Order ARMA Model Research Articles

Estimation of ARMA Model Order Using Artificial Neural Networks

Estimation of ARMA Model Order Using Artificial Neural Networks

Effective Processing of Radar Data for Bridge Damage Detection

This paper presents the practical results of the evaluation of the data obtained by using ground‐based radar interferometer during measurements carried out on bridge structures. Due to the nature of the objects studied, the authors proposed a comprehensive method of data analysis, which identifies whether the passage of the vehicle did not damage the bridge. The effective use of vehicles as a source of bridge excitation allowed us to first develop a method for determining the damping parameters resistant to potentially occurring beating frequencies. As a result, it is possible to determine these subsets of data registered with radar, for which it is possible to assume compliance with linear systems. This type of data, often omitted in other works, forms the basis for the second important element of the research—an algorithm based on the ARMA model supporting defect detection. The optimization of the performed calculations, in particular the proposed optimal ARMA model order, the method of fault identification based on the DSF parameter, or fault identification based on a nonmetrical Cook’s distance leads to a robust and scalable method. The method’s low computational complexity allows for implementation in real‐time solutions. In addition, the distribution of errors and the sensitivity of classifiers based on the DSF parameter and Cook’s distances leaving them will enable the automation of the classification process using machine learning. The proposed method is universal; in particular, it can be used for radar interferometry methods because it is resistant to potentially variable environmental conditions.

Forecasting the Daily Transaction Data Utilizing a Day of the Week Index in the Case of Web Site

The daily web site access data’s forecasting is an important factor for the web master in order to improve the quality of the site, and to increase the sales from the site. In this paper, the authors propose a new method to improve forecasting accuracy and confirm them by the Web transaction data (Nail consulting site). Focusing that the equation of exponential smoothing method (ESM) is equivalent to (1,1) order ARMA model equation, a new method of estimation of smoothing constant in exponential smoothing method is proposed before by us which satisfies minimum variance of forecasting error. Generally, smoothing constant is selected arbitrarily. But in this paper, we utilize above stated theoretical solution. Firstly, the authors make estimation of ARMA model parameter and then estimate smoothing constants. Thus theoretical solution is derived in a simple way and it may be utilized in various fields. Combining the trend removing method with this method, we aim to improve forecasting accuracy. Furthermore, “a day of the week index” is newly introduced for the daily data and we have obtained good result. The effectiveness of this method should be examined in various cases.

Some weighted mixed portmanteau tests for diagnostic checking in linear time series models

ABSTRACTThe popular diagnostic checking methods in linear time series models are portmanteau tests based on either residual autocorrelation functions (acf) or partial autocorrelation functions (pacf). In this paper, we device some new weighted mixed portmanteau tests by appropriately combining individual tests based on both acf and pacf. We derive the asymptotic distribution of such weighted mixed portmanteau statistics and study their size and power. It is found that the weighted mixed tests outperform when higher order ARMA models are fitted and diagnostic checks are performed via testing lack of residual autocorrelations. Simulation results suggest to use the proposed tests as complementary to those classical tests found in literature. An illustrative application is given to demonstrate the usefulness of the mixed test.

PEMILIHAN MODEL DAN ESTIMASI PARAMETER BAYESIAN HIRARKI UNTUK MODEL SUBSET ARMA MENGGUNAKAN ALGORITMA REVERSIBLE JUMP SIMULATED ANNEALING MCMC

If the Subset ARMA models fitted to real data, then the true value of the order and model parameters are often unknown. The purpose of this paper is to find an estimator-estimator for the order and parameters of the model based on the data. In this paper, the identification of order and subset ARMA model parameter estimation is done in a hierarchical Bayesian framework. Within this framework, the order and model parameters are assumed distributed priors. All order information about the characteristics and parameters of the model then expressed in the posterior distribution. Determination of the probability of the order and parameters of the posterior models requires the integration of the resulting posterior distribution, is an operation which is very difficult to do analytically. Here the algorithm Reversible Jump MCMC Simulated Annealing developed to perform the necessary integration through simulated posterior distribution.

BOOTSTRAP FOR ORDER IDENTIFICATION IN ARMA(p,q) STRUCTURES

The identification of de order p,q, of ARMA models is a critical step in time-series modelling. In classic Box-Jenkins method of identification the autocorrelation function (ACF) and the partial autocorrelation (PACF) function should be estimated, but the classical expressions used to measure the variability of the respective estimators are obtained on the basis of asymptotic results. In addition, when having sets of few observations, the traditional confidence intervals to test the null hypotheses display low performance. The bootstrap method may be an alternative for identifying the order of ARMA models, since it allows to obtain an approximation of the distribution of the statistics involved in this step. Therefore it is possible to obtain more accurate confidence intervals than those obtained by the classical method of identification. In this paper we propose a bootstrap procedure to identify the order of ARMA models. The algorithm was tested on simulated time series from models of structures AR(1), AR(2), AR(3), MA(1), MA(2), MA(3), ARMA(1,1) and ARMA (2,2). This way we determined the sampling distributions of ACF and PACF, free from the Gaussian assumption. The examples show that the bootstrap has good performance in samples of all sizes and that it is superior to the asymptotic method for small samples.

The simplified STR applied to an asymmetric hydraulic servo system

A single–rod cylinder servo system driving a single–side load is typically a 4th–order non–linear and discontinuous system. However, its asymmetric nature will cause steady state error in position control. At the low frequency of interest, this system can be simplified as a 1st–order ARMA model and the PEDF algorithm is used for parameter adaptation. In addition to tracing the time–varying and discontinuous parameters, the PEDF is to ensure the covariance matrix is bounded so as to guard against peak in the parameter adaptation process. To eliminate steady state error, an integrator is included in the structure of implicit STR and it only estimates two controller parameters by applying the final value theorem of the z–transform. The proposed implicit STR not only avoids unstable pole–zero cancellation, but also prevents the redundant zero of the high order model from being hidden. Finally, various experiments prove its effectiveness and adaptation numerically.

Building BTO System in the Sanitary Materials Manufacturer with the Utilization of the High Accuracy Forecasting

In recent years, BTO (Build to Order) system is prevailing. It pursues short lead time, minimum stocks, and thereby minimum cost. But the high accuracy demand forecasting is inevitable for the parts manufacturers. In this paper, well organized BTO system in the sanitary materials manufacturer is seek with the aid of high accuracy demand forecasting, which is newly developed by us. Focusing that the equation of ESM is equivalent to (1,1) order ARMA model equation, a new method of estimation of smoothing constant in ESM was derived. Trend removal method was also devised. AR model is also used for forecasting. After removing trend, AR model is utilized and forecasting is executed. Better one in the forecasting accuracy between them was chosen for the final forecasting. Thus, we could obtain the high accuracy demand forecasting. These methods are examined by the data of sanitary materials manufacturer and the BTO system is newly built by utilizing this method. Further development of this system should be performed hereafter.

A Hybrid Method to Improve Forecasting Accuracy in the Case of Sanitary Materials Data

Sales forecasting is a starting point of supply chain management, and its accuracy influences business management significantly. In industries, how to improve forecasting accuracy such as sales, shipping is an important issue. In this paper, a hybrid method is introduced and plural methods are compared. Focusing that the equation of exponential smoothing method(ESM) is equivalent to (1,1) order ARMA model equation, a new method of estimation of smoothing constant in exponential smoothing method is proposed before by Takeyasu et.al. which satisfies minimum variance of forecasting error. Firstly, we make estimation of ARMA model parameter and then estimate smoothing constants. In this paper, combining the trend removing method with this method, we aim to improve forecasting accuracy. Trend removing by the combination of linear and 2nd order non-linear function and 3rd order non-linear function is carried out to the manufacturer’s data of sanitary materials. The new method shows that it is useful for the time series that has various trend characteristics and has rather strong seasonal trend. The effectiveness of this method should be examined in various cases.

Study on Identification Method of GIS Insulation Defects Based on ARMA

GIS is an important part in power system. The operating status of GIS is closely related to the operation of stability and security for grid. For existing problems in GIS insulation defects of mainstream identification method, a new identification method of GIS insulation defects based on ARMA is put forward in this paper. The paper proposes a method of multi-cycle time-domain average data preprocessing, a construction method of identifying reference data, a diagnosis method of regarding the coefficient of a certain order ARMA model as comparative quantity. At the same time, the author of the paper conduct a test on new identification method using laboratory devices, and confirms data validation of new identification method. The result suggests that the new identification method is effective and reliable.

Predictive Control of Permanent Magnet Synchronous Motor Based on Optimization Model Algorithmic Control

This paper presents an optimization model algorithmic control (OMAC) for permanent magnet synchronous motor drive system. The OMAC controller is designed based on the second order ARMA model of permanent magnet synchronous motor. It optimizes the correction coefficient of calculation error and prediction error coefficient of output as well as the amount of the weighting factor in the traditional model algorithmic control. Then selecting only one future time of predictive values to calculate the optimal control law simplifies the calculation process and so overcomes the shortcomings of traditional control needed to select the number of prediction horizon and required to choose a longer sampling period to calculate appropriate control quantity. The algorithm is simple and robustness of the system can be guaranteed. Therefore, the OMAC is well positioned to meet the dynamic and rapid motor real-time requirements. Simulation is conducted to verify the performance of the proposed control scheme.

A Hybrid Method to Improve Forecasting Accuracy Utilizing Genetic Algorithm –An Application to the Data of Operating equipment and supplies

In industries, how to improve forecasting accuracy such as sales, shipping is an important issue. There are many researches made on this. In this paper, a hybrid method is introduced and plural methods are compared. Focusing that the equation of exponential smoothing method(ESM) is equivalent to (1,1) order ARMA model equation, new method of estimation of smoothing constant in exponential smoothing method is proposed before by us which satisfies minimum variance of forecasting error. Generally, smoothing constant is selected arbitrarily. But in this paper, we utilize above stated theoretical solution. Firstly, we make estimation of ARMA model parameter and then estimate smoothing constants. Thus theoretical solution is derived in a simple way and it may be utilized in various fields. Furthermore, combining the trend removing method with this method, we aim to improve forecasting accuracy. An approach to this method is executed in the following method. Trend removing by the combination of linear and 2nd order non-linear function and 3rd order non-linear function is executed to the data of Operating equipment and supplies for three cases (An injection device and a puncture device, A sterilized hypodermic needle and A sterilized syringe). The weights for these functions are set 0.5 for two patterns at first and then varied by 0.01 increment for three patterns and optimal weights are searched. Genetic Algorithm is utilized to search the optimal weight for the weighting parameters of linear and non-linear function. For the comparison, monthly trend is removed after that. Theoretical solution of smoothing constant of ESM is calculated for both of the monthly trend removing data and the non-monthly trend removing data. Then forecasting is executed on these data. The new method shows that it is useful for the time series that has various trend characteristics and has rather strong seasonal trend. The effectiveness of this method should be examined in various cases.

EXPLOITING INEFFICIENCIES IN FINANCIAL AND SPORTS GAMBLING MARKETS: EXPLORATORY DRIFT MODELING

Cointegrated time series associated with financial and sports gambling markets are analyzed in terms of time-varying parameter models. Parameter drift is modeled in terms of lagged disequilibria. Model forecasts are intended to capitalize on periods of market inefficiency. Modeling premises are that (1) present and past disequilibria—shocks both within and between time series—may affect subsequent changes and rates of these changes within individual series and (2) sufficiently large shocks may disrupt/alter model structure such that resulting forecasts may be temporarily unreliable. Reduced forecasting equations are in terms of higher order ARMA models that are not limited to bilinear processes. Sports forecasting models based on public information are usually more effective—in terms of profitable trading/wagering strategies—than those for the financial sector for two reasons: (1) Insider information is less prevalent. (2) Modeling is simplified since lagged shocks associated with the gambling lines/spreads are known—in contrast with financial modeling where there are no comparable gambling shocks, only unknown, lagged statistical shocks in terms of MA variables. Forecasting is illustrated for NFL and NBA playoff games. In financial markets, cointegration is discussed in terms of candlestick chart variants with modeling illustrations given in terms of recent Google price changes.

Tuning SISO offset-free Model Predictive Control based on ARX models

In this paper, we present a tuning methodology for a simple offset-free SISO Model Predictive Controller (MPC) based on autoregressive models with exogenous inputs (ARX models). ARX models simplify system identification as they can be identified from data using convex optimization. Furthermore, the proposed controller is simple to tune as it has only one free tuning parameter. These two features are advantageous in predictive process control as they simplify industrial commissioning of MPC. Disturbance rejection and offset-free control is important in industrial process control. To achieve offset-free control in face of unknown disturbances or model-plant mismatch, integrators must be introduced in either the estimator or the regulator. Traditionally, offset-free control is achieved using Brownian disturbance models in the estimator. In this paper we achieve offset-free control by extending the noise model with a filter containing an integrator. This filter is a first order ARMA model. By simulation and analysis, we argue that it is independent of the parameterization of the underlying linear plant; while the tuning of traditional disturbance models is system dependent. Using this insight, we present MPC for SISO systems based on ARX models combined with the first order filter. We derive expressions for the closed-loop variance of the unconstrained MPC based on a state space representation in innovation form and use these expressions to develop a tuning procedure for the regulator. We establish formal equivalence between GPC and state space based off-set free MPC. By simulation we demonstrate this procedure for a third order system. The offset-free ARX MPC demonstrates satisfactory set point tracking and rejection of an unmeasured step disturbance for a simulated furnace with a long time delay.

Two-dimensional ARMA model order determination

Determination of the order of a model is the key first step towards modeling any dynamic systems, particularly two-dimensional processes. In this paper, a new method for two-dimensional (2-D) Gaussian ARMA model order determination is proposed. In the proposed method, the AR and MA orders are first independently determined, then the procedure for model order determination of the 2-D ARMA model is outlined. The model is assumed to be causal, stable, linear, and spatial shift-invariant with p 1 × p 2 quarter-plane (QP) support. Numerical simulations are presented to show the effectiveness of the proposed new approach.

Torque balancing control in ignition event based scale for multi-cylinder SI engines

In this paper, the torque balancing problem for multi-cylinder SI engines is focused on. The deviation in average torque generation of sections with equal crank angle interval according to ignition event is introduced as index for balancing and an estimation method for this index from engine speed measurement is proposed based on crank shaft dynamics in crank angle domain. According to the coupling characteristic in torque generation between cylinders, a simple 2nd order ARMA model is established to describe the dynamics from spark ignition to the index. Based on this model, model predictive control technique is used in regulation. Finally, the validity of the proposed approach is demonstrated by simulation performed on a six-cylinder engine simulator with physical background.

Rank pattern-based selection of input/output ARMA model order

Rational transfer functions are standard models for radar targets and adaptive beamforming. Fitting these models essentially involves estimating the transfer function ''poles and zeroes.'' A key preliminary step in this estimation process is to determine the numbers of poles and zeros, or equivalently to determine the order of the corresponding ARMA model. A pattern-based method of order selection using matrix ranks is proposed for input/output (I/O) ARMA models, where ARMA model inputs and outputs are each observed in additive noise with known variances. This I/O ARMA model encompasses two distinct scenarios: observational studies in which all observations-those of both inputs and outputs-are erred, and controlled experiments in which outputs are observed with error while inputs are known without error. The proposed rank pattern method exploits the eigenvalue structure of the covariance matrices associated with the observed data and performs well for short data records at moderate SNRs.

Large-scale homogenization in mammoth silos: calculating homogenization efficiency and modeling input properties

The homogenization theory of mammoth silos is investigated in order to establish the homogenization efficiency of mammoth silos. These silos, where homogenization is achieved by intersecting multiple layers during reclaiming of the silo, e.g., by inclining the screw conveyor, can be used for large-scale homogenization of both cohesive and free-flowing materials and are therefore an alternative for blending piles. The presented homogenization model and the calculation of the homogenization efficiency in mammoth silos depend on two variables: the volume distribution and the input properties of the bulk material to be homogenized. The silo geometry and the chosen stacking and reclaiming method determine the first variable. The second variable, time series representing the input properties of a material flow, depends on the material to be homogenized. This paper focuses on modeling input properties and shows that higher order ARMA( p, q) models are required for describing these input properties, instead of the frequently assumed AR(1) models in literature. It does not concentrate on the comparison of predicted and simulated output variances. Conducted simulations of the homogenization efficiency with both ARMA and AR(1) models are found to be very encouraging because the standard deviation of the output properties is reduced on average by a factor 5, i.e., the standard deviation of the output properties is reduced to 20% of the standard deviation of the input properties.

Long memory time series and short term forecasts

This article studies the usefulness of low order ARMA models in the prediction of long memory time series with fractionally differenced ARFIMA(0, d,0) structure, −0.5< d<0.5. We argue that if the interest is in short term prediction, a suitably adapted ARMA(2,2) model can produce competitive forecasts. Numerical evaluation shows its prediction error variance is at most 0.6% higher than that of the true model at one step ahead, and at most 2.8% higher up to 10 steps ahead. However, caution needs to be taken when using the adapted ARMA model for long term prediction of strongly persistent time series. The predictability memory content of the adapted ARMA(2,2) model is also studied and compared to that of the ARFIMA(0, d,0). For illustration, we forecast the US consumer price index and inflation rates for four countries. Adapted ARMA(2,2) is compared to ARFIMA(0, d,0) fit using an out-of-sample prediction mean square errors criterion. Empirical results suggest that the performance of ARMA(2,2) compares favorably to ARFIMA(0, d,0) for forecasts up to 100 steps ahead.

Robust and accurate ARX and ARMA model order estimation of non-Gaussian processes

The field of higher order statistics is emerging rapidly for analyzing non-Gaussian processes. There are several motivations behind the use of higher order statistics. The emphasis of this paper is based on the property that higher order cumulants are blind to any kind of Gaussian process. Hence, when the processed signal is non-Gaussian stationary and the additive noise is stationary Gaussian, the noise will vanish in the cumulant domain. This paper presents an extension to the results of Liang et al. (1993). This extension is a straightforward generalization of Liang's approach to third-order cumulants (TOCs). The new cumulant-based algorithm provides a higher level of accuracy in the presence of noise than the original second-order algorithm. In addition, the original results of Liang have been extended to the case of colored Gaussian noise. Examples are given to demonstrate the performance of this algorithm even when the observed signal is heavily corrupted by Gaussian noise.