高阶统计量地震子波估计建模

本文在反射系数序列为非高斯、平稳和统计独立的随机过程,地震子波为非因果、混合相位的假设条件下,分别应用滑动平均(MA)和自回归滑动平均(ARMA)模型对地震记录进行建模,并采用运算代价较小的基于高阶累积量的线性化求解方法——累积量矩阵方程法进行了子波提取和模型适应性的研究。数值模拟结果和实际地震数据处理结果表明:自回归滑动平均(ARMA)模型比滑动平均(MA)模型具有参数节省、模型更为高效的特点;累积量矩阵方程法可以有效地压制加性高斯噪声,但对累积量样本估计的准确性要求较高;如果累积量样本估计的误差和方差适度,结合自回归滑动平均(ARMA)模型描述的累积量矩阵方程法可以高效、准确地估计出地震子波。     

'PURIFYING' NOISY SIGNALS

Abstract. A method is presented for obtaining the set of all possible pure origins of a given noisy ARMA(2,2) signal. By a transformation to a new set of variables the locus of this set becomes a straight line.     

ARMA噪声中的正弦波检测

本文提出一种ＡＲＭＡ噪声中正弦波检测的方法，本方法先用改进的Ｐｒｏｎｙ法估计可能存在的正弦波，然后利用一种综合考虑衰减因子以及ＭＵＳＩＣ值的准则从估计结果中区分正统率波的真伪。数值例子表明，本文方法比Ｐｒｏｎｇ方法及ＭＵＳＩＣ方法具有更高的分辨力。     

一种有效的振动信号分离算法

振动信号包含随机成分与周期成分 ,其中的随机成分占据了很宽的频域 ,其能量极易引起其它设备特别是电子设备的共振 ,从而导致设备失效。为评估随机成分对设备的影响 ,需要将周期成分从振动信号中去除。为此 ,首先使用ARMA建模法对振动信号中周期成分出现的频率位置进行估计 ,然后设计阻带带宽极窄 (小于 0 .5Hz)的V型滤波器来完成相应的滤波。实验表明本文中的方法能有效地去除振动信号中的周期成分 ,而完整地保留随机成分     

非平稳ARMA信号自校正滤波器及其应用

本文处理带白色观测噪声的非平稳ARMA信号估计问题.应用状态空间方法和现代时 间序列分析方法[1],基于ARMA新息模型,提出了非平稳ARMA信号自校正滤波器,推广了 Hagander和Wittenmafk的结果[2],并给出了在雷达跟踪系统和检测数据数字滤波方面的应 用.仿真结果说明了本文结果的实用性和有效性.     

Bullwhip reduction for ARMA demand: The proportional order-up-to policy versus the full-state-feedback policy

A ‘proportional’ order-up-to policy reacting to ARMA demand is analyzed using stochastic optimal control theory. This policy is compared with a full-state-feedback order-up-to policy. Necessary conditions for an optimum of a weighted sum of the inventory and the ordering variances for both policies are formulated. Based on this a relatively simple expression for the ‘full-state’ policy is derived. The comparison between the two policies demonstrates that the ‘intuitively’ designed proportional policy does not fulfill the objective of controlling both the inventory and ordering variance for all parameter values of the demand model as well as the full-state-feedback policy. The full-state-feedback policy outperforms the proportional policy in several aspects.     

SPECTRAL RADIUS,KRONECKER PRODUCTS AND STATIONARITY

Abstract. We provide a stochastic proof of the inequality ρ(A?A+B?B) ≥ρ(A?A), where ρ(M) denotes the spectral radius of any square matrix M, i.e. max{|eigenvalues| of M}, and M?N denotes the Kronecker product of any two matrices M and N. The inequality is then used to show that stationarity of the bilinear model will imply stationarity of the linear part, i.e. the linear ARMA model for r= 1 and q= 1. Furthermore, it is shown that stationarity of the subdiagonal model, i.e. the bilinear model with b_ij=0 for i< j, again implies stationarity of its linear part, provided that the stationarity condition given by Bhaskara Rao and his colleagues is met. Interestingly, the conclusion that stationarity of the subdiagonal models, implies that the linear component models cannot be extended to the general non-subdiagonal bilinear models. The last observation is demonstrated via a simple example with p=m= 1, r= 0 and q= 2.     

PERIODIC CORRELATION IN STRATOSPHERIC OZONE DATA

Abstract. A 50-year time series of monthly stratospheric ozone readings from Arosa, Switzerland, is analyzed. The time series exhibits the properties of a periodically correlated (PC) random sequence with annual periodicities. Spectral properties of PC random sequences are reviewed and a test to detect periodic correlation is presented. An autoregressive moving-average (ARMA) model with periodically varying coefficients (PARMA) is fitted to the data in two stages. First, a periodic autoregressive model is fitted to the data. This fit yields residuals that are stationary but non-white. Next, a stationary ARMA model is fitted to the residuals and the two models are combined to produce a larger model for the data. The combined model is shown to be a PARMA model and yields residuals that have the correlation properties of white noise.     

THIRD-ORDER ASYMPTOTIC PROPERTIES OF ESTIMATORS IN GAUSSIAN ARMA PROCESSES WITH UNKNOWN MEAN

Abstract. This paper deals with the third-order asymptotic theory for Gaussian autoregressive moving-average (ARMA) processes with unknown mean μ. We are interested in the estimation of ρ = ( α₁…, α_p, β₁…, β_q ), where α ₁…, α_ρ and β ₁…, β_q are the coefficients of the autoregressive part and the moving-average part, respectively. First, we investigate the third-order asymptotic optimality of the bias adjusted maximum likelihood estimator (MLE) of ρ in the presence of the nuisance parameters μ and ² (innovation variance). Next, for a Gaussian AR(1μ μ, ²), we propose a mean corrected estimator α_c1c2 of the autoregressive coefficient. We make a comparison between the bias adjusted estimator α_c1c2* and the bias adjusted MLE, in terms of their probabilities of concentration around the true value, or equivalently, in terms of their mean squared errors. Finally some numerical studies are provided in order to verify the third-order asymptotic theory.     

A METHOD FOR GENERATING INDEPENDENT REALIZATIONS OF A MULTIVARIATE NORMAL STATIONARY AND INVERTIBLE ARMA(p, q) PROCESS

Abstract. A method for generating finite independent realizations of a normal multivariate stationary ARMA( p, q ) process is proposed. It is based on an AR (1) representation of an ARMA( p, q ) process allowing for an exact generation of the initial values of the simulation algorithm. Input facilities are supplied in order to assure stationarity and invertibility of the considered process.