Generalized autoregressive and moving average models: multicollinearity, interpretation and a new modified model

Three important parametric models for describing the correlation functions and spectra of stationary stochastic processes are the autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Quite recently, the MATLAB toolbox “ARMASA” has been made publicly available. This toolbox provides state-of-the-art algorithms to perform automatic identification and selection between the models based on the estimated prediction error. ARMASA works on a single segment of data, whereas in some applications, the data are available as multiple segments. We could process each segment independently and average the estimated autocorrelation functions or spectra afterward. Better performance, however, can be expected when all segments are processed simultaneously, for two reasons. Initially, the bias in the estimated model parameters depends on the number of observations in a segment. Averaging models from segments does not reduce this bias, in contrast to identification from all the data at once. In either case, the variance of the estimated model parameters will decrease. By considering all the data at once this variance reduction can be considered in the order selection stage, decreasing the selection bias. In this paper, we extend the parameter estimation algorithms of the ARMASA toolbox to the case of multiple segments. AR parameter estimation from segments has been considered before, but not for the MA and ARMA models. In addition, in the AR case, model order selection can be done easily when the segments are independent. But, in the application we are primarily interested in, the segments are formed by lines of scanning transmission electron microscopy (STEM) images, which can be correlated with each other. Because the correlation among data segments influences the effective number of independent observations available it becomes necessary to estimate that number. This is not an easy problem in general. For observations from a stochastic process with an isotropic 2-D autocorrelation function we can, however, formulate an accurate estimator in terms of the line autocorrelation function. This situation arises, for example, in STEM images of amorphous specimens. From the AR model identification for segments, the extension to the MA and ARMA models is rather straightforward because MA and ARMA algorithms are based on Durbin's methods, whose first step is the estimation of a long AR model. We compare the segment-based algorithms to conventional ARMASA with simulations of stationary stochastic processes. An illustrative example involving simulated STEM images shows large potential benefits.

This paper presents a new fast algorithm for synthesizing sequences of generalized Autoregressive Moving Average (GARMA) processes. These can be used to model time series which exhibit both short-range and long- range dependencies, as well as periodic behavior. The proposed synthesis scheme is based upon parameterizing the Gegenbauer coefficients by ARMA models using well-established signal modeling techniques such as Padé, Prony, Shanks, or Steiglitz-Mcbride methods. The proposed method is computationally efficient, sufficiently accurate, and very simple to implement. The generated sequences can be used in simulation studies such as network traffic.

This paper discusses the formation of one temporal spatial model, the Generalized Space Time Autoregressive (GSTAR) model, if the data of model is count data. The development of the GSTAR model is an update or problem completion of the count data which tends to be stationary and non-normal / Gaussian data, because GSTAR model is assumed normal distributed and stationarity. GSTAR modelling for count data refers to the Time series model for count data, which are the Generalized Autoregressive Moving Average (GARMA) model and modeling Count Time Series which has the Generalized Linear Model (GLM) concept. The model formed is called the Poisson GSTAR model

\n Generalized 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 the GARMA model with discrete distributions and application of resampling techniques to this class of models. We also proposed The Bayesian approach on GARMA models. The TGARMA (Transformed Generalized Autoregressive Moving Average) models was proposed, using the Box-Cox power transformation. Last but not least we proposed the Bayesian approach for the TGARMA (Transformed Generalized Autoregressive Moving Average).\n

Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir

ABSTRACTThis paper presents a new method for the causal quarter-plane region of support two-dimensional (2-D) moving average (MA) model parameter estimation. The new approach is based on approximation of 2-D MA by the 2-D AR model. To achieve this aim, the corresponding relations are extended to a 2-D case and the related algorithm is presented. In this method, a 2-D series with the MA model has been approximated by a 2-D AR model with higher order and then the parameters of the AR model are estimated by the new method that is presented. Then the relation between the parameters of the 2-D AR and 2-D MA model is obtained and finally by using this relation, the parameters of the 2-D MA model are obtained. Since the proposed method does not involve complex and time consuming matrix computations, it is computationally efficient. The presented method also has good accuracy in standard deviation and mean value; a fact that has been shown by applying this method to a numerical example and presenting the results of simulation.

Autoregressive moving average models of crown profiles for two California hardwood species

This paper presents a novel method of estimating the optimal steady state Kalman filter gain of a linear discrete time-invariant system from a non-optimal Kalman filter residual sequence. The relation between the optimal residual sequence and a signal derived from the non-optimal residual sequence is described by a Moving Average (MA) model whose coefficients are expressed in terms of the state space parameters and the optimal steady state Kalman filter gain. In order to identify the MA model, a whitening filter of the derived signal, which corresponds to an AutoRegressive (AR) model of the signal, is first identified using the least-squares method. Then the inverse filter of the whitening filter, which corresponds to the MA model, is calculated. From the coefficients of the identified MA model, the optimal steady state Kalman filter gain can be obtained. Numerical example is provided to illustrate the feasibility of this approach.

The performance of Autoregressive Moving Average and Multiple Linear Regression Models in predicting minimum and maximum temperatures of Ogun State is herein reported. Maximum and Minimum temperatures data covering a period of 29 years (1982 -2009) obtained from the Nigerian Meteorological Agency (NiMet), Abeokuta office, Nigeria, were used for the analyses. The data were first processed and aggregated into annual time series. Mann-Kendal non-parametric test and spectral analysis were carried out to detect whether there is trend, seasonal pattern, and either short or long memory in the time series. Mann-Kendal Z-values obtained are –0.47 and –2.03 for minimum and maximum temperatures respectively, indicating no trend, though the plot shows a slight change. The Lo’s R/S Q(N,q) values for minimum and maximum temperatures are 3.67 and 4.43, which are not within the range 0.809 and 1.862, thus signifying presence of long memory. The data was divided into two and the first 20 years data was used for model development, while the remaining was used for validation. Autoregressive Moving Average (ARMA) model of order (5, 3) and Autoregressive (AR) model of order 2 are found best for predicting minimum and maximum temperatures respectively. Multiple Linear Regression (MLR) model with 4 features (moving average, exponential moving average, rate of change and oscillator) were fitted for both temperatures. The ARMA and AR models were found to perform better with Mean Absolute Percentage Error (MAPE) values of -2.89 and -1.37 for minimum and maximum temperatures, compared with the Multiple Linear Regression Models with MAPE values of 141 and 876 respectively. Results of ARMA model can be relied on in generating forecast of temperature of the study area because of their minimal error values. However, it is recommended other climatic elements that were not captured in this paper due to unavailability of information be considered too in order to see which model is best for them.

The paper describes the derivation, design and evaluation of a parameter-adaptive integrated controller for a turbogenerator. The control strategy is to minimise the variances between the outputs of the turbogenerator and the outputs of a linear optimal predictor under all operating conditions. The design of the controller is based on an autoregressive moving-average model, and does not require any information about the parameters of the turbogenerator. A nonlinear feedback approach to the control strategy is achieved by a simple recursive algorithm, which can be implemented as an online real-time computer control scheme for a turbogenerator without persistent excitation of inputs. The performance of the adaptive controller depends on the successful design of the optimal predictor, which can be achieved by choosing suitable pole values. Results obtained using a detailed nonlinear simulation of a turbogenerator are presented.

This article is intended to complement previous research (Sivo, 1997; Sivo & Willson, 1998, in press) by discussing the propriety and practical advantages of specifying multivariate time series models in the context of structural equation modeling for time series and longitudinal panel data. Three practical considerations motivated this article. Unlike Marsh (1993), Sivo and Willson (2000) did not offer multiple indicator (latent order) equivalents to their autoregressive (AR), moving average (MA), and autoregressive-moving average (ARMA) models. Moreover, such models have yet to be discussed, despite Marsh's (1993) advocacy for multiple indicator models in general. Further motivating multiple indicator extensions of the AR, MA, and ARMA equivalent models is the fact that longitudinal studies often collect data on more than 1 related variable per occasion. Such multiple indicator models capitalize on 1 of the chief analytical advantages of structural equation modeling in that measurement error may be estimated directly.

Exponentially weighted moving average (EWMA) charts and cumulative sum (CUSUM) control charts based on fitting a generalized linear model (GLM) to estimate the time‐varying mean of the process have been used for health surveillance due to its efficiency to detect soon small shifts in count data as morbidity or mortality rates. However, in these proposals, the serial correlation is usually omitted implying that the charts may fail.In this paper, generalized autoregressive moving average (GARMA) models that include lagged terms to model the autocorrelation are proposed to analyze the performance of regression EWMA control charts based on fitting of GLM models with negative binomial distribution for monitoring time series.The main contributions of the current paper are two new statistics based on the likelihood function to be monitored and three procedures to build one‐sided EWMA charts and to measure the impact on the performance of these EWMA charts when the serial correlation is neglected in the regression model. For the simulated scenarios, the statistics based on the likelihood and the winsorized EWMA presented the best performance. Also, a real data analysis detected outbreaks in the hospitalization time series due to respiratory diseases of elderly people in São Paulo city.

Over the past several years, great strides have been made in the effort to monitor the small-signal stability of power systems. These efforts focus on estimating electromechanical modes, which are a property of the system that dictate how generators in different parts of the system exchange energy. Though the algorithms designed for this task are powerful and important for reliable operation of the power system, they are susceptible to severe bias when forced oscillations are present in the system. Forced oscillations are fundamentally different from electromechanical oscillations in that they are the result of a rogue input to the system, rather than a property of the system itself. To address the presence of forced oscillations, the frequently used AutoRegressive Moving Average (ARMA) model is adapted to include sinusoidal inputs, resulting in the AutoRegressive Moving Average plus Sinusoid (ARMA+S) model. From this model, a new Two-Stage Least Squares algorithm is derived to incorporate the forced oscillations, thereby enabling the simultaneous estimation of the electromechanical modes and the amplitude and phase of the forced oscillations. The method is validated using simulated power system data as well as data obtained from the western North American power system (wNAPS) and Eastern Interconnection (EI).

This study has been able to reveal that the Combine White Noise model outperforms the existing Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Moving Average (MA) models in modeling the errors, that exhibits conditional heteroscedasticity and leverage effect. MA process cannot model the data that reveals conditional heteroscedasticity and GARCH cannot model the leverage effect also. The standardized residuals of GARCH errors are decomposed into series of white noise, modeled to be Combine White Noise model (CWN). CWN model estimation yields best results with minimum information criteria and high log likelihood values. While the EGARCH model estimation yields better results of minimum information criteria and high log likelihood values when compare with MA model. CWN has the minimum forecast errors which are indications of best results when compare with the GARCH and MA models dynamic evaluation forecast errors. Every result of CWN outperforms the results of both GARCH and MA. The contribution of this study to the scientific community is that the CWN gives good results that improve the weaknesses of the existing models.

In this article, we develop the theory of k-factor Gegenbauer Autoregressive Moving Average (GARMA) process with infinite variance innovations which is a generalization of the stable seasonal fractional Autoregressive Integrated Moving Average (ARIMA) model introduced by Diongue et al. (2008). Stationarity and invertibility conditions of this new model are derived. Conditional Sum of Squares (CSS) and Markov Chains Monte Carlo (MCMC) Whittle methods are investigated for parameter estimation. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques. Finally, the usefulness of the model is corroborated with the application to streamflow data for Senegal River at Bakel.