周期系统的辩识与自适应控制

对用期性参数ＡＲＭＡＸ模型系统提出了二种不同的参数估计算法，由此提供了对该类系统实施自适应控制的新思路、这二种算法是基于适时分时处理和批处理分别构造的。在一定条件下均能证明估计的收敛性以及自适应跟踪性。这些条件大多是与线性定常系统的通常假定相当的。     

On Mixture Periodic Vector Autoregressive Models

This article deals with the study of some properties of a mixture periodically correlated n-variate vector autoregressive (MPVAR) time series model, which extends the mixture time invariant parameter n-vector autoregressive (MVAR) model that has been recently studied by Fong et al. (2007 Fong, P.W., Li, W.K., Yau, C.W., Wong, C.S. (2007). On a mixture vector autoregressive model. The Canadian Journal of Statistics 35:135–150.[Crossref], [Web of Science ®] , [Google Scholar]). Our main contributions here are, on the one side, the obtaining of the second moment periodically stationary condition for a n-variate MPVAR_S(n; K; 2, …, 2) model; furthermore, the closed-form of the second moment is obtained and, on the other side, the estimation, via the Expectation-Maximization (EM) algorithm, of the coefficient matrices and the error variance matrix.     

Positive-rule stein-type almost unbiased ridge estimator in linear regression model

Abstract

In this article, when it is suspected that regression coefficients may be restricted to a subspace, we discuss the parameter estimation of regression coefficients in a multiple regression model. Then, in order to improve the preliminary test almost ridge estimator, we study the positive-rule Stein-type almost unbiased ridge estimator based on the positive-rule stein-type shrinkage estimator and almost unbiased ridge estimator. After that, quadratic bias and quadratic risk values of the new estimator are derived and compared with some relative estimators. And we also discuss the option of parameter k. Finally, we perform a real data example and a Monte Carlo study to illustrate theoretical results.     

一阶周期系数线性微分方程的周期解

本文通过通解公式和变量变换对一阶周期系数线性微分方程的周期解作较系统的探讨。     

一类泛函微分方程的周期解

利用重合度方法研究了一类具复杂偏差变元的非自治泛函微分方程x(t) = kx(t) + u(t)))((txgm + e(t)周期解的存在性,得到了方程具有周期解的充分条件.     

THE CONVERGENCE OF AUTOCORRELATIONS AND AUTOREGRESSIONS1

For a general class of scalar stationary processes, essentially those for which the best linear predictor is the best predictor (in the mean square sense), it is shown that, under fairly minor additional conditions, the sample autocorrelations converge to the true values almost surely and hniformly in the lag, t, at a rate (T^-1log T)^1/2, where T is the sample size. For ARMA processes, if |t|(log T)^a, a < ∞, the rate is the best possible, namely (T^-1log log T)^1/2. In particular the somewhat implausible condition, on the innovations, that E{ε(t)²| F_t-l} is constant is avoided in these results. The theorems are used to discuss autoregressive approximation. When the stationary process is a vector process the condition on the innovation sequence, ε(t), that E{ε(t)ε(t)| F_t-l} be constant, cannot be entirely avoided in relation to autoregressive approximation. This is also discussed.     

一类广义Liénard型泛函微分方程的周期解

利用拓扑度方法研究了一类高次迭代的广义Liénard型泛函微分方程x"(t)+f(x(t)) x'(f)+a(t)g(x(t))十b(t)x(t)=p(t)周期解的存在性,在阻尼项f有界和无界的条件下分别讨论了方程存在周期解的充分条件.     

Banach空间一阶微分方程解的存在唯一性

本文研究了Ｂａｎａｃｈ空间一阶微分方程初值问题和周期边值问题解的存在唯一性,改进和推广了他人研究的新近结果。     

On periodic autoregressive stochastic volatility models: structure and estimation

To capture both the volatility evolution and the periodicity feature in the autocorrelation structure exhibited by many nonlinear time series, a Periodic AutoRegressive Stochastic Volatility (PAR-SV ) model is proposed. Some probabilistic properties, namely the strict and second-order periodic stationarity, are provided. Furthermore, conditions for the existence of higher-order moments are established. The autocovariance structure of the squares and higher order powers of the PAR-SV process is studied. Its dynamic properties are shown to be consistent with financial time series empirical findings. Ways in which the model may be estimated are discussed. Finally, a simulation study of the performance of the proposed estimation methods is provided and the PAR-SV is applied to model the spot rates of the euro and US dollar both against the Algerian dinar. The empirical analysis shows that the proposed PAR-SV model can be considered as a viable alternative to the periodic generalized autoregressive conditionally heteroscedastic (PGARCH) model.