Computation of the autocovariances of stationary arma processes

Autoregressive-moving average (ARMA) models are often used for the purpose of forecasting a time series. As an aide to chosing a model, use is made of the autocorrelation function which is estimated from the data. If the only interest in the model is for forecasting purposes, then it is not necessary to compute the autocorrelation function associated with the chosen model. For this reason, a method for computation of the autocorrelation function is not usually included in the software used for identifying ARMA models. However, there are applications of ARMA models where it is important to compute the autocovariance function.

This paper contains an algorithm and a listing of a FORTRAN program which computes the autocovariance directly from the solution to the difference equations which govern its behavior.     

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.     

Feedback,causality and distance between arma models

The purpose of this paper is to analyze in bivariate vector autoregression the relationship between feedback in stochastic systems, Granger causality and a measure of dissimilarity between ARMA models. In particular, we consider a bivariate vector autoregressive processes of order p (a bivariate VAR(p) process) and we prove if the distance between the univariate ARMA models implied by the VAR representation is greater than a certain number that is a function of p, then Granger causality must exist in at least one direction in the variables.     

General results on the McMillan degree and the Kronecker indices of ARMA and MFD models

This paper shows that the McMillan degree of general ARMA and MFD models is equal to the pole-zero excess of the matrix consisting of the polynomial factors. Furthermore, the left Kronecker indices are equal to the row degrees of this matrix if and only if it is row-reduced and irreducible. For left coprime ARMA and MFD models the McMillan degree and the left Kronecker indices are related to the determinantal degree and the row degrees of a suitable submatrix of the polynomial factors. Under certain (necessary and sufficient) conditions this information can even be inferred from the denominator matrices in the ARMA and MFD models. Finally a rank test is presented for actually computing the McMillan degree of left coprime ARMA and MFD models.     

Measurement of language-supported reuse in object-oriented and object-based software

A major benefit of object-oriented software development is the support for reuse provided by object-oriented and object-based languages. Yet, measures and measurement tools that quantify such language-supported reuse have been lacking. Comprehensive reuse measures, particularly for reuse with modifications, are necessary to evaluate the status of reuse in an organization and to monitor improvements. We develop a set of measurable reuse attributes appropriate to object-oriented and object-based systems and a suite of measures that quantify these attributes. One of our major objectives is to measure reuse in software written in the object-based language Ada. A set of suitable primitive reuse measures are expressed in Ada Reuse Tables. These tables support the flexible use of primitive measures in programs with nested packages and subprograms, and Ada generic packages. We designed and implemented a prototype Ada Reuse Measurement Analyzer (ARMA) to generate measurement values from Ada programs. ARMA produces a reuse data representation and a corresponding forest representation of an Ada system that contain the information necessary to produce the primitive measures. Developers can use the representations to produce customized reports to satisfy a wide range of measurement goals. We use ARMA to measure primitive reuse attributes for a set of industrial Ada software. We also show that ARMA can be used to generate a set of component access and package visibility measures.     

Computational intelligence approaches and linear models in case studies of forecasting exchange rates

Artificial neural networks and fuzzy systems, have gradually established themselves as a popular tool in approximating complicated nonlinear systems and time series forecasting. This paper investigates the hypothesis that the nonlinear mathematical models of multilayer perceptron and radial basis function neural networks and the Takagi–Sugeno (TS) fuzzy system are able to provide a more accurate out-of-sample forecast than the traditional auto regressive moving average (ARMA) and ARMA generalized auto regressive conditional heteroskedasticity (ARMA-GARCH) linear models. Using series of Brazilian exchange rate (R$/US$) returns with 15 min, 60 min and 120 min, daily and weekly basis, the one-step-ahead forecast performance is compared. Results indicate that forecast performance is strongly related to the series’ frequency and the forecasting evaluation shows that nonlinear models perform better than their linear counterparts. In the trade strategy based on forecasts, nonlinear models achieve higher returns when compared to a buy-and-hold strategy and to the linear models.     

Optimal Choice of AR and MA Parts in Autoregressive Moving Average Models

This paper deals with the Bayesian method of choosing the best model for a given one-dimensional series among a finite number of candidates belonging to autoregressive (AR), moving average (MA), ARMA, and other families. The series could be either a sequence of observations in time as in speech applications, or a sequence of pixel intensities of a two-dimensional image. The observation set is not restricted to be Gaussian. We first derive an optimum decision rule for assigning the given observation set to one of the candidate models so as to minimize the average probability of error in the decision. We also derive an optimal decision rule so as to minimize the average value of the loss function. Then we simplify the decision rule when the candidate models are different Gaussian ARMA models of different orders. We discuss the consistency of the optimal decision rule and compare it with the other decision rules in the literature for comparing dynamical models.     

ARMA时间序列模型的研究与应用

ARMA模型是一种最常见的重要的时间序列模型,它被广泛应用到各种行业预测中,本文在给出ARMA三种模式和实现方法的同时,给出ARMA模型在股市应用的一个实例。     

ARMA canonical forms obtained from constructibility invariants

In recent approaches, multivariable ARMA models have been derived from observable canonical MFDs, but it was realized that these models have a number of serious limitations and disadvantages. This paper presents a new approach based on the idea of observing the state from past outputs, which leads to the construction of monic ARMA models defined by the constructibility invariants. The derivation and structural properties of these constructibility forms are investigated.     

Computational intelligence approaches and linear models in case studies of forecasting exchange rates

Artificial neural networks and fuzzy systems, have gradually established themselves as a popular tool in approximating complicated nonlinear systems and time series forecasting. This paper investigates the hypothesis that the nonlinear mathematical models of multilayer perceptron and radial basis function neural networks and the Takagi–Sugeno (TS) fuzzy system are able to provide a more accurate out-of-sample forecast than the traditional auto regressive moving average (ARMA) and ARMA generalized auto regressive conditional heteroskedasticity (ARMA-GARCH) linear models. Using series of Brazilian exchange rate (R$/US$) returns with 15 min, 60 min and 120 min, daily and weekly basis, the one-step-ahead forecast performance is compared. Results indicate that forecast performance is strongly related to the series’ frequency and the forecasting evaluation shows that nonlinear models perform better than their linear counterparts. In the trade strategy based on forecasts, nonlinear models achieve higher returns when compared to a buy-and-hold strategy and to the linear models.     

On the identifiability of non-Gaussian ARMA models using cumulants

A fixed set of output cumulants of order greater than two guarantees unique identification of known-order causal ARMA (autoregressive moving-average) models, which are driven by unobservable non-Gaussian i.i.d. noise. The models are allowed to be non-minimum-phase, and their outputs may be corrupted by additive colored Gaussian noise of unknown covariance. The ARMA parameters can be estimated either by means of linear equations and closed-form expressions or by minimizing quadratic cumulant matching criteria. The latter approach requires computation of cumulants in terms of the ARMA parameters, which is carried out in the state space using Kronecker products     

ARMA models,their Kronecker indices and their McMillan degree

This paper highlights some difficulties with the use of ARMA models with leading unit coefficient matrix in system identification. It is shown that the McMillan degree of such models is not in any easy way related to the row degrees of the polynomial factors of the ARMA model. A rank test is given for the McMillan degree of such models and it is shown that this degree will generically be a multiple of the dimension of the observation vector.     

Some restrictions of the non-causal impulse response functions

The characterization of the non-causal impulse response functions is considered. Specifically, expressions for rational, continuous, non-causal impulse response functions corresponding to different rational factorizations of the spectral density function of continuous ARMA(p, q) models are derived. Furthermore, with the restriction on the continuity condition of impulse response at the origin, certain models are found to be inadmissible representations of the non-causal impulse response functions.     

An innovations approach to least-squares estimation--Part VII: Some applications of vector autoregressive-moving average models

We use the innovations method to solve some linear estimation problems for stochastic processes described as the solution of high-order linear difference equations driven by colored noise. Such models are often called vector or multivariable auto-regressive-moving average (ARMA) models. We illustrate how the use of ARMA models can provide some simplifications and some new results in the problem of state estimation in colored noise.     

含ARMA噪声系统模型的参数辨识方法*

实际问题中，大量的动态系统控制问题可归结为含ＭＡ，ＡＲＭＡ噪声系统模型的参数辨识问题。本文提出ＲＭＡ，ＲＡＲＭＡ两种系统模型参数辨识的一种新方法，主要手段是构造和研究特殊的辅助线性模型。理论分析和实际计算表明，本文方法较传统表度有明显提高。     

一类生理信号的采集、建模和辨识

本文对生理信号的采集、建模和辨识作了较系统的探讨。在生理信号的采集方面,介绍了实时和离线信号的采集的设计思想和实现方案。在生理信号的数据建模方面,引入了ARMA建模方案,着重研讨了模型的实现途径、参数辨识和平稳化方法,编制建模程序及实现框图。在心功能病类辨识方面,对典型心功能信号——ECG、CAG和ACG,根据类比原则,利用模型分析结果,对三类心血管病——高血压、冠心病和心肌炎作了聚类辨识,取得用参数域值辨识病理的结果。     

应用于地震数据去卷的自校正白噪声估值器

本文把地震数据去卷问题处理为估计带观测噪声的ARMA模型的白噪声问题,应用时间 序列分析方法提出了不同于Mendel的新的稳态最优白噪声估值器,文章基于两个ARMA新 息模型的在线辨识,进一步给出了自校正白噪声估值器.     

The development of a model reference adaptive controller to controlthe knee joint of paraplegics

Functional neuromuscular stimulation is a technique for restoring motor function by directly activating paralyzed muscles. The design and development of closed-loop controllers that, when used in a simulation system, achieve regulated, repeatable control of the lower limb joints is discussed. Models describing the dynamic behavior of the unloaded lower limb joints under electrical stimulation are described. These models consist of a nonlinear part followed by linear dynamics described by deterministic autoregressive moving average (ARMA) models. These models are used in the design of an adaptive controller to control the movement of the leg joints. Design requirements including a severe constraint on the control rate so as not to excite spastic reflexes, are formulated, and a model reference adaptive controller design which was modified and implemented is discussed     

Stochastic approximation algorithms for identifying ARMA processes

Following the convergence proofs for stochastic approximation identification of pure autoregressive (AR) processes with dependent observations, as derived by Saridis and Stein, it is shown that the convergence for mixed autoregressive-moving-average (ARMA) cases can also be proved when none of the AR or the MA parameters or of the covariances are assumed known. Consequently, a generalized stochastic approximations identification procedure for ARMA processes is derived, which is extendable to any linear Kalrman filter models.     

Robust adaptive control of nonaffine nonlinear plants with small input signal changes

Assuming small input signal magnitudes, ARMA models can approximate the NARMA model of nonaffine plants. Recently, NARMA-L1 and NARMA-L2 approximate models were introduced to relax such input magnitude restrictions. However, some applications require larger input signals than allowed by ARMA, NARMA-L1 and NARMA-L2 models. Under certain assumptions, we recently developed an affine approximate model that eliminates the small input magnitude restriction and replaces it with a requirement of small input changes. Such a model complements existing models. Using this model, we present an adaptive controller for discrete nonaffine plants with unknown system equations, accessible input-output signals, but inaccessible states. Our approximate model is realized by a neural network that learns the unknown input-output map online. A deadzone is used to make the weight update algorithm robust against modeling errors. A control law is developed for asymptotic tracking of slowly varying reference trajectories.