A CONSTRAINED LEAST SQUARES FITTING TECHNIQUE FOR ARMA MODELING

Several ARMA modeling approaches are addressed. In these methods only part of a correlation sequence is employed for estimating parameters. It is satisfying, if the given correlation sequence is of real ARMA, since an ARMA process can be completely determined by part of its correlation se -quence. But for the case of a measured correlation sequence the whole sequence may be used to reduce the effect of error on model parameter estimation. In addition, these methods now do not guarantee a nonnegative spectral estimate. In view of the above-mentioned fact, a constrained least squares fitting technique is proposed which utilizes the whole measured correlation sequence and guarantees a nonnegative spectral estimate.

A Study of Wind Statistics Through Auto-Regressive and Moving-Average (ARMA) Modeling

Statistical properties of winds near the Taichung Harbour are investigated. The 26 years'incomplete data of wind speeds, measured on an hourly basis, are used as reference. The possibility of imputation using simulated results of the Auto-Regressive (AR), Moving-Average (MA), and/ or Auto-Regressive and Moving-Average (ARMA) models is studied. Predictions of the 25-year extreme wind speeds based upon the augmented data are compared with the original series. Based upon the results, predictions of the 50- and 100-year extreme wind speeds are then made.

The Prediction for the Consumer Price Index of Residents in Perspective of Time Series Method in Case of Chongqing

The consumer price index (CPI) measures the relative number of changes in the price level of consumer goods and services over time, reflecting the trend and degree of changes in the price level of goods and services purchased by residents. This article uses the ARMA model to analyze the fluctuation trend of the CPI (taking Chongqing as an example) and make short-term predictions. To test the predictive performance of the model, the observation values from January to December 2023 were retained as the reference object for evaluating the predictive accuracy of the model. Finally, through trial predictions of the data from May to August 2023, it was found that the constructed model had good fitting performance.

Study on Optimality of Two-Stage Estimation with ARMA Model Random Bias

The optimality of two-stage state estimation with ARMA model random bias is studiedin this paper. Firstly, the optimal augmented state Kalman filter is given; Secondly, the two-stageKalman estimator is designed. Finally, under an algebraic constraint condition, the equivalencebetween the two-stage Kalman estimator and the optimal augmented state Kalman filter is proved.Thereby, the algebraic constraint conditions of optimal two-stage state estimation in the presence ofARMA model random bias are given.

Parameter Estimation of Time-Varying ARMA Model

The auto-regressive moving-average (ARMA) model with time-varying parameters is analyzed. The time-varying parameters are assumed to be a linear combination of a set of basis time-varying functions, and the feedback linear estimation algorithm is used to estimate the time-varying parameters of the ARMA model. This algorithm includes 2 linear least squares estimations and a linear filter. The influence of the order of basis time-(varying) functions on parameters estimation is analyzed. The method has the advantage of simple, saving computation time and storage space. Theoretical analysis and experimental results show the validity of this method.

A simplified NARMAX method using nonlinear input-output data

A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling （GMDH） method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.

ARMA-GM combined forewarning model for the quality control

Three forecasting models are set up: the auto\|regressive moving average model, the grey forecasting model for the rate of qualified products P t, and the grey forecasting model for time intervals of the quality catastrophes. Then a combined forewarning system for the quality of products is established, which contains three models, judgment rules and forewarning state illustration. Finally with an example of the practical production, this modeling system is proved fairly effective.

Cyclic moving average control approach to cylinder pressure and its experimental validation

Cyclic variability is a factor adversely affecting engine performance. In this paper a cyclic moving average regulation approach to cylinder pressure at top dead center （TDC） is proposed, where the ignition time is adopted as the control input. The dynamics from ignition time to the moving average index is described by ARMA model. With this model, a one-step ahead prediction-based minimum variance controller （MVC） is developed for regulation. The performance of the proposed controller is illustrated by experiments with a commercial car engine and experimental results show that the controller has a reliable effect on index regulation when the engine works under different fuel injection strategies, load changing and throttle opening disturbance.

Decoupled Wiener state fuser for descriptor systems

By the modem time series analysis method, based on the autoregressive moving average （ARMA） innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distributed descriptor Wiener state fuser is presented by weighting the local Wiener state estimators for the linear discrete stochastic descriptor systems with multisensor. It realizes a decoupled fusion estimation for state components. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are presented based on cross-covariances among the local innovation processes, input white noise, and measurement white noises. It can handle the fused filtering, smoothing, and prediction problems in a unified framework. Its accuracy is higher than that of each local estimator. A Monte Carlo simulation example shows its effectiveness and correctness.

在线结构断点估计的非平稳时间序列模型(英文)

Non-stationary time series could be divided into piecewise stationary stochastic signal. However, the number and locations of breakpoints, as well as the approximation function of the respective segment signal are unknown. To solve this problem, a novel on-line structural breaks estimation algorithm based on piecewise autoregressive processes is proposed. In order to find the "best" combination of the number, lengths, and orders of the piecewise autoregressive (AR) processes, the Akaikes Information Criterion (AIC) and Yule-Walker equations are applied to estimate an AR model fit to the data. Numerical results demonstrate that the proposed estimation algorithm is suitable for different data series. Furthermore, the algorithm is used in a clinical study of electroencephalogram (EEG) with satisfactory results, and the ability to deal with real-time data is the most outstanding characteristic of on-line structural breaks estimation algorithm proposed.

Instantaneous spectrum estimation of earthquake ground motions based on unscented Kalman filter method

Representing earthquake ground： motion as time varying ARMA model, the instantaneous spectrum can only be determined by the time varying coefficients of the corresponding ARMA model. In this paper, unscented Kalman filter is applied to estimate the time varying coefficients. The comparison between the estimation results of unscented Kalman filter and Kalman filter methods shows that unscented Kalman filter can more precisely represent the distribution of the spectral peaks in time-frequency plane than Kalman filter, and its time and frequency resolution is finer which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity or abruptness. Moreover, the estimation results of ARMA models with different orders indicate that the theoretical frequency resolving power of ARMA model which was usually ignored in former studies has great effect on the estimation precision of instantaneous spectrum and it should be taken as one of the key factors in order selection of ARMA model.

Seismic wavelet estimation via a system identification method

On the assumption that the wavelet is causal and nonminimum phase, an autoregressive moving average （ARMA） model is introduced to fit the seismic trace. Seismic wavelet extraction is converted to parameters estimation of the ARMA model. Singular value decomposition （SVD） of an appropriate matrix formed by autocorrelation is exploited to determine the autoregressive （AR） order, and the cumulant-based SVD-TLS （total least squares） approach is proposed to obtain the AR parameters. The author proposes a new moving average （MA） model order determination method via combining the information theoretic criteria method and higher-order cumulant method. The cumulant approach is used to achieve the MA parameters. Theoretical analysis and numerical simulations demonstrate the feasibility of the wavelet extraction approach.

Empirical Analysis of ARCH Family Models on Oil Price Fluctuations

This paper selects the daily data of national oil prices from January 2, 2014 to February 28, 2019, establishes an ARMA (2, 0) model, and tests its residuals for ARCH effects. Finally, the TARCH (1, 1) model is determined to quantitatively analyze the volatility of the crude oil market.

Time series modeling and filtering method of electric power load stochastic noise

Stochastic noises have a great adverse effect on the prediction accuracy of electric power load.Modeling online and filtering real-time can effectively improve measurement accuracy.Firstly,pretreating and inspecting statistically the electric power load data is essential to characterize the stochastic noise of electric power load.Then,set order for the time series model by Akaike information criterion(AIC)rule and acquire model coefficients to establish ARMA(2,1)model.Next,test the applicability of the established model.Finally,Kalman filter is adopted to process the electric power load data.Simulation results of total variance demonstrate that stochastic noise is obviously decreased after Kalman filtering based on ARMA(2,1)model.Besides,variance is reduced by two orders,and every coefficient of stochastic noise is reduced by one order.The filter method based on time series model does reduce stochastic noise of electric power load,and increase measurement accuracy.

ASYMPTOTIC CANONICAL FORMS AND ITERATED LOGARITHM RATE RESULTS OF LEAST SQUARES ESTIMATES FOR UNSTABLE ARMA MODELS

Herein we give the asymptotic canonical forms of the design mains Pn where is an unstable ARMA process B denotes the backshift operator such that B, and p is the order of the polynomial having all roots outside or on the unit circle. These asymptotic canonical forms for Pn, which behave a.s. approximately diagonally, are then used to obtain the itersted logarithm rates of almost sure convergence of the least-squares estimates to the unknown true parameter for an unstable time series.

RECURSIVE METH0D FOR ARMA MODEL ESTIMATION (Ⅱ)

In this paper a new recursive method for ARMA model estimation is given. Same as in [1], theorder's estimator is strongly consistent, and the parameter's estimators defer to CLT and LILunder a natural condition. Compared with the previous metheds suggested by Hannan & Kavalieris(1984), Wang Shouren & Chen Zhaoguo (1985) and Franke (1985), this methed has some advantages:the amount of calculat on work is smaller, the minimum-phase property of coeffcient estimators canbe guaranteed,the BAN estimators for MA or AR model can be obtained directly,and the simulationshows that this method is more accurate in estimating the order and parameters.

The ARMA model’s pole characteristics of Doppler signals fromthe carotid artery and their classification application

In order to diagnose the cerebral infarction, a classification system based on the ARMA model and BP (Back-Propagation) neural network is presented to analyze blood flow Doppler signals from the carotid artery. In this system, an ARMA model is first used to analyze the audio Doppler blood flow signals from the carotid artery. Then several characteristic parameters of the pole's distribution are estimated. After studies of these characteristic parameters' sensitivity to the textcolor cerebral infarction diagnosis, a BP neural network using sensitive parameters is established to classify the normal or abnormal state of the cerebral vessel. With 474 cases used to establish the appropriate neural network, and 52 cases used to test the network, the results show that the correct classification rate of both training and testing are over 94%. Thus this system is useful to diagnose the cerebral infarction.

Chinese speaker-recognition based on ARMA model

A Chinese speaker recognition system, which only use speech material of nasal initials and is text-independent, is presented in this paper. According to the properties of speaker's fixed nasal cavity and stable pharynx cavity when Chinese nasal initials is spoken and a few Chinese nasal initials (the total number of them is only 101 which consists of 53 Tn- and 48 n-), the spectrum parameters of zero and pole point coefficients of all Chinese nasal initials can be gotten by using ARMA model. The performance of this system for 20 speakers is as follows' The correct recognition rate (CRR) is 87.92% for each speaker to test all initials, when randomly choosing 2, 3, 4 and 5 initials in each speaker's and then averaging their spectrum to test individual template, the average' CRRs are 91.67%, 95.00%, 96.67% and 99.97% respectively.

Low frequency characteristic parameters measurement of vented-box loudspeaker system using total least squares method

The interrelationship between the ARMA model parameters of a vented-box loud-speaker system and lowthequency characteristic parameters is analysed in this paper. These AANA model parameters are deterndned by the total least squares (TLS) method. Therefore, we can measure in the timedomain the fow frequency characteristic parameters of a vented-box loudspeaker system, its impendance curvs and low-frquency response curves. These measured results show a satisfactory agreement with the values obtained by the frequency-domain measurement.

Application of Time-Series Model to Predict Groundwater Dynamic in Sanjiang Plain, Northeast China

To study the groundwater dynamic in the typical region of Sanjiang Plain, long-term groundwater level observation data in the Honghe State Farm were collected and analyzed in this paper. The seasonal and long-term groundwater dynamic was explored. From 1996 to 2008, groundwater level kept declining due to intensive exploitation of groundwater resources for rice irrigation. A decline of nearly 5 m was found for almost all the monitoring wells. A time-series method was established to model the groundwater dynamic. Modeled results by time-series model showed that the groundwater level in this region would keep declining according to the current exploitation intensity. A total dropdown of 1.07 m would occur from 2009 to 2012. Time-series model can be used to model and forecast the groundwater dynamic with high accuracy. Measures including control on groundwater exploitation amount and application of water saving irrigation technique should be taken to prevent the continuing declining of groundwater in the Sanjiang Plain.