Asymptotic normality of error density estimator in stationary and explosive autoregressive models

In this paper,we consider the limit distribution of the error density function estima-tor in the rst-order autoregressive models with negatively associated and positively associated random errors.Under mild regularity assumptions,some asymptotic normality results of the residual density estimator are obtained when the autoregressive models are stationary process and explosive process.In order to illustrate these results,some simulations such as con dence intervals and mean integrated square errors are provided in this paper.It shows that the residual density estimator can replace the density\estimator"which contains errors.

A cloud model target damage effectiveness assessment algorithm based on spatio-temporal sequence finite multilayer fragments dispersion

To solve the problem of target damage assessment when fragments attack target under uncertain projectile and target intersection in an air defense intercept,this paper proposes a method for calculating target damage probability leveraging spatio-temporal finite multilayer fragments distribution and the target damage assessment algorithm based on cloud model theory.Drawing on the spatial dispersion characteristics of fragments of projectile proximity explosion,we divide into a finite number of fragments distribution planes based on the time series in space,set up a fragment layer dispersion model grounded in the time series and intersection criterion for determining the effective penetration of each layer of fragments into the target.Building on the precondition that the multilayer fragments of the time series effectively assail the target,we also establish the damage criterion of the perforation and penetration damage and deduce the damage probability calculation model.Taking the damage probability of the fragment layer in the spatio-temporal sequence to the target as the input state variable,we introduce cloud model theory to research the target damage assessment method.Combining the equivalent simulation experiment,the scientific and rational nature of the proposed method were validated through quantitative calculations and comparative analysis.

Traveling Wave Solutions of a SIR Epidemic Model with Spatio-Temporal Delay

In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution.

River channel flood forecasting method of coupling wavelet neural network with autoregressive model

Based on analyzing the limitations of the commonly used back-propagation neural network （BPNN）, a wavelet neural network （WNN） is adopted as the nonlinear river channel flood forecasting method replacing the BPNN. The WNN has the characteristics of fast convergence and improved capability of nonlinear approximation. For the purpose of adapting the timevarying characteristics of flood routing, the WNN is coupled with an AR real-time correction model. The AR model is utilized to calculate the forecast error. The coefficients of the AR real-time correction model are dynamically updated by an adaptive fading factor recursive least square（RLS） method. The application of the flood forecasting method in the cross section of Xijiang River at Gaoyao shows its effectiveness.

AUTOREGRESSIVE MODEL AND POWER SPECTRUM CHARATERISTICS OF CURRENT SIGNAL IN HIGH FREQUENCY GROUP PULSE MICRO-ELECTROCHEMICAL MACHINING

The identification of the inter-electrode gap size in the high frequency group pulse micro-electrochemical machining （HGPECM） is mainly discussed. The auto-regressive（AR） model of group pulse current flowing across the cathode and the anode are created under different situations with different processing parameters and inter-electrode gap size. The AR model based on the current signals indicates that the order of the AR model is obviously different relating to the different processing conditions and the inter-electrode gap size; Moreover, it is different about the stability of the dynamic system, i.e. the white noise response of the Green＇s function of the dynamic system is diverse. In addition, power spectrum method is used in the analysis of the dynamic time series about the current signals with different inter-electrode gap size, the results show that there exists a strongest power spectrum peak, characteristic power spectrum（CPS）, to the current signals related to the different inter-electrode gap size in the range of 0～5 kHz. Therefore, the CPS of current signals can implement the identification of the inter-electrode gap.

JUMP DETECTION BY WAVELET IN NONLINEAR AUTOREGRESSIVE MODELS

Wavelets are applied to detection of the jump points of a regression function in nonlinear autoregressive model x(t) = T(x(t-1)) + epsilon t. By checking the empirical wavelet coefficients of the data,which have significantly large absolute values across fine scale levels, the number of the jump points and locations where the jumps occur are estimated. The jump heights are also estimated. All estimators are shown to be consistent. Wavelet method ia also applied to the threshold AR(1) model(TAR(1)). The simple estimators of the thresholds are given,which are shown to be consistent.

Constructing a raster-based spatio-temporal hierarchical data model for marine fisheries application

Marine information has been increasing quickly. The traditional database technologies have disadvantages in manipulating large amounts of marine information which relates to the position in 3-D with the time. Recently, greater emphasis has been placed on GIS （geographical information system）to deal with the marine information. The GIS has shown great success for terrestrial applications in the last decades, but its use in marine fields has been far more restricted. One of the main reasons is that most of the GIS systems or their data models are designed for land applications. They cannot do well with the nature of the marine environment and for the marine information. And this becomes a fundamental challenge to the traditional GIS and its data structure. This work designed a data model, the raster-based spatio-temporal hierarchical data model （RSHDM）, for the marine information system, or for the knowledge discovery fi＇om spatio-temporal data, which bases itself on the nature of the marine data and overcomes the shortages of the current spatio-temporal models when they are used in the field. As an experiment, the marine fishery data warehouse （FDW） for marine fishery management was set up, which was based on the RSHDM. The experiment proved that the RSHDM can do well with the data and can extract easily the aggregations that the management needs at different levels.

Empirical likelihood for first-order mixed integer-valued autoregressive model

In this paper, we not only construct the confidence region for parameters in a mixed integer-valued autoregressive process using the empirical likelihood method, but also establish the empirical log-likelihood ratio statistic and obtain its limiting distribution. And then, via simulation studies we give coverage probabilities for the parameters of interest. The results show that the empirical likelihood method performs very well.

Examining spatiotemporal distribution and CPUE-environment relationships for the jumbo flying squid Dosidicus gigas offshore Peru based on spatial autoregressive model

The spatiotemporal distribution and relationship between nominal catch-per-unit-ef fort(CPUE) and environment for the jumbo flying squid( Dosidicus gigas) were examined in of fshore Peruvian waters during 2009–2013. Three typical oceanographic factors aff ecting the squid habitat were investigated in this research, including sea surface temperature(SST), sea surface salinity(SSS) and sea surface height(SSH). We studied the CPUE-environment relationships for D. gigas using a spatially-lagged version of spatial autoregressive(SAR) model and a generalized additive model(GAM), with the latter for auxiliary and comparative purposes. The annual fishery centroids were distributed broadly in an area bounded by 79.5°–82.7°W and 11.9°–17.1°S, while the monthly fishery centroids were spatially close and lay in a smaller area bounded by 81.0°–81.2°W and 14.3°–15.4°S. Our results show that the preferred environmental ranges for D. gigas offshore Peru were 20.9°–21.9°C for SST, 35.16–35.32 for SSS and 27.2–31.5 cm for SSH in the areas bounded by 78°–80°W/82–84°W and 15°–18°S. Monthly spatial distributions during October to December were predicted using the calibrated GAM and SAR models and general similarities were found between the observed and predicted patterns for the nominal CPUE of D. gigas. The overall accuracies for the hotspots generated by the SAR model were much higher than those produced by the GAM model for all three months. Our results contribute to a better understanding of the spatiotemporal distributions of D. gigas off shore Peru, and off er a new SAR modeling method for advancing fishery science.

PARTICLE FILTERING BASED AUTOREGRESSIVE CHANNEL PREDICTION MODEL

A particle filtering based AutoRegressive (AR) channel prediction model is presented for cognitive radio systems. Firstly, this paper introduces the particle filtering and the system model. Secondly, the AR model of order p is used to approximate the flat Rayleigh fading channels; its stability is discussed, and an algorithm for solving the AR model parameters is also given. Finally, an AR channel prediction model based on particle filtering and second-order AR model is presented. Simulation results show that the performance of the proposed AR channel prediction model based on particle filtering is better than that of Kalman filtering.

A Spatio-temporal Data Model for Road Network in Data Center Based on Incremental Updating in Vehicle Navigation System

The technique of incremental updating,which can better guarantee the real-time situation of navigational map,is the developing orientation of navigational road network updating.The data center of vehicle navigation system is in charge of storing incremental data,and the spatio-temporal data model for storing incremental data does affect the efficiency of the response of the data center to the requirements of incremental data from the vehicle terminal.According to the analysis on the shortcomings of several typical spatio-temporal data models used in the data center and based on the base map with overlay model,the reverse map with overlay model (RMOM) was put forward for the data center to make rapid response to incremental data request.RMOM supports the data center to store not only the current complete road network data,but also the overlays of incremental data from the time when each road network changed to the current moment.Moreover,the storage mechanism and index structure of the incremental data were designed,and the implementation algorithm of RMOM was developed.Taking navigational road network in Guangzhou City as an example,the simulation test was conducted to validate the efficiency of RMOM.Results show that the navigation database in the data center can response to the requirements of incremental data by only one query with RMOM,and costs less time.Compared with the base map with overlay model,the data center does not need to temporarily overlay incremental data with RMOM,so time-consuming of response is significantly reduced.RMOM greatly improves the efficiency of response and provides strong support for the real-time situation of navigational road network.

Multivariate Generalized Autoregressive Conditional Heteroscedastic Model

In this paper, by making use of the Hadamard product of matrices, a natural and reasonable generalization of the univariate GARCH (Generalized Autoregressive Conditional heteroscedastic) process introduced by Bollerslev (J. Econometrics 31(1986), 307-327) to the multivariate case is proposed. The conditions for the existence of strictly stationary and ergodic solutions and the existence of higher-order moments for this class of parametric models are derived.

Study of Feature Extraction Based on Autoregressive Modeling in ECG Automatic Diagnosis

This article explores the ability of multivariate autoregressive model(MAR)and scalar AR model to extract the features from two-lead electrocardiogram signals in order to classify certain cardiac arrhythmias.The classification performance of four different ECG feature sets based on the model coefficients are shown.The data in the analysis including normal sinus rhythm, atria premature contraction,premature ventricular contraction,ventricular tachycardia,ventricular fibrillation and superventricular tachyeardia is obtained from the MIT-BIH database.The classification is performed using a quadratic diacriminant function.The results show the MAR coefficients produce the best results among the four ECG representations and the MAR modeling is a useful classification and diagnosis tool.

SOME LEAST SQUARES ESTIMATES OF THE AUTOREGRESSIVE MODELS

In this paper, we present some iterative methods for solving lth order autoregressive models, prove global convergence for l=1 case, and the numerical results of new algorithms seem to be more efficient than the ones of Cochrane-Orcutt iterative method.

The First Order Autoregressive Model with Coefficient Contains Non-Negative Random Elements: Simulation and Esimation

This paper considered an autoregressive time series where the slope contains random components with non-negative values. The authors determine the stationary condition of the series to estimate its parameters by the quasi-maximum likelihood method. The authors also simulates and estimates the coefficients of the simulation chain. In this paper, we consider modeling and forecasting gold chain on the free market in Hanoi, Vietnam.

PC-VAR Estimation of Vector Autoregressive Models

In this paper PC-VAR estimation of vector autoregressive models (VAR) is proposed. The estimation strategy successfully lessens the curse of dimensionality affecting VAR models, when estimated using sample sizes typically available in quarterly studies. The procedure involves a dynamic regression using a subset of principal components extracted from a vector time series, and the recovery of the implied unrestricted VAR parameter estimates by solving a set of linear constraints. PC-VAR and OLS estimation of unrestricted VAR models show the same asymptotic properties. Monte Carlo results strongly support PC-VAR estimation, yielding gains, in terms of both lower bias and higher efficiency, relatively to OLS estimation of high dimensional unrestricted VAR models in small samples. Guidance for the selection of the number of components to be used in empirical studies is provided.

Spatio-temporal Changes and Associated Uncertainties of CENTURYmodelled SOC for Chinese Upland Soils, 1980-2010

Detailed information on the spatio-temporal changes of cropland soil organic carbon(SOC) can significantly contribute to the improvement of soil fertility and mitigate climate change. Nonetheless, information and knowledge on the national scale spatio-temporal changes and the corresponding uncertainties of SOC in Chinese upland soils remain limited. The CENTURY model was used to estimate the SOC storages and their changes in Chinese uplands from 1980 to 2010. With the Monte Carlo method, the uncertainties of CENTURY-modelled SOC dynamics associated with the spatial heterogeneous model inputs were quantified. Results revealed that the SOC storage in Chinese uplands increased from 3.03(1.59 to 4.78) Pg C in 1980 to 3.40(2.39 to 4.62) Pg C in 2010. Increment of SOC storage during this period was 370 Tg C, with an uncertainty interval of –440 to 1110 Tg C. The regional disparities of SOC changes reached a significant level, with considerable SOC accumulation in the Huang-Huai-Hai Plain of China and SOC loss in the northeastern China. The SOC lost from Meadow soils, Black soils and Chernozems was most severe, whilst SOC accumulation in Fluvo-aquic soils, Cinnamon soils and Purplish soils was most significant. In modelling large-scale SOC dynamics, the initial soil properties were major sources of uncertainty. Hence, more detailed information concerning the soil properties must be collected. The SOC stock of Chinese uplands in 2010 was still relatively low, manifesting that recommended agricultural management practices in conjunction with effectively economic and policy incentives to farmers for soil fertility improvement were indispensable for future carbon sequestration in these regions.

Spatio-temporal model for soil characteristic of reclamation land

The development of spatio-temporal data model is introduced. According to the soil characteristic of reclamation land, we adopt the base state with amendments model of multi-layer raster to organize the spatio-temporal data, using the combined data structure on linear quadtree and linear octree to code. The advantage of this model is that it can easily obtain the information of certain layer and integratedly analyze the data with other methods. Then, the methods of obtain and analyses are introduced. The method can provide a tool for the research of the soil characteristic change and spatial distribution in reclamation land.

Noise reduction of acoustic Doppler velocimeter data based on Kalman filtering and autoregressive moving average models

Oceanic turbulence measurements made by an acoustic Doppler velocimeter(ADV)suffer from noise that potentially affects the estimates of turbulence statistics.This study examines the abilities of Kalman filtering and autoregressive moving average models to eliminate noise in ADV velocity datasets of laboratory experiments and offshore observations.Results show that the two methods have similar performance in ADV de-noising,and both effectively reduce noise in ADV velocities,even in cases of high noise.They eliminate the noise floor at high frequencies of the velocity spectra,leading to a longer range that effectively fits the Kolmogorov-5/3 slope at midrange frequencies.After de-noising adopting the two methods,the values of the mean velocity are almost unchanged,while the root-mean-square horizontal velocities and thus turbulent kinetic energy decrease appreciably in these experiments.The Reynolds stress is also affected by high noise levels,and de-noising thus reduces uncertainties in estimating the Reynolds stress.

Spatio-Temporal Dynamics and Structure Preserving Algorithm for Computer Virus Model

The present work is related to the numerical investigation of the spatio-temporal susceptible-latent-breaking out-recovered(SLBR)epidemic model.It describes the computer virus dynamics with vertical transmission via the internet.In these types of dynamics models,the absolute values of the state variables are the fundamental requirement that must be fulfilled by the numerical design.By taking into account this key property,the positivity preserving algorithm is designed to solve the underlying SLBR system.Since,the state variables associated with the phenomenon,represent the computer nodes,so they must take in absolute.Moreover,the continuous system(SLBR)acquires two steady states i.e.,the virus-free state and the virus existence state.The stability of the numerical design,at the equilibrium points,portrays an exceptional aspect about the propagation of the virus.The designed discretization algorithm sustains the stability of both the steady states.The computer simulations also endorse that the proposed discretization algorithm retains all the traits of the continuous SLBR model with spatial content.The stability and consistency of the proposed algorithm are verified,mathematically.All the facts are also ascertained by numerical simulations.