Autoregressive Moving Average Coefficients Research Articles

A New Technique for ARMA-System Identification Based on QR-Decomposition of Third Order Cumulants Matrix

In this paper a new technique to estimate the coefficients of a general Autoregressive Moving Average (ARMA) (p, q) model is proposed. The ARMA system is excited by an un-observable independently identically distributed (i.i.d) non-Gaussian process. The proposed ARMA coefficients estimation method uses the QR-Decomposition (QRD) of a special matrix built with entries of third order cumulants (TOC) of the available output data only. The observed output may be corrupted with additive colored or white Gaussian noise of unknown power spectral density. The proposed technique was compared with several good methods such as the residual time series (RTS) and the Q-slice algorithm (QSA) methods. Simulations for several examples were tested. The results for these examples confirm the good performance of the proposed technique with respect to existing well-known methods.

Non stationary‐ARMA flicker model for squirrel cage induction generators based wind farms

Time varying nature of the wind power is studied previously considering different time intervals from seconds to days. However for power quality problems such as flicker, a model which considers the extremely fast variations is essential. Here by using large number of actual records, a time-varying model is proposed which considers the extremely short-time variations of wind active and reactive powers. The wind farm is modelled as a current source with time varying amplitude and phase which change every 0.01 s. Autoregressive moving-average (ARMA) models are utilized to model the variations and ARMA coefficients are calculated for every record. Same to the actual behaviour, the proposed model is non-stationary as the ARMA order and coefficients are different at every run of the model. The proposed model is confirmed through utilizing several applications which need the power time series with extremely short sampling intervals. The following studies are performed by using the actual data and then the proposed model: power spectral density of active and reactive power variations, instantaneous flicker, short term flicker (Pst), estimating the Pst using the maximum value of the instantaneous flicker, estimation of cumulative Pst for multiple wind turbines, and the impact of SVC on flicker mitigation.

Autoregressive Moving Average Graph Filtering

One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which (i) are able to approximate any desired graph frequency response, and (ii) give exact solutions for tasks such as graph signal denoising and interpolation. The design philosophy, which allows us to design the ARMA coefficients independently from the underlying graph, renders the ARMA graph filters suitable in static and, particularly, time-varying settings. The latter occur when the graph signal and/or graph are changing over time. We show that in case of a time-varying graph signal our approach extends naturally to a two-dimensional filter, operating concurrently in the graph and regular time domains. We also derive sufficient conditions for filter stability when the graph and signal are time-varying. The analytical and numerical results presented in this paper illustrate that ARMA graph filters are practically appealing for static and time-varying settings, as predicted by theoretical derivations.

Enhancement of electric arc furnace reactive power compensation using Grey–Markov prediction method

The time varying nature of electric arc furnace (EAF) gives rise to voltage fluctuations, which produces the effect known as flicker. Employing reactive power compensation devices such as static VAr compensator (SVC) is one of the main approaches to mitigate this phenomenon. By utilising prediction methods to forecast EAFs reactive power consumption for a half-cycle ahead, performance of SVC can be enhanced substantially. This study proposes a rolling Grey model and a Grey–Markov method to predict the actual reactive power of Mobarakeh Steel Company, Isfahan/Iran. To investigate the efficiency of the proposed methods the results are compared with the results of EAFs reactive power compensation when no prediction method is employed. Furthermore, autoregressive moving average (ARMA) models with updating coefficients, which are studied in the literature are used to predict EAF reactive power. Various methods for updating ARMA coefficients including normalised least mean square, recursive least square method and an online genetic algorithm are used. By comparing the indices which are defined using the concept of flicker frequency and power spectral density, the superiority of Grey–Markov and rolling Grey model over the aforementioned prediction methods is investigated.

A Portmanteau Test for ARMA Processes with Infinite Variance

We propose a portmanteau test for autoregressive moving average (ARMA) time series models with infinite variance. Our test is based on the partial autocorrelation function (PACF) of trimmed residuals from the fitted model. The asymptotic null distribution of the test statistic is derived when the innovation has a Pareto-type distribution and the estimators of the ARMA coefficients satisfy certain condition. The effectiveness of our test is established through extensive simulation studies. In general, our test agrees very well with that of Lee and Ng (2010) and under some circumstances it performs even better. Three real world examples are also provided to demonstrate its usage.

Linear and nonlinear dynamic systems in financial time series prediction

Article history: Received April 28, 2012 Accepted 6 July 2012 Available online July 12 2012 Autoregressive moving average (ARMA) process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX) are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF) to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE) and mean absolute deviation (MAD) statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction. © 2012 Growing Science Ltd. All rights reserved.

Human control of an inverted pendulum: Is continuous control necessary? Is intermittent control effective? Is intermittent control physiological?

Human motor control is often explained in terms of engineering 'servo' theory. Recently, continuous, optimal control using internal models has emerged as a leading paradigm for voluntary movement. However, these engineering paradigms are designed for high band-width, inflexible, consistent systems whereas human control is low bandwidth and flexible using noisy sensors and actuators. By contrast, engineering intermittent control was designed for bandwidth-limited applications. Our general interest is whether intermittent rather than continuous control is generic to human motor control. Currently, it would be assumed that continuous control is the superior and physiologically natural choice for controlling unstable loads, for example as required for maintaining human balance. Using visuo-manual tracking of an unstable load, we show that control using gentle, intermittent taps is entirely natural and effective. The gentle tapping method resulted in slightly superior position control and velocity minimisation, a reduced feedback time delay, greater robustness to changing actuator gain and equal or greater linearity with respect to the external disturbance. Control was possible with a median contact rate of 0.8±0.3 s(-1). However, when optimising position or velocity regulation, a modal contact rate of 2 s(-1) was observed. This modal rate was consistent with insignificant disturbance-joystick coherence beyond 1-2 Hz in both tapping and continuous contact methods. For this load, these results demonstrate a motor control process of serial ballistic trajectories limited to an optimum rate of 2 s(-1). Consistent with theoretical reasoning, our results suggest that intermittent open loop action is a natural consequence of human physiology.

Unscented Kalman filter for time varying spectral analysis of earthquake ground motions

A novel parametric time-domain method for time varying spectral analysis of earthquake ground motions is presented. Based upon time varying autoregressive moving average (ARMA) modeling of earthquake ground motion, unscented Kalman filter (UKF) is used to estimate the time varying ARMA coefficients. Then, time varying spectrum is yielded according to the time varying ARMA coefficients. Analysis of the ground motion record El Centro (1940, N–S) shows that compared to Kalman filter (KF) based method, short-time Fourier transform (STFT) and wavelet transform (WT), UKF based method can more reasonably represent the distribution of the seismic energy in time–frequency plane, which ensures its better ability to track the local properties of earthquake ground motions and to identify the systems with nonlinearity. Analysis of the seismic response of a building during the 1994 Northridge earthquake shows that UKF based method can be potentially a useful tool for structural damage detection and health monitoring. Lastly, it is found that the theoretical frequency resolving power of ARMA models usually neglected in some studies has considerable effect on time varying spectrum and it is one of the key factors for ARMA modeling of earthquake ground motion.

ARMA modelled time-series classification for structural health monitoring of civil infrastructure

Structural health monitoring (SHM) is the subject of a great deal of ongoing research leading to the capability that reliable remote monitoring of civil infrastructure would allow a shift from schedule-based to condition-based maintenance strategies. The first stage in such a system would be the indication of an extraordinary change in the structure's behaviour. A statistical classification algorithm is presented here which is based on analysis of a structure's response in the time domain. The time-series responses are fitted with Autoregressive Moving Average (ARMA) models and the ARMA coefficients are fed to the classifier. The classifier is capable of learning in an unsupervised manner and of forming new classes when the structural response exhibits change. The approach is demonstrated with experimental data from the IASC–ASCE benchmark four-storey frame structure, the Z24 bridge and the Malaysia–Singapore Second Link bridge. The classifier is found to be capable of identifying structural change in all cases and of forming distinct classes corresponding to different structural states in most cases.

Identification of ARMA Speech Models Using an Effective Representation of Voice Source

A two-stage least square identification method is proposed for estimating ARMA (autoregressive moving average) coefficients from speech signals. A pulse-train like input sequence is often employed to account for the source effects in estimating vocal tract parameters of voiced speech. Due to glottal and radiation effects, the pulse train, however, does not represent the effective voice source. The authors have already proposed a simple but effective model of voice source for estimating AR (autoregressive) coefficients. This letter extends our approach to ARMA analysis to wider varieties of speech sounds including nasal vowels and consonants. Analysis results on both synthetic and natural nasal speech are presented to demonstrate the analysis ability of the method.

An efficient approach for computing non-Gaussian ARMA model coefficients using Pisarenko's method

This paper addresses the problem of estimating the coefficients of a general autoregressive moving average (ARMA) model from only third order cumulants (TOCs) of the noisy observations of the system output. The observed signal may be corrupted by additive coloured Gaussian noise. The system is driven by a zero-mean independent and identically distributed (i.i.d.) non-Gaussian sequence. The input is not observed. The unknown model coefficients are obtained using eigenvalue–eigenvector decomposition. The derivation of this procedure is an extension of Pisarenko harmonic autocorrelation-based (PHA) method to third order statistics. It will be shown that the desired ARMA coefficients vector corresponds to the eigenvector associated with the minimum eigenvalue of a data covariance matrix of TOCs. The proposed method is also compared with well-known algorithms as well as with the PHA method. Copyright © 2005 John Wiley & Sons, Ltd.

The analysis of indexed astronomical time series – I. Basic methods

The application of autoregressive moving-average (ARMA) modelling to discrete time or indexed data is discussed. An essential tool is the autocorrelation function, and its utility is demonstrated with some examples. Extensions of the ARMA models to include non-stationarity are described; variability in both the series mean and the ARMA coefficients can be dealt with by recursively calculated or state space models. A number of tests for non-stationarity of the series mean are described in detail. Particular attention is devoted to the effects of serial dependence of the data. A problem with the O-C (observed-calculated) method as traditionally used in astronomy is pointed out

Estimation of coherence and time delay with ARMA models

Magnitude squared coherence (MSC) and time delay are two important quantities needed for passive detection and localization of a radiating source using several sensors. This paper presents a novel approach to estimating the MSC and time delay from the outputs of two sensors. It first models the MSC as the product of the transfer functions of two autoregressive moving-average (ARMA) filters. The ARMA coefficients are then determined by a least squares, matrix pseudoinverse solution to the estimation equation. Time delay estimation follows as a byproduct, since both phase and MSC estimates are now available. Simulation results obtained from this modeling approach are compared against those estimated from the traditional periodograms. In the majority of cases studied, the ARMA approach appears to be superior, giving smaller bias and variances in both MSC and time delay estimations.