Order Autoregressive Model Research Articles

A Theoretical Analysis on Sampling Size in WiFi Fingerprint-Based Localization

This paper deals with a key problem in WiFi fingerprint-based localization, namely how to sample a sufficient number of received signal strength (RSS) measurements during an offline site survey. To this end, a probabilistic framework is firstly presented to characterize the ability of distinguishing two fingerprints, and is then applied in both the ideally infinite sampling case and the realistically finite sampling case with correlated samples. On these grounds, it is shown that the Euclidean distance between the vectors of mean RSS measurements at any two positions is the key factor of determining localization performance, and how several other factors affect localization performance. More importantly, based on the central limit theory, a quantitative analysis is conducted to describe the degradation in localization performance introduced by finite and correlated samples. In addition, provided that correlated samples satisfy the first order autoregressive model, an explicit formula is derived to describe the relationship between the correlation coefficient and the sampling sizes, which can be employed to guide the offline site survey. Extensive simulations are conducted to confirm the effectiveness of the probabilistic framework as well as the correctness of different analytical results, and an experiment is also carried out for validation. This paper not only helps to understand the basic mechanism of WiFi fingerprint-based localization, but also provides insightful guidelines for efficiently building a fingerprint database.

Modeling Best Practice Life Expectancy Using Gumbel Autoregressive Models

Best practice life expectancy has recently been modeled using extreme value theory. In this paper we present the Gumbel autoregressive model of order one—Gumbel AR(1)—as an option for modeling best practice life expectancy. This class of model represents a neat and coherent framework for modeling time series extremes. The Gumbel distribution accounts for the extreme nature of best practice life expectancy, while the AR structure accounts for the temporal dependence in the time series. Model diagnostics and simulation results indicate that these models present a viable alternative to Gaussian AR(1) models when dealing with time series of extremes and merit further exploration.

On Scheduling Performance of Multi-User Full-Duplex Two-Way Relaying System With Rician Distributed RSI

In this paper, a multi-user full-duplex (FD) two-way relaying system with decode-and-forward protocol is considered where all the nodes are assumed to be mobile and to have FD abilities. The residual self-interference (RSI) at each node is modeled as a Rician distributed random variable and the effect of mobility is incorporated by adopting the first order auto-regressive (AR) model. Then, the signal-to-interference-plus-noise-ratio (SINR) based scheduling schemes namely random scheduling, absolute channel power-based (CPB) scheduling, hybrid scheduling, and normalized CPB scheduling, are modified and the user pair selection is carried out on the basis of instantaneous channel statistics. The performance of the considered framework is analyzed for the modified scheduling schemes in terms of error probability and average rate. Next, the closed-form expressions for the symbol error probability (SEP) and average rate are derived for independent and non-identically distributed Rayleigh fading channels. Also, the numerical analysis highlighting the impact of user mobility and imperfect channel estimation on the scheduling strategies, fairness is presented. Furthermore, the impacts of the degree of traffic asymmetry, scheduling fairness, user mobility, channel estimation errors and RSI on the system performance are investigated. Numerical results are validated through the Monte Carlo simulations.

AR and ARMA model order selection for time-series modeling with ImageNet classification

We propose model order selection methods for autoregressive (AR) and autoregressive moving average (ARMA) time-series modeling based on ImageNet classifications with a 2-dimensional convolutional neural network (2-D CNN). We designed two models for two realistic scenarios: (1) a general model which emulates the scenario that validation and test datasets do not necessarily have the same dynamics as the training data, (2) a specific model which emulates the opposite scenario—the validation and test datasets share the dynamics of the training data. The results were compared to those of both Akaike Information criterion (AIC) and Bayesian Information criterion (BIC). Using simulation examples, we trained 2-D CNN-based Inception-v3 and ResNet50-v2 models for either AR or ARMA order selection for each of the two scenarios. The proposed ResNet50-v2 to use both time-frequency and the original time series data outperformed AIC and BIC for all scenarios. For the general model, the average of relative error reduction (ARER) when compared to the BIC method in the clean and three noisy environments was 19.07% (±14.22%) for the AR order for an AR process, and 5.67% (±2.83%) for the ARMA order for an ARMA process. The ARERs significantly improved to 73.92% (±30.95%) and 65.58% (±38.61%) for the AR and ARMA models, respectively, for the specific model scenario.

Comparison of BINAR(1) models with bivariate negative binomial innovations and explanatory variables

The bivariate integer-valued autoregressive model of order 1 (BINAR(1)) is popular in fitting bivariate time series of counts, and the bivariate negative binomial (BNB) distribution can be chosen as its innovation's distribution, which is more flexible than the traditional bivariate Poisson distribution. It is well known that BNB distributions can be constructed in different ways, and these distributions will be reviewed in this paper. Performances of BINAR(1) models based on these BNB distributions with explanatory variables being included in the survival probability are compared. To estimate unknown parameters, the conditional maximum likelihood method is considered and evaluated by Monte Carlo simulations. Two sales counts are used to compare performances of the above models, and some interesting conclusions are also given.

Width Estimation of Non-Gaussian Doppler Velocity Spectra of Meteorological Formations

The paper considers features of the Doppler velocity spectrum width of meteorological formations obtained on the basis of the pulse-pair method when a velocity Doppler spectrum differs from the Gaussian shape. Since the autoregressive models of various orders are widely used in practice for approximating the echo signals from meteorological formations and taking into account their spectrum shape, we have analyzed the measurement errors while using the pulse-pair method. It is shown that neglecting the information on the shape of Doppler velocity spectrum may lead to unacceptable large measurement errors and distort the true level of danger of meteorological formations. The possible methods of determining the autoregressive model orders are discussed, and the benefits of the method based on threshold processing of α-parameters of adaptive lattice filters are shown. The distribution densities of these parameters are determined for the calculation of recognition threshold of autoregressive model order. The statistical characteristics of recognition obtained by the known and proposed methods are compared. The proposed method in terms of the accuracy of order recognition actually is not inferior to the known methods, but can be implemented directly in the process of measuring the width of Doppler velocity spectrum that sets it apart from the others.

Smoothly clipped absolute deviation estimation for uncertain autoregressive model

Uncertain time series is chronological sequence overtime where each period is described by an uncertain variable. In this paper, we investigate the smoothly clipped absolute deviation (SCAD) penalized estimation method to determine the unknown parameters in the uncertain autoregressive model, and the autoregressive model order can be simultaneously obtained for a pre-given thresholding parameter λ. Besides, an iterative algorithm based on local quadratic approximations for finding the penalized estimators is provided. Based on the fitted autoregressive model, the forecast value and the future value’s confidence interval are given. Besides, the sum of the squared error approach to select the optimal λ is discussed. Finally, some examples are used to validate the effectiveness of the proposed method by the comparative analysis.

On the Tracking Performance of Adaptive Filters and Their Combinations

Combinations of adaptive filters have attracted attention as a simple solution to improve filter performance, including tracking properties. In this paper, we consider combinations of LMS and RLS filters, and study their performance for tracking time-varying solutions. Modeling the variation of the parameter vector to be estimated as a first order autoregressive (AR) model, we show that a convex combination between one LMS and one RLS filters with their optimum settings may have a tracking performance close to the optimal excess mean-square error (EMSE) and mean-square deviation (MSD) obtained via Kalman filter, but with lower computational complexity (linear in the filter length instead of quadratic — in the case of diagonal matrices in the Kalman model — or cubic, for general Kalman models).

Effect of First Order Auto-Regressive Model on the Power Function of Average Control Charts under Non-Normal Population

The Sri Lankan Journal of Applied Statistics(SLJAS) is an open-access, international, double-blind peer-reviewed journal published by the Institute of Applied Statistics, Sri Lanka (IASSL). The main purpose of the journal is to publish the results of original work on applications of Statistics and on theoretical and methodical aspects of Statistics. The journal also welcomes critical reviews including conceptual discussions, opinions and book reviews. Applications of Statistics in the area of Agriculture & Forestry, Medical, Dental and Veterinary Sciences, Natural, Physical Sciences, Social Sciences, Economics and Actuarial Science fall within the scope of the journal. This journal does not charge any fee for article processing and submission.

A study on some stochastic models in time series

A first order autoregressive model is introduced which is an extension of the EAR(1) process of Gaver and Lewis (1980) if the marginals are exponentially distributed. Discrete version of the model is introduced and studied. Some applications of the models are also mentioned.

Characterizing gait pattern dynamics during symmetric and asymmetric walking using autoregressive modeling.

Gait asymmetry is often observed in populations with varying degrees of neuromuscular control. While changes in vertical ground reaction force (vGRF) peak magnitude are associated with altered limb loading that can be observed during asymmetric gait, the challenge is identifying techniques with the sensitivity to detect these altered movement patterns. Autoregressive (AR) modeling has successfully delineated between healthy and pathological gait during running; but has been little explored in walking. Thus, AR modeling was implemented to assess differences in vGRF pattern dynamics during symmetric and asymmetric walking. We hypothesized that the AR model coefficients would better detect differences amongst the symmetric and asymmetric walking conditions than the vGRF peak magnitude mean. Seventeen healthy individuals performed a protocol that involved walking on a split-belt instrumented treadmill at different symmetric (0.75m/s, 1.0 m/s, 1.5 m/s) and asymmetric (Side 1: 0.75m/s-Side 2:1.0 m/s; Side 1:1.0m/s-Side 2:1.5 m/s) gait conditions. Vertical ground reaction force peaks extracted during the weight-acceptance and propulsive phase of each step were used to construct a vGRF peak time series. Then, a second order AR model was fit to the vGRF peak waveform data to determine the AR model coefficients. The resulting AR coefficients were plotted on a stationarity triangle and their distance from the triangle centroid was computed. Significant differences in vGRF patterns were detected amongst the symmetric and asymmetric conditions using the AR modeling coefficients (p = 0.01); however, no differences were found when comparing vGRF peak magnitude means. These findings suggest that AR modeling has the sensitivity to identify differences in gait asymmetry that could aid in monitoring rehabilitation progression.

A Markov chain approach to the predictability of surface temperature over the northeastern part of India

The present study reports a two-state Markov chain approach as well as an autoregressive approach to study the behavior of the surface temperature time series over northeast India. Considering the minimum requirement of the chi-square test, 1998–2007 (> 100 months) have been considered for testing the Markovian and autoregressive behavior. The monthly surface temperature time series involves monthly data that corresponds to a continuous random variable. This random variable has been discretized to binary data, and the transition probabilities have been computed up to the fourth-order Markov chain model. The best order of Markov chain has been derived through the minimization of the Bayesian information criterion (BIC). By analyzing the time series autocorrelation function and the Akaike information criteria (AIC), the autoregressive model of order two has been found to be a representative and the best autoregressive method for the average monthly time series of surface temperatures over northeast India.

Enhanced Redundant Measurement-Based Kalman Filter for Measurement Noise Covariance Estimation in INS/GNSS Integration

Adaptive Kalman filters (AKF) have been widely applied to the inertial navigation system (INS)/global navigation satellite system (GNSS) integrated navigation system. However, the traditional AKF methods suffer from the problems of filtering instability or covariance underestimation, especially when the GNSS measurement disturbances occur. In this paper, an enhanced redundant measurement-based AKF is developed to improve the filtering performance. The scheme is based on the mutual difference sequence derived from the redundant measurement of INS. By using the mutual difference sequence, the measurement noise covariance can be estimated without being affected by the inaccuracy estimates, hence avoiding the risk of filtering divergence. In addition, the kernel density estimation is used to estimate the GNSS measurement noise’s probability density to detect whether the Gaussian properties of the measurement noise are maintained. When the noise statistics are far from Gaussian distribution, the difference sequence will be modeled as an autoregressive process using the Burg’s method. The real variance of the difference sequence can then be updated relying on the autoregressive model in order to avoid the covariance underestimation. A field experiment was carried out to evaluate the performance of the proposed method. The test results demonstrate that the proposed method can effectively mitigate the GNSS measurement disturbances and improve the accuracy of the navigation solution.

Random order autoregressive time series model with structural break

This paper deals with the problem of modelling time series data with structural breaks occur at multiple time points that may result in varying order of the model at every structural break. A flexible and generalized class of Autoregressive (AR) models with multiple structural breaks is proposed for modelling in such situations. Estimation of model parameters are discussed in both classical and Bayesian frameworks. Since the joint posterior of the parameters is not analytically tractable, we employ a Markov Chain Monte Carlo method, Gibbs sampling to simulate posterior sample. To verify the order change, a hypotheses test is constructed using posterior probability and compared with that of without breaks. The methodologies proposed here are illustrated by means of simulation study and a real data analysis.

Modeling and Estimation of Multivariate Discrete and Continuous Time Stationary Processes

In this paper, we give an autoregressive model of order 1 type of characterization covering all multivariate strictly stationary processes indexed by the set of integers. Consequently, under square integrability, we derive continuous time algebraic Riccati equations for the parameter matrix of the characterization. This provides us with a natural way to define the corresponding estimator. In addition, we show that the estimator inherits consistency from autocovariances of the stationary process. Furthermore, the limiting distribution is given by a linear function of the limiting distribution of the autocovariances. We also present the corresponding existing results of the continuous time setting paralleling them to the discrete case treated in this paper.

Quantification of temporal variability of vertical soil moisture movement through an unsaturated zone

Understanding of the soil moisture movement process in the unsaturated zone is crucial for an accurate estimate of the rate of recharge to the aquifer. The goal of the present research is therefore to quantify the temporal variability of moisture movement through the unsaturated zone. A new framework for quantifying the temporal variability of soil moisture movement over a relatively large space scale through the unsaturated zone is proposed. The unsaturated zone is treated as a nonlinear soil moisture reservoir with a single random input, the effective infiltration, and a single random output, the recharge to the saturated zone, in time. The variation of volumetric soil moisture in response to the variation of effective infiltration is represented by a nonlinear functional series involving generalizations of the convolution integral, which underlies the concept of unit hydrograph. A second order autoregressive model is used to account for the temporal behavior of the input process. The use of Fourier-Stieltjes representation approach enables developing closed-form expressions for the variance of volumetric soil moisture and cross-covariance of the soil moisture and effective infiltration. The variance can be viewed as an index of temporal variability in soil moisture or uncertainty involved in the modeling process. The cross-covariance contains information about how two processes are correlated in time. Focus of analysis is placed on the influence of the controlling parameters on the temporal variability of soil moisture movement.

On-sky results for adaptive optics control with data-driven models on low-order modes

ABSTRACT Dedicated tip–tilt loops are commonly implemented on adaptive optics (AO) systems. In addition, a number of recent high-performance systems feature tip–tilt controllers that are more efficient than the integral action controller. In this context, linear–quadratic–Gaussian (LQG) tip–tilt regulators based on stochastic models identified from AO telemetry have demonstrated their capacity to effectively compensate for the cumulated effects of atmospheric disturbance, windshake and vibrations. These tip–tilt LQG regulators can also be periodically retuned during AO operations, thus allowing to track changes in the disturbances’ temporal dynamics. This paper investigates the potential benefit of extending the number of low-order modes to be controlled using models identified from AO telemetry. The global stochastic dynamical model of a chosen number of turbulent low-order modes is identified through data-driven modelling from wavefront sensor measurements. The remaining higher modes are modelled using priors with autoregressive models of order 2. The loop is then globally controlled using the optimal LQG regulator build from all these models. Our control strategy allows for combining a dedicated tip–tilt loop with a deformable mirror that corrects for the remaining low-order modes and for the higher orders altogether, without resorting to mode decoupling. Performance results are obtained through evaluation of the Strehl ratio computed on H-band images from the scientific camera, or in replay mode using on-sky AO telemetry recorded in 2019 July on the CANARY instrument.

Intra-day solar irradiation forecast using RLS filters and satellite images

Satellite-based solar irradiation forecasting is useful for short-term intra-day time horizons, outperforming numerical weather predictions up to 3-4 hours ahead. The main techniques for solar satellite forecast are based on sophisticated cloud motion estimates from geostationary satellite images. This work explores the use of satellite information in a simpler way, namely spatial averages that require almost no preprocessing. Adaptive auto-regressive models are used to assess the impact of this information on the forecasting performance. A complete analysis regarding model selection, the satellite averaging window size and the inclusion of satellite past measurements is provided. It is shown that: (i) satellite spatial averages are useful inputs and the averaging window size is an important parameter, (ii) satellite lags are of limited utility and spatial averages are more useful than weighted time averages, and (iii) there is no value in fine-tuning the orders of auto-regressive models for each time horizon, as the same performance can be obtained by using a fixed well-selected order. These ideas are tested for a region with intermediate solar variability, and the models succeed to outperform a proposed optimal smart persistence, used here as an exigent performance benchmark.

The Impacts of Climate Change on Food Security – Case Study: Egypt

This study analyses the impacts of climate change on food security in Egypt. The study depends on using ARDL model (Auto regressive distributed lag model) in order to estimate the impacts of climate change on food security dimensions in Egypt. The study found that there is a negative and significant impact of temperature on food production as increasing temperature leads to decreasing some crops’ production. Also, there is a positive and significant impact of temperature on food access as increasing temperature leads to increase food prices. These findings showed that unless sufficient adaptation, Egypt will suffer from negative effects on food production and food access and that will result in a high insecurity of food. This study reached a recommendation of enhancing a comprehensive adaptation system in order to lower the negative impacts of climate change on food security.

Exploring spatio-temporal patterns in mental health related emergency department use from children and adolescents

To understand the spatio-temporal patterns and associated risk factors with the frequency, we analyze records of mental health related emergency department (MHED) visits from youth. The data are extracted for the period 2002--2011 from the population-based, provincial health administrative data systems of Alberta, Canada. Guided by a descriptive analysis, we conduct generalized linear regression analyses of the counts of MHED visits from various health areas. Seasonal effects are examined via three different types of functions, including trigonometric functions. We specify the temporal correlation using an autoregressive model of order 1 and formulate the spatial correlation by a random effects model. Our analysis reveals a strong seasonal pattern and indicates that the MHED visit counts are significantly associated with age, gender, and a proxy for socio-economic status. The final statistical model may be used to forecast future MHED use and identify regions and groups at a higher risk to the MHEDs.