GEOMETRIC ERGODICITY OF A DOUBLY STOCHASTIC TIME SERIES MODEL

Abstract. We demonstrate that a large class of doubly stochastic time series models are geometrically ergodic, and hence admit second-order stationary solutions.
We also establish a version of the strong law of large numbers, the law of the interated logorithm and the central limit theorem for the stochastic processes under consideration.     

SOME DOUBLY STOCHASTIC TIME SERIES MODELS

Abstract. We consider time series models obtained by replacing the parameters of autoregressive models by stochastic processes. Special attention is given to the problem of finding conditions for stationarity and to the problem of forecasting. For the first problem we are only able to obtain solutions in special cases, and the emphasis is on techniques rather than obtaining the most general results in each case. For the second problem more complete results are obtained by exploiting similarities with discrete time (nonlinear) filtering theory. The methods introduced are illustrated on two standard examples, one of state space type and one where the parameter process is a Markov chain.     

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.     

NON‐STATIONARITY AND QUASI‐MAXIMUM LIKELIHOOD ESTIMATION ON A DOUBLE AUTOREGRESSIVE MODEL

This article first studies the non‐stationarity of the first‐order double AR model, which is defined by the random recurrence equation , where γ₀ > 0, α₀ ≥ 0, and {η_t}is a sequence of i.i.d. symmetric random variables. It is shown that the double AR(1) model is explosive under the condition . Based on this, it is shown that the quasi‐maximum likelihood estimator of (φ₀,α₀) is consistent and asymptotically normal so that the unit root problem does not exist in the double AR(1) model. Simulation studies are carried out to assess the performance of the quasi‐maximum likelihood estimator in finite samples.     

炉管蠕变损伤的随机计算模型

炉管服役寿命的预测问题一直受到人们关注。由于蠕变问题的随机性研究较困难,过去的研究主要集中在确定性蠕变损伤问题上。本文提出了新的蠕变损伤随机计算模型。通过 Ｍｏｎｔｅ Ｃａｒｌｏ 方法与蠕变损伤随机计算模型结果的比较,验证了蠕变损伤随机计算模型的正确。蠕变损伤随机性的描述为今后炉管蠕变损伤可靠性的评估奠定了基础。     

A GOODNESS-OF-FIT TEST FOR AUTOREGRESSIVE MOVING-AVERAGE MODELS BASED ON THE STANDARDIZED SAMPLE SPECTRAL DISTRIBUTION OF THE RESIDUALS

Abstract. A stochastic process derived from the standardized sample spectral density of the residuals of a causal and invertible ARMA( p, q ) model is introduced to construct a goodness-of-fit procedure. The test statistics considered have a proper limiting distribution which is free of unknown parameters and which, unlike some well-known goodness-of-fit statistics based on the residuals, does not depend on the sample size.     

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.     

副产物含量对栲胶脱硫液性质的影响

在栲胶脱硫生产过程中除了主反应外,同时还伴随Na2S2O3,Na2SO4,NaSCN及NaHCO3等盐类生成的副反应.这些副产物的生成会影响栲胶脱硫液的性质,并最终影响整个脱硫循环工艺的稳定.为了避免这些影响,从表面张力、黏度和密度三个方面分析了Na2S2O3,Na2SO4,NaSCN和NaHCO3四种栲胶脱硫工艺的副产物对栲胶脱硫溶液的影响.结果表明,副产物的积累可以引起脱硫溶液表面张力的下降以及溶液黏度和密度的增加,从而引起脱硫工艺中操作条件的改变,最终影响整个系统的脱硫效率.     

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.     

ON THE EXISTENCE OF A GENERAL MULTIPLE BILINEAR TIME SERIES

Abstract. A sufficient condition is derived for the existence of a strictly stationary solution of the general multiple bilinear time series equations (without assuming subdiagonality). The condition is shown to reduce to the condition of Stensholt and Tjostheim in the special case which they consider. Under this condition a solution is constructed which is shown to be casual in the sense we define, strictly stationary and ergodic. It is moreover the unique causal solution and the unique stationary solution of the defining equations. In the special case when the defining equations contain no non-linear terms, i.e. the multiple autoregressive moving-average (ARMA) model. the condition given here reduces to the well-known sufficient condition for the existence of a casual stationary solution.     

ON THE SPECTRAL DENSITY MATRIX OF A PERIODIC ARMA PROCESS

Abstract. After reviewing the spectral representation theorems for periodic stationary process, we derive a parametric formula for the spectral density of a periodic ARMA process via a new approach. The equivalence with the existing approach is shown.     

ON THE EXISTENCE OF THE STATIONARY AND ERGODIC NEAR(p) MODEL

Abstract. The NEAR(2) model proposed by Lawrance and Lewis in 1985 is generalized to the NEAR( p ) model. A necessary and sufficient condition for the existence of an 'innovation' sequence and a stationary ergodic process satisfying the NEAR( p ) model is derived. It is shown that the 'innovation' sequence is distributed as a mixture of exponentials.     

STOCHASTIC NUMERICAL MODEL FOR RADIO FREQUENCY VACUUM DRYING OF TIMBERS

A new numeric method to simulate stochastic dispersion (a natural phenomenon that occurs when a magnitude cannot be associated to a specific value, but to the probability of being within a range of values) is proposed and applied to predict Radio Frequency Vacuum (RFV) drying of timber. A theoretical formulation of the method is described and complemented to take into account the frequency distribution of the timber initial moisture content, so that it can be applied to industrial runs. Experimental data obtained from mixed western hemlock and amabilis fir dried in a commercial RFV kiln are used to validate the stochastic model, and the results are compared through moisture content histograms and probability charts. A numerical example is shown in order to provide an idea of the movement of the moisture profiles during RFV drying.     

ON THE PROBABILITY OF ESTIMATING A DETERMINISTIC COMPONENT IN THE LOCAL LEVEL MODEL

Abstract. A local level model has a deterministic level when the signal-to-noise ratio q is zero. In this paper we investigate the properties of the maximum likelihood estimator of q , paying particular attention to the case where its true value is zero. These properties are shown to be crucially dependent on the initial conditions employed.     

ON THE DISTRIBUTION OF A SIMPLE STATIONARY BILINEAR PROCESS

Abstract. We show that, under the Gaussian assumption of the white noise, the probability density function of a simple stationary first order bilinear process with 'heterogeneous' errors may be unbounded, whilst that with 'homogeneous' errors is always bounded. Simulation aspects of the distribution are also included.     

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.     

ON THE SOLUTION OF A MODEL CASE F DEACTIVATION BY SITE POISONING ND PORE BLOCKAGE

The problem of deactivation by active site poisoning and pore blockage is analyzed. A solution technique is presented which considerably simplifies the numerical effort involved in the analysis of the problem. For problems with slab geometry, in particular, closed form solutions are developed which can be conveniently utilized in reactor design problems.

Numerical examples are presented which show that the effect of pore blockage can be quite detrimental to the life of the catalyst, sometimes even more so than the effect of site coverage by a poison.     

ON THE ERGODICITY OF BILINEAR TIME SERIES MODELS

Abstract. Existence, strict stationarity and ergodicity of Bilinear Time Series Models for a given input White Noise and parameter values are studied in detail in this paper. The use of ergodicity in the estimation of parameters is also hinted at in this article.     

STATIONARITY OF THE SOLUTION OF Xt= AtXt-1+εt AND ANALYSIS OF NON-GAUSSIAN DEPENDENT RANDOM VARIABLES

Abstract. We give general and concrete conditions in terms of the coefficient (stochastic) process {A_t} so that the (doubly) stochastic difference equation X_t= A_tX_t-1+ε_t has a second-order strictly stationary solution. It turns out that by choosing {A_t} and the "innovation" process {ε_t} properly, a host of stationary processes with non-Gaussian marginals and long-range dependence can be generated using this difference equation. Examples of such nowGaussian marginals include exponential, mixed exponential, gamma, geometric, etc. When {A_t} is a binary time series, the conditional least-squares estimator of the parameters of this model is the same as those of the parameters of a Galton-Watson branching process with immigration.     

ON THE THIRD-ORDER MOMENT STRUCTURE AND BISPECTRAL ANALYSIS OF SOME BILINEAR TIME SERIES

For the bilinear time series model X_t=βX_t-k^e_t-t+^e_t, k > l, k = l and k < l formulae for the third-order theoretical moments and an expression for the bispectral density function are obtained. These results can be used to distinguish between bilinear models and white noise and, in general, linear models. Furthermore, they give an indication of the type combination (k, l) in the above model. The modulus of the bispectral density function of the above bilinear time series model for different combinations of (k, l) and values of β are computed and the properties are studied.