Parameters Of ARMA Model Research Articles

Prediction of China’s Total Energy Consumption Based on Bayesian ARIMA-Nonlinear Regression Model

Energy management is the key to China’s economy prosperity and environment protection in the future. This paper makes predictions on whether China’s energy 13th Five-Year plan can be achieved and the trend of energy consumption in the next stage. Aiming at the shortcoming of insufficient extraction of nonlinear features in the energy system from existing energy consumption models, and low prediction accuracy due to single models. Based on the derivation of the joint posterior distribution density function of the stationary ARMA model parameters under the Normal-gamma prior distribution, this paper proposes a Bayesian ARIMA-nonlinear regression energy consumption prediction model. Bayesian parameter estimation makes full use of prior information and Markov Chain Monte Carlo (MCMC) technique gets rid of the tedious calculation of high-dimensional integrals. Compared with the existing model, the improved model has higher prediction accuracy. Its Root Mean Square Error and Mean Absolute Percentage Error are 3452.0294 and 0.4727%. In line with the development goals set out in the 13th Five-Year plan, an empirical study of the fluctuation law of China’s total energy consumption was carried out using data on China’s energy consumption from 1990 to 2019 and its factors. The results show that affected by the Corona Virus Disease 2019 epidemic, the growth rate of China’s energy demand will fluctuate slightly in 2020. By the end of the 13th Five-Year plan, the total energy consumption can reach the expected goal. After the epidemic is under control, energy demand for the whole society will usher in a rebound growth. In the next five years (2020∼2024), China’s energy consumption will continue to maintain a steady upward trend of slowing growth. In view of these situations, this paper suggests that, on the one hand, we should attach equal importance to energy conservation and technology development to improve energy efficiency; on the other hand, we should adjust industrial structure and establish a unified energy management system to promote sustainable development of the energy industry.

Finance Leasing and ARMA Forecasting: Evidence from Albania

Ten financial institutions are offering finance leasing-loans in Albania. Even though finance leasing is a potential financing resource for small and medium enterprises in Albania (which are on average 95% of national enterprises), the value of finance leasing is one thousand times smaller than other forms of medium and long-term loans or real estate loans. Developing of finance leasing is a challenge for the progress of the financial sector, and untapped potential as well. Currently, the finance leasing portfolio is dominated by financing for personal vehicles and work-vehicles, therefore diversification of leasing products is an immediate need of consumers. This study analyzes the value of finance leasing in Albania with time series from 2008 to 2020 (with quarterly frequency). The methodology applied for data processing is the co-integration method of finance leasing and other forms of medium-term and long-term financing. Also, the ARMA method is used to forecast the value of finance leasing. We found out that there is no long-run relationship between finance leasing with medium and long-term loans. Therefore, econometric tests suggest optimal forecasting ARMA (1,1) modeling. The parameters of ARMA model are positive statistically significant with autocorrelation AR (1) and negative statistically significant with the moving average MA (1), and forecasting values have a short-run equilibrium with a wide interval.

Variance stabilizing filters#

In this paper new filters for removing unspecified form of heteroscedasticity are proposed. The filters build on the assumption that the variance of a pre-whitened time series can be viewed as a latent stochastic process by its own. This makes the filters flexible and useful in many situations. A simulation study shows that removing heteroscedasticity before fitting a model leads to efficiency gains and bias reductions when estimating the parameters of ARMA models. A real data study shows that pre-filtering can increase the forecasting precision of quarterly US GDP growth.

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.

A general result on the estimation bias of ARMA models

A general result is derived on the finite-sample approximate bias of the Gaussian maximum likelihood estimator of the full vector of parameters in ARMA models when the error term may be nonnormally distributed and exogenous regressors may be included. It is found that there is typically estimation bias for parameters associated with the AR and MA terms and the bias depends only on these parameters themselves and the exogenous regressors. Parameters associated with the exogenous regressors are estimated approximately unbiased. The error variance is estimated with a downward bias, proportional to the number of exogenous regressors and the orders of AR and MA terms in the model. The distributional assumption on the error term does not affect the general bias result. Monte Carlo experiments are provided to illustrate the effectiveness of using analytical bias for the purpose of bias correction.

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.

Auto Regressive Moving Average (ARMA) Modeling Method for Gyro Random Noise Using a Robust Kalman Filter.

To solve the problem in which the conventional ARMA modeling methods for gyro random noise require a large number of samples and converge slowly, an ARMA modeling method using a robust Kalman filtering is developed. The ARMA model parameters are employed as state arguments. Unknown time-varying estimators of observation noise are used to achieve the estimated mean and variance of the observation noise. Using the robust Kalman filtering, the ARMA model parameters are estimated accurately. The developed ARMA modeling method has the advantages of a rapid convergence and high accuracy. Thus, the required sample size is reduced. It can be applied to modeling applications for gyro random noise in which a fast and accurate ARMA modeling method is required.

A New Method for Modal Parameter Identification Based on Natural Excitation Technique and ARMA Model in Ambient Excitation

Due to the interference of strong vibration signal, a big error exists in modal parameter identification based on traditional ARMA model. In order to solve this problem, a new method for modal parameter identification based on natural excitation technique (NExT) and ARMA model is presented. Firstly, NExT is used to obtain cross-correlation function of different response sequences. Then, ARMA model of cross-correlation function is established, and the parameters of ARMA model are estimated by least squares method. Finally, the modal parameter identification is achieved using the relationship between the ARMA parameters and structural modal parameters. Experiment shows that the identification results of our method are more accurate than the traditional ARMA model.

Research on Weighted Iterative Stage Parameter Estimation Algorithm of Time Series Model

Time series analysis has been extensively used in many fields, such as system identification, modeling and data predication, and played an important role in system design, planning and performance analysis. The focus of time series application study is how to improve the accuracy and computation speed of the parameter estimation. Many researchers have carried out system modeling study by applying time series analysis and have gained their research results. The traditional methods such as maximum likelihood estimation, moment estimate and least square estimate which exit the defect of low precision, poor convergence and parameter estimation white noises coupling, are mostly utilized in parameter estimation for model. Taking this as basis the data forecasting and anomaly detection are conducted, which is hard to ensure the system’s stability. Different from the traditional algorithm, this paper proposes a new weighted iterative stage parameter estimation algorithm which avoids the coupling with white noise estimation of ARMA model parameter and improves the accuracy of parameter estimation. In theory, this algorithm tends to provide a good convergence performance. The experimental results based on ARIMA model show that the algorithm can improve the accuracy of parameter estimation and provide a good convergence performance.

Empirical Likelihood for Partial Parameters in ARMA Models with Infinite Variance

This paper proposes a profile empirical likelihood for the partial parameters in ARMA(p,q)models with infinite variance. We introduce a smoothed empirical log-likelihood ratio statistic. Also, the paper proves a nonparametric version of Wilks’s theorem. Furthermore, we conduct a simulation to illustrate the performance of the proposed method.

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.

Analysis and application of a novel fast algorithm for 2-D ARMA model parameter estimation

In this paper, we analyze a novel algorithm for 2-D ARMA model parameter estimation in the presence of noise and then develop a fast and efficient blind image restoration algorithm. We show that the novel algorithm can minimize a quadratic convex optimization problem and has a lower computational complexity than the conventional algorithms. As a result, the novel algorithm involves no convergence and local minimum issue. Moreover, the proposed blind image restoration algorithm can overcome the local minimization problem. Computed results confirm that the novel algorithm can more quickly obtain more accurate estimates than the conventional algorithms in the presence of noise.

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.

Self-tuning weighted measurement fusion white noise deconvolution estimator and its convergence analysis

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. For the multisensor linear discrete time-invariant stochastic systems with correlated measurement noises, and with unknown ARMA model parameters and noise statistics, the on-line AR model parameter estimator based on the Recursive Instrumental Variable (RIV) algorithm, the on-line MA model parameter estimator based on Gevers-Wouters algorithm and the on-line noise statistic estimator by using the correlation method are presented. Using the Kalman filtering method, a self-tuning weighted measurement fusion white noise deconvolution estimator is presented based on the self-tuning Riccati equation. It is proved that the self-tuning fusion white noise deconvolution estimator converges to the optimal fusion steady-state white noise deconvolution estimator in a realization by using the dynamic error system analysis (DESA) method, so that it has the asymptotic global optimality. The simulation example for a 3-sensor system with the Bernoulli-Gaussian input white noise shows its effectiveness.

Band-Limited Stochastic Processes in Discrete and Continuous Time

A theory of band-limited linear stochastic processes is described and it is related to the familiar theory of ARMA models in discrete time. By ignoring the limitation on the frequencies of the forcing function, in the process of fitting a conventional ARMA model, one is liable to derive estimates that are severely biased. If the maximum frequency in the sampled data is less than the Nyquist value, then the underlying continuous function can be reconstituted by sinc function or Fourier interpolation. The estimation biases can be avoided by re-sampling the continuous process at a rate corresponding to the maximum frequency of the forcing function. Then, there is a direct correspondence between the parameters of the band-limited ARMA model and those of an equivalent continuous-time process.

NM–QELE for ARMA–GARCH models with non-Gaussian innovations

Although the quasi maximum likelihood estimator based on Gaussian density (Gaussian-QMLE) is widely used to estimate parameters in ARMA models with GARCH innovations (ARMA–GARCH models), it does not perform successfully when error distribution of ARMA–GARCH models is either skewed or leptokurtic. In order to circumvent such defects, Lee and Lee (submitted for publication) proposed the quasi maximum estimated-likelihood estimator using Gaussian mixture-based likelihood (NM–QELE) for GARCH models. In this paper, we adopt the NM–QELE method for estimating parameters in ARMA–GARCH models and demonstrate the validity of NM–QELE by verifying its consistency.

One New Method on ARMA Model Parameters Estimation

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Testing hypotheses on the “drift” of parameters in ARMA and ARCH models

For an ARMA model, we test the hypothesis that the coefficients of this model remain constant in time and satisfy the stationarity condition against the alternative that the coefficients change (“drift”) in time. We propose asymptotically distribution free tests for such hypothesis based on sequential residual processes. A similar problem is solved for the ARCH model.

Automated dynamic characteristics estimation of highway bridge under ambient vibration by block companion form realization

In this research, vibration characteristics are estimated from the ambient vibration of highway bridge by the block companion form realization theory. Two methods are stated herein such as formulation of block companion system matrix; (i) directly from block Hankel matrix, (ii) from ARMA model parameter G through Yule-Walker equation. These methods have applied to a 152m long Langer bridge and its dynamic characteristics were estimated automatically from multipoint measurement of ambient vibration. As the ambient vibration characteristics affect the estimation accuracy, two different cases were taken into consideration and the estimation accuracy was evaluated.

Identification of Hydrogen Generation Characteristics from Activated Aluminum Particles Using ARMA Model on the Assumption of the Applications for Fuel-cell Electric Vehicle

The purpose of this study is to describe the experiments of hydrogen generation from water molecules reacting with activated aluminum particles and the identification of its characteristics using an ARMA model on the assumption of the applications for a fuel-cell vehicle. Because 1 gram of the activated aluminum particles can generate about 1.1 liters of pure hydrogen, they have application possibility as the hydrogen resource of a fuel cell car. However, the details of hydrogen generation characteristics by this reaction are not well known. The reaction has non-linearity and time-varying due to the characteristics of the sample, the external environment and so on. Therefore, it is difficult to construct a mathematical model based on the physiochemical law of the reaction. Here, the dynamic characteristics of hydrogen generation are assumed to be described as a linear ARMA model using the reaction temperature and hydrogen generation. The parameters of ARMA model are identified by a constant trace adaptive algorithm using the measured data. The outputs of the ARMA model are well accorded with the measured data.