The effects of model parameter deviations on the variance of a linearly filtered time series

We consider a general linear filtering operation on an autoregressive moving average (ARMA) time series. The variance of the filter output, which is an important quantity in many applications, is not known with certainty because it depends on the true ARMA parameters. We derive an expression for the sensitivity (i.e., the partial derivative) of the output variance with respect to deviations in the model parameters. The results provide insight into the robustness of many common statistical methods that are based on linear filtering and also yield approximate confidence intervals for the output variance. We discuss applications to time series forecasting, statistical process control, and automatic feedback control of industrial processes. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Assessing the value of demand sharing in supply chains

We consider the problem of assessing the value of demand sharing in a multistage supply chain in which the retailer observes stationary autoregressive moving average demand with Gaussian white noise (shocks). Similar to previous research, we assume each supply chain player constructs its best linear forecast of the leadtime demand and uses it to determine the order quantity via a periodic review myopic order‐up‐to policy. We demonstrate how a typical supply chain player can determine the extent of its available information in the presence of demand sharing by studying the properties of the moving average polynomials of adjacent supply chain players. The retailer's demand is driven by the random shocks appearing in the autoregressive moving average representation for its demand. Under the assumptions we will make in this article, to the retailer, knowing the shock information is equivalent to knowing the demand process (assuming that the model parameters are also known). Thus (in the event of sharing) the retailer's demand sequence and shock sequence would contain the same information to the retailer's supplier. We will show that, once we consider the dynamics of demand propagation further up the chain, it may be that a player's demand and shock sequences will contain different levels of information for an upstream player. Hence, we study how a player can determine its available information under demand sharing, and use this information to forecast leadtime demand. We characterize the value of demand sharing for a typical supply chain player. Furthermore, we show conditions under which (i) it is equivalent to no sharing, (ii) it is equivalent to full information shock sharing, and (iii) it is intermediate in value to the two previously described arrangements. Although it follows from existing literature that demand sharing is equivalent to full information shock sharing between a retailer and supplier, we demonstrate and characterize when this result does not generalize to upstream supply chain players. We then show that demand propagates through a supply chain where any player may share nothing, its demand, or its full information shocks (FIS) with an adjacent upstream player as quasi‐ARMA in—quasi‐ARMA out. We also provide a convenient form for the propagation of demand in a supply chain that will lend itself to future research applications. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 515–531, 2014     

光学表面的分形特点与模拟表征算法

根据光学表面在微观结构呈现出的自相似性,利用尺度无关的分形模型描述了其结构特征;采用结构函数法对抛光表面的分形维数进行计算,分析了粗糙度参数RMS值、误差波长、测量尺度、采样长度和采样点数对分形维数的影响规律。在此基础上,提出了采用一阶自回归分形模型对抛光表面进行模拟的新方法,分析了界定尺度、模型参数对分形特征和分形维数的影响规律。利用分形维数描述光学表面的微观结构具有评价方法简单、在一定范围内与测量尺度无关等优点。     

Defense–Growth Causality: Considerations of Regime-Switching and Time- and Country-Varying Effects

This paper develops a panel smooth transition vector autoregressive model to investigate the economic growth–defense causality. This model simultaneously resolves the estimation problems of endogeneity, heterogeneity, and nonlinearity. Empirical results support that the causality is bidirectional, nonlinear, time- and country-varying. Economic growth has a negative impact on military spending and vice versa. The larger the HDI, the smaller the negative causality. Evidently, the increase in the level of country development can reduce the negative impact of military outlays on economic growth. Reducing the ratio of military spending to GDP is beneficial for countries with low HDI scores; however, moderately increasing the share of military expenditure is favorable for countries with extremely high HDI scores. Policy authority needs to set optimal education, health, and economic development shares of GDP for purchasing a maximum economic growth rate.     

On the effectiveness of top‐down strategy for forecasting autoregressive demands

We investigate the relative effectiveness of top‐down versus bottom‐up strategies for forecasting the demand of an item that belongs to a product family. The demand for each item in the family is assumed to follow a first‐order univariate autoregressive process. Under the top‐down strategy, the aggregate demand is forecasted by using the historical data of the family demand. The demand forecast for the items is then derived by proportional allocation of the aggregate forecast. Under the bottom‐up strategy, the demand forecast for each item is directly obtained by using the historical demand data of the particular item. In both strategies, the forecasting technique used is exponential smoothing. We analytically evaluate the condition under which one forecasting strategy is preferred over the other when the lag‐1 autocorrelation of the demand time series for all the items is identical. We show that when the lag‐1 autocorrelation is smaller than or equal to 1/3, the maximum difference in the performance of the two forecasting strategies is only 1%. However, if the lag‐1 autocorrelation of the demand for at least one of the items is greater than 1/3, then the bottom‐up strategy consistently outperforms the top‐down strategy, irrespective of the items' proportion in the family and the coefficient of correlation between the item demands. A simulation study reveals that the analytical findings hold even when the lag‐1 autocorrelation of the demand processes is not identical. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

量测误差的时间序列分析方法

针对工程实践中实际量测误差大多并非纯白噪声特点,运用概率统计学的一个分支——时间序列分析中提供的动态数据处理的方法,采用多种的参数估计算法来对量测误差进行拟合和仿真,给出了实验室仿真过程中需叠加的量测误差的新生成办法。所用方法可以推广到对其它数据序列的处理。     

AR模型仿真相关高斯序列的阶数选择

采用模型仿真相关高斯序列,具有灵活性强、效率高的优点,但如何选择合适的阶数一直是模型谱估计中的关键问题.比较了四种信息量准则和修正的Levison递推方法确定阶数的优缺点,并讨论了采样点数对阶数选择和仿真结果的影响.通过选择合适的信息量准则和采样点数来确定模型阶数,可以有效地仿真功率谱服从高斯谱、n次方谱和指数谱等多种谱形的相关高斯序列,大大降低了仿真过程的计算量.