Estimation of the parameters of symmetric stable ARMA and ARMA–GARCH models

In this article, we first propose the modified Hannan–Rissanen Method for estimating the parameters of autoregressive moving average (ARMA) process with symmetric stable noise and symmetric stable generalized autoregressive conditional heteroskedastic (GARCH) noise. Next, we propose the modified empirical characteristic function method for the estimation of GARCH parameters with symmetric stable noise. Further, we show the efficiency, accuracy and simplicity of our methods with Monte-Carlo simulation. Finally, we apply our proposed methods to model the financial data.     

Rate efficient estimation of realized Laplace transform of volatility with microstructure noise

In this paper, we consider the problem of estimating the Laplace transform of volatility within a fixed time interval [0,T] using high‐frequency sampling, where we assume that the discretized observations of the latent process are contaminated by microstructure noise. We use the pre‐averaging approach to deal with the effect of microstructure noise. Under the high‐frequency scenario, we obtain a consistent estimator whose convergence rate is , which is known as the optimal convergence rate of the estimation of integrated volatility functionals under the presence of microstructure noise. The related central limit theorem is established. The simulation studies justify the finite‐sample performance of the proposed estimator.     

Infinite Variation Tempered Stable Ornstein–Uhlenbeck Processes with Discrete Observations

We investigate transition law between consecutive observations of Ornstein–Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one with stability index in (0, 1) and the other with index in (1, 2). We discuss simulation techniques for those three random elements. With the exact transition law and proposed simulation techniques, sample paths simulation proves significantly more efficient, relative to the known approximative technique based on infinite shot noise series representation of tempered stable Lévy processes.     

Parameter Estimation for the Discrete Stable Family

The discrete stable family constitutes an interesting two-parameter model of distributions on the non-negative integers with a Paretian tail. The practical use of the discrete stable distribution is inhibited by the lack of an explicit expression for its probability function. Moreover, the distribution does not possess moments of any order. Therefore, the usual tools—such as the maximum-likelihood method or even the moment method—are not feasible for parameter estimation. However, the probability generating function of the discrete stable distribution is available in a simple form. Hence, we initially explore the application of some existing estimation procedures based on the empirical probability generating function. Subsequently, we propose a new estimation method by minimizing a suitable weighted L ²-distance between the empirical and the theoretical probability generating functions. In addition, we provide a goodness-of-fit statistic based on the same distance.     

Asymptotic distribution of regression type estimators of parameters of stable laws

Asymptotic distributions of regression-type estimators for the parameters of stable distributions am obtained. The asymptotic normalized standard deviations of the estimators are computed for various values of the parameters and various choices of the number of points used in getting the regression estimates.     

利用稳定分布构建开放式基金业绩评价体系

经典的基金业绩评价方法是在收益率服从正态分布假设下构建风险指标，该指标或者高估风险，或者低估风险。可引入稳定分布来描述收益率，并利用稳定分布，构建风险调整的基金业绩评价体系，并利用该体系对我国开放式基金的业绩进行评价。     

Throughput and delay analysis of an opportunistic tree algorithm

Tree algorithms are a well-known class of random access algorithms with a provable maximum stable throughput under the infinite population model (as opposed to ALOHA or the binary exponential backoff algorithm). In this article, we propose a tree algorithm for opportunistic spectrum usage in cognitive radio networks. A channel in such a network is shared among so-called primary and secondary users, where the secondary users are allowed to use the channel only if there is no primary user activity. The tree algorithm designed in this article can be used by the secondary users to share the channel capacity left by the primary users.

We analyze the maximum stable throughput and mean packet delay of the secondary users by developing a tree structured Quasi-Birth Death Markov chain under the assumption that the primary user activity can be modeled by means of a finite state Markov chain and that packets lengths follow a discrete phase-type distribution.

Numerical experiments provide insight on the effect of various system parameters and indicate that the proposed algorithm is able to make good use of the bandwidth left by the primary users.     

有限理性下的社保基金投资监管进化博弈研究

社保基金的投资监管是复杂的决策问题,无法满足主流博弈论“完全理性”的要求。因此从有限理性角度出发,分别建立了基金经理人之间、社保基金管理机构与基金经理人之间的进化博弈模型,求出模型的复制动态方程,研究不同情况下的进化稳定策略,并得到博弈群体的复制动态相位图。     

吉林省2000-2005年生育情况分析

吉林省2005年人口出生率7.89‰,低于全国平均水平,人口和计划生育工作形式总体是好的。但通过对吉林省2000-2005年生育情况的调查发现,全省低生育水平面临反弹的现实风险。我们必须清醒地看到,违法生育数量相对增加,一胎违法生育所占比例较大,再婚违法生育占违法多胎生育比例较大。在详细分析产生问题原因的基础上结合工作实际提出解决违法生育增多问题的建议。     

A note on mixingale limit theorems and stable convergence in law

A gap in the proof of a non stationary mixingale invariance principle is identified and fixed by introducing a skipped subsampling of a partial sum process and letting the skipped interval vanish asymptotically at an appropriate rate as the sample size increases. The corrected proof produces a mixingale limit theorem in the form of a mixing convergence in law, occurring jointly with the stable convergence in law for the same σ-field relative to which they are stable and mixing. The applicability of established results to a high-frequency estimation of the quadratic variation of financial price process is discussed.