AUTOREGRESSIVE MOVING AVERAGE PROCESSES WITH NON-NORMAL RESIDUALS

Abstract. ARMA processes with non-normal residuals have applications in surface metrology and have recently been shown by Nelson and Granger (1979) to occur in modelling economic time series. In this paper we obtain the theoretical relationship between the skewness and kurtosis of an ARMA process and the corresponding parameters of its generating noise series and consider some of the implications of these results. Simulation methods for any ARMA process with given skewness and kurtosis, using Johnson transformations are briefly discussed.     

MAXIMUM LIKELIHOOD ESTIMATION FOR AUTOREGRESSIVE PROCESSES DISTURBED BY A MOVING AVERAGE

Abstract. Maximum likelihood estimation for stationary autoregressive processes when the signal is subject to a moving-average sampling error is discussed. A modified maximum likelihood estimator is proposed. An algorithm for computing derivatives of the modified likelihood is suggested. Maximum likelihood estimators of the parameter vector are shown to be strongly consistent and to have a multivariate normal limiting distribution. A Monte Carlo simulation shows that the modified maximum likelihood estimator performs better than other available estimators. US current labour force data are analysed as an example.     

THE ESTIMATION OF PARAMETERS FOR AUTOREGRESSIVE MOVING AVERAGE MODELS

Abstract. This paper provides some new and improved versions of an earlier procedure for the estimation of parameters for autoregressive moving average models suggested by the author (1979). Some numerical examples of the application of the procedure are also given.     

ON THE STRUCTURE OF THE LIKELIHOOD FUNCTION OF AUTOREGRESSIVE AND MOVING AVERAGE MODELS

Abstract. In finite order normal moving average models the maximum likelihood estimates always exist. For finite order normal autoregressive models sufficient conditions for the existence of maximum likelihood estimates is given. Some cases not satisfying the conditions are studied.     

ON THE PARTIAL SUMS OF RESIDUALS IN AUTOREGRESSIVE AND MOVING AVERAGE MODELS

Abstract. The limiting process of partial sums of residuals in stationary and invertible autoregressive moving-average models is studied. It is shown that the partial sums converge to a standard Brownian motion under the assumptions that estimators of unknown parameters are root- n consistent and that innovations are independent and identically distributed random variables with zero mean and finite variance or, more generally, are martingale differences with moment restrictions specified in Theorem 1. Applications for goodness-of-fit and change-point problems are considered. The use of residuals for constructing nonparametric density estimation is discussed.     

我国复合材料拉挤成型技术及应用发展情况分析

2013年,我国拉挤制品产量达28万吨,约占全球产量的50%。拉挤型材广泛用于电气/器、耐腐蚀解决方案、建筑、运输、军事及消费品领域。本文分析了我国拉挤成型技术及应用的发展历程、主要成就,指出行业发展存在的主要问题,并对今后发展提出建议。     

ESTIMATION OF THE ORDER OF A MOVING AVERAGE MODEL FROM AUTOREGRESSIVE AND WINDOW ESTIMATES OF THE INVERSE CORRELATION FUNCTION

Abstract. The autoregressive and window estimates of the inverse correlation function are used for estimating the order of a finite moving average process by using criteria similar to the FPEα criterion of Bhansali and Downham (1977). The asymptotic distribution of the estimates is derived. Their finite sample behaviour is examined by means of a simulation study.     

THE SIZE OF THE STATIONARITY AND INVERTIBILITY REGION OF AN AUTOREGRESSIVE-MOVING AVERAGE PROCESS

Abstract. The hypervolume of the stationarity and invertivility regions for the parameters of autoregressive-moving average processes is computed, and the severity of these constraints for higher order models is discussed.     

A NOTE ON SOME STATISTICS USEFUL IN IDENTIFYING THE ORDER OF AUTOREGRESSIVE MOVING AVERAGE MODEL

Abstract. Several recursive relations concerning some statistics useful in identifying the order of autoregressive moving average are derived and the asymptotic behaviour of these statistics are studied.     

RECURSIVE COMPUTATION OF THE PARAMETERS OF PERIODIC AUTOREGRESSIVE MOVING-AVERAGE PROCESSES

Abstract. An algorithm for recursive computation of the parameters of periodic autoregressive moving-average (ARMA) processes is given. It also provides recursions for stationary multivariate ARMA processes. A procedure for simultaneous estimation of the order and the parameters of a periodic ARMA process is outlined.     

ESTIMATION OF THE MULTIVARIATE AUTOREGRESSIVE MOVING AVERAGE HAVING PARAMETER RESTRICTIONS AND AN APPLICATION TO ROTATIONAL SAMPLING

Abstract. The vector autoregressive moving average model with nonlinear parametric restrictions is considered. A simple and easy-to-compute Newton-Raphson estimator is proposed that approximates the restricted maximum likelihood estimator which takes full advantage of the information contained in the restrictions. In the case when there are no parametric restrictions, our Newton-Raphson estimator is equivalent to the estimator proposed by Reinsel et al. (Maximum likelihood estimators in the multivariate autoregressive moving-average model from a generalized least squares view point. J. Time Ser. Anal. 13 (1992), 133–45). The Newton-Raphson estimation procedure also extends to the vector ARMAX model. Application of our Newton-Raphson estimation method in rotational sampling problems is discussed. Simulation results are presented for two different restricted models to illustrate the estimation procedure and compare its performance with that of two alternative procedures that ignore the parametric restrictions.     

丁二烯法制己二酸

详细介绍了丁二烯羰烷氧基化、氢氰化、氢羧基化法合成己二酸的３种工艺,并对丁二烯法、环己烷法和环己烯法生产己二酸的生产成本进行了比较,得出丁二烯法生产己二酸成本最低,并已引起人们的关注。     

ON THE INVERTIBILITY OF MULTIVARIATE LINEAR PROCESSES

Abstract. It is shown that a multivariate linear stationary process whose coefficients are absolutely summable is invertible if and only if its spectral density is regular everywhere. This general characterization of invertibility is applied later to the case of a linear process having an autoregressive moving-average (ARMA) representation. Under the usual assumptions, it is deduced that a process Y described by an ARMA(φ, TH) model is invertible if and only if the polynomial detTH( z ) has no roots on the unit circle. Given an invertible process Y which has an ARMA representation, it is finally shown that the process YT , where YT , =ε _i =0^l S _i Y _t-i , is invertible if and only if the matrix S ( z ) =ε _{i =0}^l S _i z ⁱ is of full rank for all z of modulus 1. It follows, in particular, that any subprocess of an invertible ARMA process is also invertible.     

A NOTE ON THE EMBEDDING OF DISCRETE-TIME ARMA PROCESSES

Abstract. Let {X_n, n= 0, 1, 2,…} be a discrete-time ARMA(p, q) process with q < p whose autoregressive polynomial has r (not necessarily distinct) negative real roots. According to a recent result of He and Wang (On embedding a discrete-parameter ARMA model in a continuous-parameter ARMA model. J. Time Ser. Anal. 10 (1989), 315–23) there exists a continuous-time ARMA (p', q') process {Y(t), t≥0} with q' < p'=p+r such that {Y(n), n= 0, 1, 2,…} has the same autocorrelation function as {X_n}. In this paper we show that this result is false by considering the case when {X_n} is a discrete-time AR(2) process whose autoregressive polynomial has distinct complex conjugate roots. We identify the proper subset of such processes which are embeddable in a continuous-time ARMA(2, 1) process. We show that every discrete-time AR(2) process with distinct complex conjugate roots can be embedded in either a continuous-tie ARMA(2, 1) process or a continuous-time ARMA(4, 2) process, or in some cases both. We derive an expression for the spectral density of the process obtained by sampling a general continuous-time ARMA(p, q) process (with distinct autoregressive roots) at arbitrary equally spaced time points. The expression clearly shows that the sampled process is a discrete-time ARMA (p', q') process with q' < p.     

MODELLING FOR THE WAVELET COEFFICIENTS OF ARFIMA PROCESSES

We consider a model for the discrete nonboundary wavelet coefficients of autoregressive fractionally integrated moving average (ARFIMA) processes in each scale. Because the utility of the wavelet transform for the long‐range dependent processes, which many authors have explained in semi‐parametrical literature, is approximating the transformed processes to white noise processes in each scale, there have been few studies in a parametric setting. In this article, we propose the model from the forms of the (generalized) spectral density functions (SDFs) of these coefficients. Since the discrete wavelet transform has the property of downsampling, we cannot directly represent these (generalized) SDFs. To overcome this problem, we define the discrete non‐decimated nonboundary wavelet coefficients and compute their (generalized) SDFs. Using these functions and restricting the wavelet filters to the Daubechies wavelets and least asymmetric filters, we make the (generalized) SDFs of the discrete nonboundary wavelet coefficients of ARFIMA processes in each scale clear. Additionally, we propose a model for the discrete nonboundary scaling coefficients in each scale.     

ASYMPTOTIC PROPERTIES OF SOME PRELIMINARY ESTIMATORS FOR AUTOREGRESSIVE MOVING AVERAGE TIME SERIES MODELS

Abstract. Some simple preliminary estimators for the coefficients of mixed autoregressive moving average time series models are considered. As the first step the estimators require the fitting of a long autoregression to the data. The first two methods of the paper are non-iterative and generally inefficient. The estimators are Yule-Walker type modifications of the least squares estimators of the coefficients in auxiliary linear regression models derived, respectively, for the coefficients of the long autoregression and for the coefficients of the corresponding long moving average approximation of the model. Both of these estimators are shown to be strongly consistent and their asymptotic distributions are derived. The asymptotic distributions are used in studying the loss in efficiency and in constructing the third estimator of the paper which is an asymptotically efficient two-step estimator. A numerical illustration of the third estimator with real data is given.     

ON THE EXISTENCE OF STATIONARY THRESHOLD AUTOREGRESSIVE MOVING-AVERAGE PROCESSES

Abstract. Conditions for the existence of causal and strictly stationary solutions of the equations defining a self-exciting threshold autoregressive moving-average (SETARMA) model are derived. For threshold autoregressive models we allow the autoregressive coefficients to be random and derive sufficient conditions for geometric ergodicity and the existence of strictly and weakly stationary solutions of the defining equations.     

世界主要聚乙烯生产工艺简介

发展低能耗、产品多样化、无污染的聚乙烯生产工艺是当今世界的主流。本文介绍了有代表性的几种聚乙烯生产工艺,并对其进行了简单评述。     

SUBORDINATION OF STATIONARY PROCESSES

Abstract. Let X ={ X ( t ), t ε T ∁ R} be a ( L ₂ -) stationary process and suppose that N ={ N ( t ), t ≥ 0} is an infinitely divisible process, independent of X. Then ={ ( t ) = X ( N ( t )), t ≥ 0} is again a stationary process. In this paper, we relate the spectral properties of the original process X and the derived or subordinated process .