed estimate is established. We then extend this result to linear regression models with long-memory time series errors. In particular, we show that when the objective is to consistently estimate the inverse autocovariance matrix of the error process, the same approach still works well if the estimated (by least squares) errors are used in place of the unobservable ones. Applications of this result to estimating unknown parameters in the aforementioned regression model are also given. Finally, a simulation study is performed to illustrate our theoretical findings.

AR(1) model with skew-normal innovations

In this paper, we consider an autoregressive model of order one with skew-normal innovations. We propose several methods for estimating the parameters of the model and derive the limiting distributions of the estimators. Then, we study some statistical properties and the regression behavior of the proposed model. Finally, we provide a Monte Carlo simulation study for comparing performance of estimators and consider a real time series to illustrate the applicability of the proposed model.