Moments of Mixture Periodic Autoregressive Models

This article deals with the study of some properties of a mixture periodically correlated autoregressive (MPAR _S ) time series model, which extends the mixture time invariant parameter autoregressive (MAR) model, that has recently received a considerable interest from many economic time series analysts, to mixture periodic parameter autoregressive model. The aim behind this extension is to make the model able to capture, in addition to all features captured by the classical MAR model, the periodicity feature exhibited by the autocovariance structure of many encountered financial and environmental time series with eventual multimodal distributions. Our main contribution here is obtaining of the second moment periodically stationary condition for a MPAR _S (K; 2,…, 2) model, furthermore the closed-form of the second moment is obtained.     

Book Review: New Introduction to Multiple Time Series Analysis

ABSTRACT

This paper proposes a test for the null hypothesis of periodic stationarity against the alternative hypothesis of periodic integration. We derive the limiting distribution of the test statistic and its characteristic function, which are the same as those of the test developed in Kwiatkowski, Phillips, Schmidt and Shin.[15] Kwiatkowski, D., Phillips, P.C. B., Schmidt, P. and Shin, Y. 1992. Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root.. Journal of Econometrics, 54: 159–178. [Crossref], [Web of Science ®] , [Google Scholar] We find that some parameters, which we must assume under the alternative, have an important effect on the limiting power, so we should choose such parameters carefully. A Monte Carlo simulation reveals that the test has reasonable power but may be affected by the lag truncation parameter that is used for the correction of nuisance parameters.     

Higher Order Asymptotic Cumulants of Studentized Estimators in Covariance Structures

In covariance structure analysis, the Studentized pivotal statistic of a parameter estimator is often used since the statistic is asymptotically normally distributed with mean zero and unit variance. For more accurate asymptotic distribution, the first and third asymptotic cumulants can be used to have the single-term Edgeworth, Cornish-Fisher, and Hall type asymptotic expansions. In this paper, the higher order asymptotic variance and the fourth asymptotic cumulant of the statistic are obtained under nonnormality when the partial derivatives of a parameter estimator with respect to sample variances and covariances up to the third order and the moments of the associated observed variables up to the eighth order are available. The result can be used to have the two-term Edgeworth expansion. Simulations are performed to see the accuracy of the asymptotic results in finite samples.     

On Properties of Percentile Bootstrap Confidence Intervals for Period Using Periodogram

Periodic functions have many applications in astronomy. They can be used to model the magnitude of light intensity of the period variable stars that their brightness vary with time. Because the data related to the astronomical applications are commonly observed at the time points that are not regularly spaced, the use of the periodogram as a good tool for estimating period is highlighted. Our bootstrap inference about period is based on maximizing the periodogram and consists of percentile two-sided bootstrap confidence intervals construction for the true period. We also obtain their coverage levels theoretically, and discuss the benefit of double-bootstrap confidence intervals for the parameter by which the coverage levels are substantially improved. Precisely, we show that the coverage error of single-bootstrap confidence intervals is of order n ^?1, decreasing to order n ^?2 when applying double-bootstrap methods. The simulation study given here is a numerical assessment of the theoretical work.     

Interactions between formal structures and knowing communities: What does open source community involvement mean?

The purpose of this paper is to study the interactions between formal structures and knowing communities and to show how formal structures can support external communities. Indeed, the literature reveals the critical role of external knowing communities for innovation. This research is based on a sequential mixed-method research design with a multi study sequential approach. Three studies are performed to analyze the interactions between IT formal structures and open source communities. Study 1 and study 3 are quantitative and rely on the same sample of 157 IT business managers. Study 2 is qualitative and is based on four managers of three formal structures deeply rooted in open source communities. These studies show that the use of open source within the formal structure has an impact on the three forms in which formal structures involve themselves in external knowing communities: formalized, result-oriented and inter-connected involvement. They also reveal the difficulties and possibilities of inter-connected involvement and highlight the central role of formalization in community involvement.     

平稳振荡研究中的Liapunov函数

本文采用对系统具体构造一个Liapunov函数的方法,研究了系统的周期解问题,可使问题的研究变得非常简单。     

视角·结构·策略——从《鬼作家》到《退场的鬼魂》叙事的承袭与嬗变

自1979年发表《鬼作家》到2007年出版《退场的鬼魂》,菲利普·罗斯的叙事技巧既有承袭也有嬗变:虽然在叙事视角上都采用回溯的第一人称"内聚焦",但视角与声音的相异或一致凸显叙事的稚嫩或成熟;虽然在叙事结构上都采用框架式,但叙述时间与故事时间却有简单和复杂之别;虽然在叙事策略上都采用虚实相间的后现代小说艺术手法,但就叙述者与作者、叙述本身、叙述文本中主人公的真实性与虚构性界线而言,《退场的鬼魂》比《鬼作家》的叙述更复杂、更娴熟.从视角、结构、策略三个维度看,《退场的鬼魂》承袭前作叙事主体、文本语境与叙事风格,含而不露地生成兼具文本间性的独异性,其充满叙事性想象的小说文本为"祖克曼系列小说"画上完美的句点,可视为菲利普·罗斯"祖克曼系列"叙事艺术技巧上的扛鼎之作.