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.     

非线性格兰杰因果关系在计算神经科学的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系的应用越来越广泛,但都是用来分析线性时间序列数据之间的内在联系。将线性格兰杰因果关系推广到非线性的情形,首先利用核函数的方法建立非线性时间序列模型,再按照线性格兰杰因果关系的基本思想定义非线性格兰杰因果关系,最后通过一个模拟的例子验证该方法的有效性。模拟数据的结果表明,该方法能有效地分析非线性数据之间的内在联系。     

ARMA model parameter estimation based on the equivalent MA approach

The paper investigates the relation between the parameters of an autoregressive moving average (ARMA) model and its equivalent moving average (EMA) model. On the basis of this relation, a new method is proposed for determining the ARMA model parameters from the coefficients of a finite-order EMA model. This method is a three-step approach: in the first step, a simple recursion relating the EMA model parameters and the cepstral coefficients of an ARMA process is derived to estimate the EMA model parameters; in the second step, the AR parameters are estimated by solving the linear equation set composed of EMA parameters; then, the MA parameters are obtained via simple computations using the estimated EMA and AR parameters. Simulations including both low- and high-order ARMA processes are given to demonstrate the performance of the new method. The end results are compared with the existing method in the literature over some performance criteria. It is observed from the simulations that our new algorithm produces the satisfactory and acceptable results.     

向量自回归模型Granger因果图的条件互信息辨识与应用

Grangerl因果性是衡量系统变量间动态关系的重要依据．传统的两变量Grangerl因果分析法容易产生伪因果关系,且不能刻画变量间的即时因果性．本文利用图模型方法研究时间序列变量间的Grangerl因果关系,建立了时间序列Granger因果图,提出Grangerl因果图的条件互信息辨识方法,利用混沌理论中的关联积分估计条件互信息,统计量的显著性由置换检验确定．仿真结果证实了方法的有效性,并利用该方法研究了空气污染指标以及中国股市间的Grangerl因果关系．     

Spurious Granger causality between a broken-trend stationary process and a stochastic trend process

This paper examines spurious Granger causality between a trend stationary process with structural breaks and a stochastic trend process. Monte Carlo simulations show that whether or not there are deterministic variables in the testing models, the sample size and the parameter values of the data generation process can affect the empirical frequencies of spurious Granger causality relations in different degrees. The analysis also points out that an alternative rank-based causality test method can avoid the risk of spurious causality to some extent by adopting an intercept and deterministic trend term in the testing regressions.     

Inferring Causal Interactions in Financial Markets Using Conditional Granger Causality Based on Quantile Regression

Computational Economics - Granger causality analysis emerges as a typical method for inferring causal interactions in economics variables. Yet the traditional pairwise approach to Granger causality...     

基于混合自回归潜周期模型的网络结构分析

格兰杰因果关系是推导网络结构最强有力的工具,特别是对于时间序列数据而言,它有非常精确的时间空间和频率空间的表示形式,所以它的应用越来越广泛。但是实际问题中的很多数据表现出明显的周期特点,且实际测量到的数据通常会受到历史记录的影响,对于这种类型的数据,可以用混合自回归潜周期模型来进行处理。将传统格兰杰因果关系模型应用到包含调和振子的混合自回归潜周期模型,对模型中的参数进行了估计,在此基础上,利用格兰杰因果关系的思想推导出网络的结构。     

A dynamic causal topic model for mining activities from complex videos

In this paper, a novel probabilistic topic model is proposed for mining activities from complex video surveillance scenes. In order to handle the temporal nature of the video data, we devise a dynamical causal topic model (DCTM) that can detect the latent topics and causal interactions between them. The model is based on the assumption that all temporal relationships between latent topics at neighboring time steps follow a noisy-OR distribution. And the parameter of the noisy-OR distribution is estimated by a data driven approach based on the idea of nonparametric Granger causality statistic. Furthermore, for convergence analysis during model learning process, the Kullback-Leibler between the prior and the posterior distributions is calculated. At last, using the causality matrix learned by DCTM, the total causal influence of each topic is measured. We evaluate the proposed model through experimentations on several challenging datasets and demonstrate that our model can identify the high influence activity in crowded scenes.     

融合先验约束的拓扑霍克斯过程格兰杰因果发现算法

离散时序数据的格兰杰因果关系发现算法具有重要应用价值。现有方法主要采用霍克斯过程建模,无法适用于非独立同分布数据和带有时间误差的数据。为此,提出了一种融合先验约束的拓扑霍克斯过程格兰杰因果关系发现算法（PTHP）。首先,使用基于约束的方法筛选出一批显著性水平较高的因果边,提升算法对故障发生时间误差的容忍性;随后,将上一步获取的边作为先验约束融合到拓扑霍克斯过程中,解决序列间的非独立同分布问题。模拟数据和真实数据的实验证明了该方法的有效性,并获得了PCIC 2021因果推理大赛第一名。     

Development of Box–Jenkins type time series models by combining conventional and orthonormal basis filter approaches

A unified scheme for developing Box–Jenkins (BJ) type models from input–output plant data by combining orthonormal basis filter (OBF) model and conventional time series models, and the procedure for the corresponding multi-step-ahead prediction are presented. The models have a deterministic part that has an OBF structure and an explicit stochastic part which has either an AR or an ARMA structure. The proposed models combine all the advantages of an OBF model over conventional linear models together with an explicit noise model. The parameters of the OBF–AR model are easily estimated by linear least square method. The OBF–ARMA model structure leads to a pseudo-linear regression where the parameters can be easily estimated using either a two-step linear least square method or an extended least square method. Models for MIMO systems are easily developed using multiple MISO models. The advantages of the proposed models over BJ models are: parameters can be easily and accurately determined without involving nonlinear optimization; a prior knowledge of time delays is not required; and the identification and prediction schemes can be easily extended to MIMO systems. The proposed methods are illustrated with two SISO simulation case studies and one MIMO, real plant pilot-scale distillation column.     

Root cause diagnosis of plant-wide oscillations using Granger causality

Oscillations are common in closed-loop controlled processes which, once generated, can propagate along process flows and feedback paths of the whole plant. It is important to detect and diagnose such oscillations to maintain high control performance. This paper presents a new data-driven time series method for diagnosing the sources and propagation paths of plant-wide oscillations. The proposed method first uses a latent variable method to select features which carry significant common oscillations, then applies both time-domain Granger causality and spectral Granger causality to provide reliable diagnosis of oscillation sources and propagations. Simulation tests and an industrial case study are shown to demonstrate the effectiveness of the proposed method.     

Diagnosis of poor control-loop performance using higher-order statistics

Higher-order statistical (HOS) techniques were first proposed over four decades ago. This paper is concerned with higher-order statistical analysis of closed-loop data for diagnosing the causes of poor control-loop performance. The main contributions of this work are to utilize HOS tools such as cumulants, bispectrum and bicoherence to develop two new indices: the non-Gaussianity index (NGI) and the nonlinearity index (NLI) for detecting and quantifying non-Gaussianity and nonlinearity that may be present in regulated systems, and to use routine operating data to diagnose the source of nonlinearity. The new indices together with some graphical plots have been found to be useful in diagnosing the causes of poor performance of control loops. Successful applications of the proposed method are demonstrated on simulated as well as industrial data. This study clearly shows that HOS-based methods are promising for closed-loop performance monitoring.     

Parameter estimation of excitation systems from sampled data

The parameter estimation of excitation systems using a proposed indirect stochastic method is presented. In this method, the discrete-time ARMA model corresponding to each block of the excitation system is first identified from sampled input/output data. Then, the proper reduced order of the continuous-time model is determined using the concept of dominant energy modes. Finally, the parameters of the continuous-time model are found by matching its frequency response to that of the identified ARMA model. The proposed method is used to estimate the parameters of an excitation system in a pumped storage power plant. The results show that the estimated continuous-time models are rather close to those supplied by the vender     

基于GMDH因果关系的软件缺陷预测模型

软件缺陷预测是软件可靠性研究的一个重要方向。基于自组织数据挖掘(GMDH)网络与因果关系检验理论提出了一种软件缺陷预测模型,借鉴Granger检验思想,利用GMDH网络选择与软件失效具有因果关系的度量指标,建立软件缺陷预测模型。该方法从复杂系统建模角度研究软件度量指标与软件缺陷之间的因果关系,可以检验多变量之间在非线性意义上的因果关系。最后基于两组真实软件失效数据集,将所提出的方法与基于Granger因果检验的软件缺陷预测模型进行比较分析。结果表明,基于GMDH因果关系的软件缺陷预测模型比Granger因果检验方法具有更为显著的预测效果。     

频域格兰杰因果关系及其在信号处理中的应用

自从格兰杰1969年提出因果关系的概念之后,格兰杰因果关系在信号处理、计算神经科学等许多领域的应用越来越广。人们可以利用格兰杰因果关系来分析多个变量之间的直接的相互作用,从而进一步研究各类变量之间的内在联系。以往都是在时域空间进行分析的,也就是说分析的对象都是时间序列数据,研究这些变量之间随着时间的变化是如何联系的。在时域空间的基础上,进一步从频域空间上对变量进行研究,分析在哪个频率段上变量之间存在相互作用,所得到的结论当然更具有意义。     

Linear identification of ARMA processes

A new method for estimating the parameters of an ARMA process is presented. The method consists of three linear least-squares estimations. In the first an autoregressive model is fitted to the observation sequence, yielding an estimate of the values of the driving white noise sequence. Linear least squares is then used to fit an ARMA model to the observation and estimated white noise sequences. This model is used to filter the observation and estimated white noise sequences. Finally an ARMA model is fitted to the filtered sequences. It is shown that the resultant estimator is ‘p-consistent’ (the asymptotic bias tends to zero as the degree p of the autoregressive model tends to infinity) and is ‘p-efficient’ (the asymptotic efficiency approaches the theoretical maximum as p tends to infinity).     

Hammerstein system identification by non-parametric instrumental variables

A mixed, parametric–non-parametric routine for Hammerstein system identification is presented. Parameters of a non-linear characteristic and of ARMA linear dynamical part of Hammerstein system are estimated by least squares and instrumental variables assuming poor a priori knowledge about the random input and random noise. Both subsystems are identified separately, thanks to the fact that the unmeasurable interaction inputs and suitable instrumental variables are estimated in a preliminary step by the use of a non-parametric regression function estimation method. A wide class of non-linear characteristics including functions which are not linear in the parameters is admitted. It is shown that the resulting estimates of system parameters are consistent for both white and coloured noise. The problem of generating optimal instruments is discussed and proper non-parametric method of computing the best instrumental variables is proposed. The analytical findings are validated using numerical simulation results.     

Estimation and inference in the yield curve model with an instantaneous error term

Many variations exist of yield curve modeling based on the exponential components framework, but most do not consider the generating process of the error term. In this paper, we propose a method of yield curve estimation using an instantaneous error term generated with a standard Brownian motion. First, we add an instantaneous error term to Nelson and Siegel’s instantaneous forward rate model [C.R. Nelson, A.F. Siegel, Parsimonious modeling of yield curves, Journal of Business 60 (1987) 473–489]. Second, after differencing multiperiod spot rate models transformed using Nelson and Siegel’s instantaneous forward rate model [C.R. Nelson, A.F. Siegel, Parsimonious modeling of yield curves, Journal of Business 60 (1987) 473–489], we obtain a model with serially uncorrelated error terms because of independent increment properties of Brownian motion. As the error term in this model is heteroskedastic and not serially correlated, we can apply weighted least squares estimation techniques. That is, this specification of the error term does not lead to incorrect estimation methods. In an empirical analysis, we compare the instantaneous forward rate curves estimated by the proposed method and an existing method. We find that the shape from the proposed estimation equation differ from the latter method when fluctuations in the interest rate data used for the estimation are volatile.     

面向故障间格兰杰因果发现的霍克斯过程研究

现有因果关系建模方法应用于故障事件序列时,难以有效引入因果先验,使得算法结果过于稠密,同时在稀疏、时间精度低的数据上因果关系可靠性较差。将不同故障类型事件的因果关系建模为基于霍克斯过程的格兰杰因果关系,提出一种面向故障序列的格兰杰因果发现的霍克斯过程模型。将霍克斯过程拓展到离散时间域,解决低时间精度数据的建模问题,并通过构造基于贝叶斯信息准则的目标函数,保证因果结构稀疏性,进而利用基于EM算法与爬山法的迭代优化算法引入因果先验,提高模型的可靠性。实验结果表明,该方法在由不同参数生成的模拟数据上均表现突出,且在两个通信网络的真实数据集中,F1评分相比ADM4、MLE-SGL、TSSO和PCMCI算法提升15.18%以上。而通过引入根因标注和因果依赖性先验,算法的F1评分进一步提升22.43%以上,验证了引入先验的有效性。     

State space modelling and spectral analysis of cointegrated vector processes (evidence from the U.S. and Scandinavian economies)

We provide new evidence on the impact of the U.S. economy on two Scandinavian economies (Finland and Sweden). Initially, we test for the presence of unit roots among the observed input-output processes. Next, Granger causality and cointegra-tion of the system is explicitly tested, to justify the estimated vector-valued state space model. The trend and cyclical components of the endogenous vector are extracted by three alternative decomposition methods. Finally, the content of the cyclical component is analysed by spectral analysis.