THE ASYMPTOTIC PROPERTIES OF THE SAMPLE AUTOCORRELATIONS FOR A MULTIPLE AUTOREGRESSIVE PROCESS WITH ONE UNIT ROOT

Abstract. In this paper the large sample behaviour of the sample autocorrelation matrix R _n( h ), ( h being the lag, n the sample size), of a multivariate autoregressive time series with one of its characteristic roots equal to unity and the rest of the roots lying inside the unit circle is studied. It is shown that R _n( h ) converges almost surely to a constant matrix. Further, the asymptotic distribution of R _n( h ) is characterized as that of a random matrix which is a function of jointly normal random variables.     

ON THE ASYMPTOTIC DISTRIBUTION OF THE GENERALIZED PARTIAL AUTOCORRELATION FUNCTION IN AUTOREGRESSIVE MOVING-AVERAGE PROCESSES

Abstract. It has been conjectured and illustrated that the estimate of the generalized partial autocorrelation function (GPAC), which has been used for the identification of autoregressive moving-average (ARMA) models, has a thick-tailed asymptotic distribution. The purpose of this paper is to investigate the asymptotic behaviour of the GPAC in detail. It will be shown that the GPAC can be represented as a ratio of two functions, known as the θ function and the Λ function, each of which itself has a useful pattern for ARMA model identification. We shall show the consistencies of the extended Yule-Walker estimates of the three functions and present their asymptotic distributions.     

SOME ASYMPTOTIC PROPERTIES OF THE SAMPLE COVARIANCES OF GAUSSIAN AUTOREGRESSIVE MOVING-AVERAGE PROCESSES

Abstract. The paper deals with the asymptotic variances of the sample covariances of autoregressive moving average processes. Using state-space representations and some matrix Lyapunov equation theory, closed-form expressions are derived for the asymptotic variances of the sample covariances and for the Cramer-Rao bounds on the process covariances. The main results obtained from these expressions are as follows: For ARMA ( p, q ) processes with p ≥ q , the sample covariance of order n is asymptotically efficient if and only if 0 ≤ n ≤ p – q .
For ARMA ( p, q ) processes with p < q , none of the sample covariances is asymptotically efficient.     

ASYMPTOTIC EFFICIENCY OF THE SAMPLE COVARIANCES IN A GAUSSIAN STATIONARY PROCESS

Abstract. This paper deals with the asymptotic efficiency of the sample autocovariances of a Gaussian stationary process. The asymptotic variance of the sample autocovariances and the Cramer–Rao bound are expressed as the integrals of the spectral density and its derivative. We say that the sample autocovariances are asymptotically efficient if the asymptotic variance and the Cramer–Rao bound are identical. In terms of the spectral density we give a necessary and sufficient condition that they are asymptotically efficient. This condition is easy to check for various spectra.     

On processes with hyperbolically decaying autocorrelations

We discuss some relations between autocorrelations (ACFs) and partial autocorrelations (PACFs) of weakly stationary processes. First, we construct an extension of a process ARIMA(0,d,0) for d ∈ (?∞, 0), which enjoys non‐summable partial autocorrelations and autocorrelations decaying as rapidly as ρ_n ? n^?1+2d. Such a situation is impossible if the absolute sum of autocorrelations is sufficiently small. We show that then the PACF is less than the ACF up to a multiplicative constant. Our second result complements a similar result of Baxter (1962).     

TEMPORAL AGGREGATION IN THE ARIMA PROCESS

Abstract. The effect of temporal aggregation on ARIMA models is investigated. The paper discusses the change of model form resulting from aggregation. For the IMA model it is noted that reduction of model order may occur, due to aggregation, which takes an arbitrarily high order IMA ( d , q) process to an IMA ( d , 0) process for the aggregates. For the AR process, we derive the exact order for the aggregate model and show that aggregation of an AR (p) series does not necessarily produce an ARMA (p, q) aggregate series as has been suggested in the literature. In particular, the AR order of AR (p) and ARIMA (p, d, q) can be reduced upon aggregation. The paper gives the general conditions under which this reduction of order may occur.     

HIGHER ORDER MOMENTS OF SAMPLE AUTOCOVARIANCES AND SAMPLE AUTOCORRELATIONS FROM AN INDEPENDENT TIME SERIES

Abstract. Given length- n sampled time series, generated by an independent distributed process, in this paper we treat the problem of determining the greatest order, in n , that moments of the sample autocovariances and sample autocorrelations can attain. For the sample autocovariance moments, we achieve quite general results; but, for the autocorrelation moments, we restrict study to Gaussian white noise (normal, independent and identically distributed). Our main theorem relates to the cross-moments of the non-centred sample autocovariances, but we also establish a relation between these and the corresponding moments for the centred sample autocovariances.     

STOCHASTIC ORDERS OF MAGNITUDE ASSOCIATED WITH TWO-STAGE ESTIMATORS OF FRACTIONAL ARIMA SYSTEMS

Abstract. Two-stage estimators have been proposed in fractional autoregressive integrated moving-average (ARIMA) systems which first estimate the long-run features of the system semi-parametrically and then estimate the short-run features by usual methods in a second stage. Although asymptotic theory is available for the estimates in the first stage of such a procedure, we are aware of no results concerning the estimates in the second stage. In this paper we provide a stochastic order of magnitude associated with an estimator in this class and discuss this result.     

莫来石纤维多孔陶瓷的制备与性能

对纤维多孔陶瓷的制备及性能进行了研究。在制备纤维多孔陶瓷时,采用酸性磷酸铝A23(P/Al原子比为2 3)作粘结剂,所制备的多孔陶瓷在各方面都具有优良的性能。如导热系数λ(22℃)为0.0529W/m.℃、热膨胀系数α为4.75×10-6/℃、孔隙率为96.22%、容重为0.1142 g/cm3等。在环保、节能领域具有广泛的应用前景和重要的社会及经济意义。     

HIGHER-ORDER ASYMPTOTIC PROPERTIES OF A WEIGHTED ESTIMATOR FOR GAUSSIAN ARMA PROCESSES

Abstract. Let { X _t } be a Gaussian ARMA process with spectral density f _θ(Λ), where θ is an unknown parameter. To estimate θ, we propose an estimator θC_w of the Bayes type. Since our standpoint in this paper is different from Bayes's original approach, we call it a weighted estimator. We then investigate various higher-order asymptotic properties of θC_w. It is shown that θC_w is second-order asymptotically efficient in the class of second-order median unbiased estimators. Furthermore, if we confine our discussions to an appropriate class D of estimators, we can show that θC_w is third-order asymptotically efficient in D . We also investigate the Edgeworth expansion of a transformation of θC_w. We can then give the transformation of θC_w which makes the second-order part of the Edgeworth expansion vanish. Finally we consider the problem of testing a simple hypothesis H:θ=θ_o against the alternative A:θ#θ_o. For this problem we propose a class of tests δ_A which are based on the weighted estimator. We derive the X ² type asymptotic expansion of the distribution of S (ζδ_A) under the sequence of alternatives A n :θ=θ_o+ε n ^1/2, ε > 0. We can then compare the local powers of various tests on the basis of their asymptotic expansions.     

GENERAL LINEAR PROCESSES:A PROPERTY OF THE EMPIRICAL PROCESS APPLIED TO DENSITY AND MODE ESTIMATION

Abstract. General linear processes do not usually satisfy strong mixing conditions. Therefore, we investigate the empirical process based on samples from such a general linear process by using a truncation argument and derive a local fluctuation inequality. It is well known that such a fluctuation inequality is of basic importance in the study of the empirical process. Here it is applied to obtain a rate of almost sure (a.s.) convergence for certain density estimators in the supremum norm. This extends a local result obtained by Chanda. As a direct corollary a rate of a.s. convergence for a mode estimator is obtained.     

一段蒸发加热器局部过热原因分析及对策

中石油宁夏石化公司一化肥二氧化碳汽提法尿素装置蒸发系统,采用升膜式一段蒸发加热器对尿液进行加热蒸发、浓缩提纯.本文通过对影响一段蒸发加热器正常运行的局部过热问题,从原因、危害两方面进行分析讨论,提出了相应的处理措施.     

高聚合度聚氯乙烯的性能及影响因素

以高聚合度聚氨乙烯（ＨＰ－４０００）对研究对象,探讨了不同聚合度,增塑剂,填料,改性剂及加工温度对体系力学性能的影响,并介绍了加工性能改良剂ＫＡＮＥ ＡＣＥ ＰＡ－２０的应用效果。     

A METHODOLOGICAL NOTE ON THE DISAGGREGATION OF TIME SERIES TOTALS

Abstract. This paper sheds new light on a generalized least squares approach for disaggregating a series of time series totals to estimate an underlying unaggregated series. By reinterpreting the generalized least squares problem as a time series prediction problem we can produce considerable computational savings relative to standard least squares approaches. Our reinterpretation gives us insight into the nature of the matrices which need to be inverted to compute the disaggregates.     

尿素合成塔的腐蚀及局部修理

针对尿素合成塔衬里腐蚀和泄漏的现象,分析衬里焊缝腐蚀的原因,提出装置定期检修或合成塔发生泄漏时应进行全面腐蚀检查,介绍合成塔衬里及碳钢壳体腐蚀的局部修理方法及保证尿素合成塔正常运行的安全措施.     

矿用抽出式局部通风机尼龙叶片的开发与应用

采用多层功能材料复合增强方法制备了阻燃，抗静电，高强度尼龙叶片，其内芯材料具有阻燃，增强的功能，外层材料具有阻燃，抗静电及耐磨性。将外层材料配制成溶胶涂履于内芯上制作的尼龙叶片，完全能满足大风量，高风压抽出式局部通风机的需要。     

ON THE ASYMPTOTIC EFFICIENCY OF ESTIMATORS OF THE PARAMETERS OF AN ARMA PROCESS

Abstract. In this paper we derive a lower bound on the asymptotic covariance matrix of an estimator of the parameters of an autoregressive moving average (ARMA) process when the innovations are not necessarily Gaussian.     

工艺对玻璃/钙长石材料性能的影响

设计CaO-Li2O-B2O3-SiO2-Al2O3玻璃/钙长石与堇青石、熔融石英、莫来石的复合,研究了它们对材料性能的影响,并探讨了工艺条件对玻璃/陶瓷复合材料性能的影响,制备了具有低温、低介与硅相匹配的低热膨胀系数的新型的复合材料。     

FINITE SAMPLE PREDICTION AND OVERDIFFERENCING

Abstract. If the process generating a time series contains a deterministic component the differencing operations carried out to achieve stationarity may lead to an ARMA model which is strictly noninvertible. This is known as overdifferencing but it is shown here that overdifferencing need not have serious implications for prediction provided that a finite sample prediction procedure is used. The proposed method is based on the Kalman filter and it allows both the optimal predictors and their mean square errors to be computed.     

ASYMPTOTIC EXPANSIONS FOR THE DISTRIBUTIONS OF SERIAL CORRELATIONS

Abstract. Let X ₁, …, X _n be a random sample from a population with a distribution function F and let E ( X ₁) = 0, E ( X ₁²) < ∞. Let r ₁=Σ _{t =1} ^{n -1} X _t X _{t +1}/Σ _{t =1} ^{n -1}( X _t ²+ X _{t +1}²). We derive a proper Edgeworth type expansion for the sampling distribution of r ₁ under the assumption that F is a mixture of Gaussian distributions of one of two given types. The result can easily be extended to the sampling distributions of serial correlations of arbitrary lag s .