Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence

Abstract. We consider semiparametric estimation in time‐series regression in the presence of long‐range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain‐weighted least squares estimates, which includes both narrow‐band ordinary least squares and narrow‐band generalized least squares as special cases. The estimates are semiparametric in the sense that focus is on the neighbourhood of the origin, and only periodogram ordinates in a degenerating band around the origin are used. This setting differs from earlier studies on time‐series regression with long‐range dependence, where a fully parametric approach has been employed. The generalized least squares estimate is infeasible when the degree of long‐range dependence is unknown and must be estimated in an initial step. In that case, we show that a feasible estimate which has the same asymptotic properties as the infeasible estimate, exists. By Monte Carlo simulation, we evaluate the finite‐sample performance of the generalized least squares estimate and the feasible estimate.     

Influence of Missing Values on the Prediction of a Stationary Time Series

Abstract. The influence of missing observations on the linear prediction of a stationary time series is investigated. Simple bounds for the prediction error variance and asymptotic behaviours for short and long‐memory processes respectively are presented.     

Effect of heating-rate on failure temperature of pre-loaded brass H62

The response and failure of brass H62 specimens subjected to different levels of pre-loaded stresses and heating rates were investigated using a Gleeble-1500 thermal-mechanical material testing system. The metallographs of the tested material were also observed and analyzed. It is found that the increase of either pre-loaded stress or heating-rate decreases the failure temperature. Metallographic analysis shows that high heating-rate may cause stronger local thermal inconsistency （LTI） and remarkably increase the microdefects in the material, which may markedly degrade the macroscopic mechanical properties of the material.     

Estimation in Random Coefficient Autoregressive Models

Abstract. We propose the quasi‐maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions.     

Consistent estimation of the memory parameter for nonlinear time series

Abstract. For linear processes, semiparametric estimation of the memory parameter, based on the log‐periodogram and local Whittle estimators, has been exhaustively examined and their properties well established. However, except for some specific cases, little is known about the estimation of the memory parameter for nonlinear processes. The purpose of this paper is to provide the general conditions under which the local Whittle estimator of the memory parameter of a stationary process is consistent and to examine its rate of convergence. We show that these conditions are satisfied for linear processes and a wide class of nonlinear models, among others, signal plus noise processes, nonlinear transforms of a Gaussian process ξ_t and exponential generalized autoregressive, conditionally heteroscedastic (EGARCH) models. Special cases where the estimator satisfies the central limit theorem are discussed. The finite‐sample performance of the estimator is investigated in a small Monte Carlo study.     

Parameter Estimation for Periodically Stationary Time Series

Abstract. The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper, we compute the asymptotic distribution for these estimates in the case, where the innovations have a finite fourth moment. These asymptotic results are useful to determine which model parameters are significant. In the process, we also develop asymptotics for the Yule–Walker estimates.     

On a Mixture GARCH Time‐Series Model

Abstract. Recently, there has been a lot of interest in modelling real data with a heavy‐tailed distribution. A popular candidate is the so‐called generalized autoregressive conditional heteroscedastic (GARCH) model. Unfortunately, the tails of GARCH models are not thick enough in some applications. In this paper, we propose a mixture generalized autoregressive conditional heteroscedastic (MGARCH) model. The stationarity conditions and the tail behaviour of the MGARCH model are studied. It is shown that MGARCH models have tails thicker than those of the associated GARCH models. Therefore, the MGARCH models are more capable of capturing the heavy‐tailed features in real data. Some real examples illustrate the results.     

DaWson型磷钨钒杂多酸催化合成苹果酯的研究

制备了Dawson型磷钨钒杂多酸催化剂，用Fr—IR分析方法对催化剂进行了结构表征，并以乙酰乙酸乙酯与乙二醇为原料催化合成了苹果酯。实验结果表明，磷钨钒杂多酸是合成苹果酯的理想催化剂，其较优反应条件为：乙酰乙酸乙酯0．1 mol，n（乙酰乙酸乙酯）：n（乙二醇）=1．0：1．5，催化剂的用量为反应物总质量的1．5％，12mL甲苯，回流反应3．0h，苹果酯的收率可达83．0％以上。     

Estimation of parameters of the Makeham distribution using the least squares method

The Makeham distribution has been used to describe human mortality and establish actuarial tables. The hazard function is defined by μ(t)=A+BC^t$\mu (t)=A+B{C}^t$, we use the least squares type estimation to estimate the parameters of Makeham distribution in this paper. Seven cases are considered, when A, B, C are known or unknown, respectively. Also, we evaluated the mean square errors of these estimators.     

Controller certification

A modern problem from aerospace control involves the certification of a large set of potential controllers with either a single plant or a fleet of potential plant systems, with both plants and controllers being MIMO and, for the moment, linear. Experiments on a limited number of controller/plant pairs should establish the stability and a certain level of margin of the complete set. We consider this certification problem for a set of controllers and provide algorithms for selecting an efficient subset for testing. This is done for a finite set of candidate controllers and, at least for SISO plants, for compact infinite set. In doing this, the ν-gap metric will be the main tool. Computational examples are given, including one of certification of an aircraft engine controller. The overarching aim is to introduce truly MIMO margin calculations and to understand their efficacy in certifying stability over a set of controllers and in replacing legacy single-loop gain and phase margin calculations.