ARMA Time Series Model Research Articles

Bootstrapping ARMA time series models after model selection

Inference after model selection is a very important problem. This article derives the asymptotic distribution of some model selection estimators for autoregressive moving average time series models. Under strong regularity conditions, the model selection estimators are asymptotically normal, but generally the asymptotic distribution is a non normal mixture distribution. Hence bootstrap confidence regions that can handle this complicated distribution were used for hypothesis testing. A bootstrap technique to eliminate selection bias is to fit the model selection estimator β ̂ M S ∗ to a bootstrap sample to find a submodel, then draw another bootstrap sample, and fit the same submodel to get the bootstrap estimator β ̂ M I X ∗ .

Evaluation and Analysis of Electric Power in China Based on the ARMA Model

With the rapid development of China’s economy, power demand has been closely linked with economic development in order to analyze and predict the future power situation in China. Based on the historical data of China’s electricity consumption, this paper analyzes the data characteristics of China’s electricity consumption by using Eviews software. The long-term trend of power consumption sequence is eliminated by fitting the regression curve, and then the residual sequence is analyzed and identified according to the relevant theory of time series. Using the data of China’s power demand from 2004 to 2019, the ARMA time series model is used to analyze China’s future power situation finally according to the test statistics of the model. Finally, the exponential regression ARMA model is selected to predict China’s electricity consumption. The index regression analysis method extracts the long-term characteristic information of the sequence, which is conducive to the stability processing and empirical analysis of long-term prediction. The result predicts China’s power demand in 2020 more accurately, which can provide a reference for the future productivity layout of China’s power.

Digital Twin Based Network Latency Prediction in Vehicular Networks

Network latency is a crucial factor affecting the quality of communications networks due to the irregularity of vehicular traffic. To address the problem of performance degradation or instability caused by latency in vehicular networks, this paper proposes a time delay prediction algorithm, in which digital twin technology is employed to obtain a large quantity of actual time delay data for vehicular networks and to verify autocorrelation. Subsequently, to meet the prediction conditions of the ARMA time series model, two neural networks, i.e., Radial basis function (RBF) and Elman networks, were employed to construct a time delay prediction model. The experimental results show that the average relative error of the RBF is 7.6%, whereas that of the Elman-NN is 14.2%. This indicates that the RBF has a better prediction performance, and a better real-time performance than the Elman-NN.

Prediction of GPS Satellite Clock Offset Based on an Improved Particle Swarm Algorithm Optimized BP Neural Network

Satellite clock offset is an important factor affecting the accuracy of real-time precise point positioning (RT-PPP). Due to missing real-time service (RTS) products provided by the International GNSS Service (IGS) or network faults, users may not obtain effective real-time corrections, resulting in the unavailability of RT-PPP. Considering this issue, an improved back propagation (BP) neural network optimized by heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizer (HPSO-BP) is proposed for clock offset prediction. The new model uses the particle swarm optimizer to optimize the initial parameters of the BP neural network, which can avoid the instability and over-fitting problems of the traditional BP neural network. IGS RTS product data is selected for the experimental analysis; the results demonstrate that the average prediction precision of the HPSO-BP model for 20-min and 60-min is better than 0.15 ns, improving by approximately 85% compared to traditional models including the linear polynomial (LP) model, the quadratic polynomial (QP) model, the gray system model (GM (1,1)), and the ARMA time series model. It indicates that the HPSO-BP model has reasonable practicability and stability in the short-term satellite clock offset prediction, and its prediction performance is superior to traditional models. Therefore, in practical applications, the clock offset products predicted by the HPSO-BP model can meet the centimeter-level positioning accuracy requirements of RT-PPP.

Detecting systematic anomalies affecting systems when inputs are stationary time series

AbstractWe develop an anomaly detection method when systematic anomalies, possibly statistically very similar to genuine inputs, are affecting control systems at the input and/or output stages. The method allows anomaly free inputs (i.e., those before contamination) to originate from a wide class of random sequences, thus opening up possibilities for diverse applications. To illustrate how the method works on data, and how to interpret its results and make decisions, we analyze several actual time series, which are originally nonstationary but in the process of analysis are converted into stationary. As a further illustration, we provide a controlled experiment with anomaly free inputs following an ARMA time series model under various contamination scenarios.

Research on the Comprehensive Evaluation of the Higher Education System Based on FCE and ARMA Models

A Higher education system is closely related to a country’s development. Governments need to make appropriate adjustments to ensure the healthy and sustainable development of higher education. To measure and evaluate the development status of the national higher education system and propose a set of policies, the following work has been done in this paper: First, this paper establishes a comprehensive evaluation index system based on the AHP‐FCE model. The healthy development of education in significant countries was compared horizontally and vertically. The results of weighted scores were used to determine the Japanese higher education system as the research object. Secondly, this paper uses factor analysis and principal component analysis to evaluate the level of sustainable development of higher education, detecting development barriers that migrate from the current to the future. This paper proposes a healthy and sustainable development policy blueprint from four aspects. Finally, this article uses the ARMA time series model to predict the development trend of Japanese higher education in the next 30 years and formulates a timetable for corresponding implementation arrangements. In addition, this paper quantitatively evaluates the effectiveness of the policies we propose and their impact on reality and provides references for other countries in the world.

Model identification for ARMA time series through convolutional neural networks

We use convolutional neural networks for model identification in ARMA time series models, where our networks are trained on synthetic data with known ground truths. Comparing the performance of these networks with traditional likelihood-based methods, in particular the Akaike and Bayesian Information Criteria, we are able to show that when it comes to statistical inference on ARMA orders, neural networks can significantly outperform likelihood-based methods in terms of accuracy and, by orders of magnitude, in terms of speed. We also observe improvements in terms of time series forecasting. Our approach shows the feasibility of using artificial neural networks for statistical inference in situations where classical likelihood-based methods are difficult or costly to implement.

Hybrid kernel approach to Gaussian process modeling with colored noises

Traditional Gaussian Process Regression (TGPR) models typically assume independent identically distributed (i.i.d.) noises for all observations. However, applications with colored noises/disturbances frequently arise in modeling of complex processes. In this work, first, we consider to model noise by an ARMA time series model and determine its covariance for subsequent Gaussian Process (GP) modeling. Then a novel approach based on hybrid kernels is proposed, thereby avoiding parametric modeling of the colored noises. Moreover, all hyper-parameters are estimated simultaneously by using a particle swarm optimization (PSO) algorithm. Finally, a synthetic data, a simulated example, as well as a polyester polymerization process are used to demonstrate the effectiveness of the proposed approach.

COMPARATIVE ANALYSIS OF FUTURE MARKET IN INDONESIAN CONTEXT

For decision making, sugar basic identification can be used as a strategic tool. In this study, accessible forecast using ARMA (p,q) time series models comparing Indonesian sugar spot and ICE future markets. The study identified that in two cities of Indonesia, there exist synchronous high and low primary movement, and volatility with correlation coefficient of 0.70, showing positive higher magnitude, and descriptive statistics. The result shows that in the selected two cities, Jakarta showed higher compare to the other city. Comparing forecasting errors between ARMA (p,q) and SARMAX (p,q) models, the monthly sugar basis model for Bande Aache is SARMAX (1,0). For Jakarta, the forecasted model is ARMA (2,0). Additionally, the Bande Aache sugar basis breakpoint month is 2008M09 and for Bande Aache, breakpoint month is 2011M11. A closer analysis suggests that the breaking points coinciding with the identifiable sugar basis level and the volatility trends in the examined period. Both forecasted models are easier and implementable and can provide informational input for efficient allocative decisions by the Indonesian sugar supply chain.

Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models

Expectiles define a least squares analogue of quantiles. They have been the focus of a substantial quantity of research in the context of actuarial and financial risk assessment over the last decade. The behaviour and estimation of unconditional extreme expectiles using independent and identically distributed heavy-tailed observations have been investigated in a recent series of papers. We build here a general theory for the estimation of extreme conditional expectiles in heteroscedastic regression models with heavy-tailed noise; our approach is supported by general results of independent interest on residual-based extreme value estimators in heavy-tailed regression models, and is intended to cope with covariates having a large but fixed dimension. We demonstrate how our results can be applied to a wide class of important examples, among which are linear models, single-index models as well as ARMA and GARCH time series models. Our estimators are showcased on a numerical simulation study and on real sets of actuarial and financial data.

Detecting Systematic Anomalies Affecting Systems When Inputs Are Stationary Time Series

We develop an anomaly-detection method when systematic anomalies, possibly statistically very similar to genuine inputs, are affecting control systems at the input and/or output stages. The method allows anomaly-free inputs (i.e., those before contamination) to originate from a wide class of random sequences, thus opening up possibilities for diverse applications. To illustrate how the method works on data, and how to interpret its results and make decisions, we analyze several actual time series, which are originally non-stationary but in the process of analysis are converted into stationary. As a further illustration, we provide a controlled experiment with anomaly-free inputs following an ARMA time series model under various contamination scenarios.

A Monte Carlo Simulation Study on the Power of Autocorrelation Tests for ARMA Models

It is often the case when assessing the goodness of fit for an ARMA time series model that a portmanteau test of the residuals is conducted to assess residual serial correlation of the fitted ARMA model. Of the many portmanteau tests available for this purpose, one of the most famous and widely used is a variant of the original Box-Pierce test, the Ljung-Box test. Despite the popularity of this test, however, there are several other more modern portmanteau tests available to assess residual serial autocorrelation of the fitted ARMA model. These include two portmanteau tests proposed by Monti and Peña and Rodríguez. This paper focuses on the results of a power analysis comparing these three different portmanteau tests against different fits of ARMA - derived time series, as well as the behavior of the three different test statistics examined when applied to a real-world data set. We confirm that for situations in which the moving average component of a fitted ARMA model is underestimated or when the sample size is small, the portmanteau test proposed by Monti is a viable alternative to the Ljung-Box test. We show new evidence that the Peña and Rodríguez may also be a viable option for testing for residual autocorrelation for data with small sample sizes. KEYWORDS: Time Series; Monte Carlo; ARMA Models; Power; Simulation; Autocorrelation Tests; Portmanteau Tests; Monti; Ljung-Box; Peña and Rodríguez

Structure Damage Identification Based on Regularized ARMA Time Series Model under Environmental Excitation

In this paper, a non-modal parametric method to identify structural damage using a regularized autoregressive moving average time series model under environmental excitation is proposed in combination with the virtual impulse response function. This method can use the structural vibration response to determine the damage caused to the structure during environmental excitation. Firstly, the virtual impulse response function is obtained by using the structural vibration response. Then, a regularized ARMA time series model is used to fit the virtual impulse response function. Based on the change of auto-regression coefficients in the regularization model under different damage cases, the structural damage is identified. The authors derive the regularization equation of an ARMA time series model to solve the problems in a time series model and obtain the regularization coefficient. Finally, this method is applied to a three-degrees-of-freedom chain structure and a three-floor shear structure of the Los Alamos National Laboratory (LANL). The experimental results show that the method based on the regularized ARMA time series model under environmental excitation can effectively identify the structural damage, which is a reliable method for damage identification. The regularized ARMA time series model can accurately extract signal features and has invaluable application prospects in the field of structural health monitoring.

ARMA(p,q) type high order fuzzy time series forecast method based on fuzzy logic relations

Within classic time series approaches, a time series model can be studied under 3 groups, namely AR (autoregressive model), MA (moving averages model) and ARMA (autoregressive moving averages model). On the other hand, solutions are based mostly on fuzzy AR time series models in the fuzzy time series literature. However, just a few fuzzy ARMA time series models have proposed until now. Fuzzy AR time series models have been divided into two groups named first order and high order models in the literature, highlighting the impact of model degree on forecast performance. However, model structure has been disregarded in these fuzzy AR models. Therefore, it is necessary to eliminate the model specification error arising from not utilizing of MA variables in the fuzzy time series approaches. For this reason, a new high order fuzzy ARMA(p,q) time series solution algorithm based on fuzzy logic group relations including fuzzy MA variables along with fuzzy AR variables has been proposed in this study. The main purpose of this article is to show that the forecast performance can be significantly improved when the deficiency of not utilizing MA variables. The other aim is also to show that the proposed method is better than the other fuzzy ARMA time series models in the literature from the point of forecast performance. Therefore, the new proposed method has been compared regarding forecast performance against some methods commonly used in literature by applying them on gold prices in Turkey, Istanbul Stock Exchange (IMKB) and the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX).

Kernel-based portmanteau diagnostic test for ARMA time series models

In this paper, the definition of the Toeplitz autocorrelation matrix is used to derive a kernel-based portmanteau test statistic for ARMA models. Under the null hypothesis of no serial correlation, the distribution of the test statistic is approximated by a standard normal using the kernel-based normalized spectral density estimator, without having to specify any alternative model. Unlike most existing portmanteau test statistics, the proposed test is defined for all lags. Simulation studies are conducted to assess the performance of the proposed test. A real application is given to demonstrate the usefulness of this goodness-of-fit test statistic.

Bayesian GARMA models for count data

ABSTRACTGeneralized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This work presents a Bayesian approach for GARMA models with Poisson, binomial, and negative binomial distributions. A simulation study was carried out to investigate the performance of Bayesian estimation and Bayesian model selection criteria. In addition, three real data sets were analyzed using the Bayesian approach on GARMA models.

Estimating safety performance trends over time for treatments at intersections in Florida

Researchers have put great efforts in quantifying Crash Modification Factors (CMFs) for diversified treatment types. In the Highway Safety Manual (HSM), CMFs have been identified to predict safety effectiveness of converting a stop-controlled to a signal-controlled intersection (signalization) and installing Red Light Running Cameras (RLCs). Previous studies showed that both signalization and adding RLCs reduced angle crashes but increased rear-end crashes. However, some studies showed that CMFs varied over time after the treatment was implemented. Thus, the objective of this study is to investigate trends of CMFs for the signalization and adding RLCs over time. CMFs for the two treatments were measured in each month and 90-day moving windows respectively. The ARMA time series model was applied to predict trends of CMFs over time based on monthly variations in CMFs. The results of the signalization show that the CMFs for rear-end crashes were lower at the early phase after the signalization but gradually increased from the 9th month. On the other hand, the CMFs for angle crashes were higher at the early phase after adding RLCs but decreased after the 9th month and then became stable. It was also found that the CMFs for total and fatal/injury crashes after adding RLCs in the first 18 months were significantly greater than the CMFs in the following 18 months. This indicates that there was a lag effect of the treatments on safety performance. The results of the ARMA model show that the model can better predict trends of the CMFs for the signalization and adding RLCs when the CMFs are calculated in 90-day moving windows compared to the CMFs calculated in each month. In particular, the ARMA model predicted a significant safety effect of the signalization on reducing angle and left-turn crashes in the long term. Thus, it is recommended that the safety effects of the treatment be assessed using the ARMA model based on trends of CMFs in the long term after the implementation of the treatment.

Strictly stationary solutions of spatial ARMA equations

The generalization of the ARMA time series model to the multidimensional index set $$\mathbb {Z}^d$$ , $$d\ge 2$$ , is called spatial ARMA model. The purpose of the following is to specify necessary conditions and sufficient conditions for the existence of strictly stationary solutions of the ARMA equations when the driving noise is i.i.d. Two different classes of strictly stationary solutions are studied, solutions of causal and noncausal models. For the special case of a first-order model on $$\mathbb {Z}^2$$ conditions are obtained, which are simultaneously necessary and sufficient.

Application of BP-ARMA Combined Model Based on Entropy Method in the Prediction of Circle Beam Displacement of Foundation Pit

The prediction of deformation of foundation pit’s supporting structure is the basis of construction control of deep foundation pit. Meanwhile, it is vital to the safe excavation of foundation pit. In the work, the 1st project of Huaqiao in Jiantao Square of Kunshan City is chosen. Besides, model of combination based on entropy method is built to predict the displacement of circle beam with BP neural network and ARMA time series model. Finally, the analysis shows that combination models improve overall prediction on the premise of better predicting accuracy. Thus, it is of practical value.

Strip/Foil Rolling Mill Stochastic Excitation Model and Its Stability

Based on the stochastic rolling force data from aluminum hot strip tandem mill, the ARMA time series model and the stochastic excitation power spectral density (PSD) model are established, and the stochastic rolling forces excitation model is established by utilizing Levenberg-Marquardt combined with generalized global planning algorithm. A two dimensional stochastic nonlinear dynamical model of rolls is presented considering the stochastic factor of the rolling force. The Hamilton function is also described as one dimension diffusion process by using stochastic average method, the singular boundary theory was taken for analyzing the global stochastic stability of the system, and the system’s stochastic stability was researched by solving the Fokker-Planck-Kolmogorov (FPK) equation. The results show that the stochastic excitation model obtained has significance for analyzing and researching stochastic dynamics characteristics to the system, and also generalized energy H in the range of 0.02 to 0.4, the system’s response has the minimum transition probability density, and the system state is not easy to change, therefore the system generalized energy H should be to limit in this range in the design and operation of the rolling mill.