Exponential Smoothing with an Adaptive Response Rate

A modification is proposed to forecasting systems employing exponential smoothing whereby the response rate is varied and made to depend on the value of a tracking signal. In a simple system, this is equivalent to varying α the smoothing constant according to the extent to which biased forecasts are being obtained. Such a system is shown to react much faster to, for example, step changes whilst still retaining the facility to filter out random noise.     

Adaptive Exponential Smoothing Revisited

Adaptive exponential smoothing models are designed to improve performance by letting the smoothing parameter vary according to the most recent forecasting accuracy. This paper argues that the constant exponential smoothing results used in two comparative studies are inadequate as benchmarks. A reexamination does not indicate that adaptive exponential smoothing methods provide superior forecasts compared to those obtainable from constant exponential smoothing with a considerate choice of the smoothing constant. No support was found for the alleged advantages of the Dennis run based adaptive procedure.     

Monitoring an Exponential Smoothing Forecasting System

The first part of this paper is concerned with the variance of the smoothed error when the forecasting system being used is exponential smoothing. The expression derived for this variance involves the variance of the noise, the smoothing constant and a sum of squared binomial coefficients. It is also shown that the variance of the sum of errors equals the variance of the smoothed error for one less degree of freedom divided by the square of the smoothing constant.The second part of the paper considers the practical application of the above result and also gives values for the tracking signal limits, obtained by simulation, which could be used in the automatic monitoring of a forecasting system.     

Model Identification in Exponential Smoothing

Model identification has traditionally been ignored in forecasting via exponential smoothing. The usual practice is to apply the same model to every time-series in a collection. This paper develops a procedure for model identification in large forecasting applications based on an examination of variances of differences of the time-series. The order of differencing yielding minimum variance suggests an appropriate model for the series. Empirical results show that this procedure selects models that give reasonable ex ante forecast accuracy.     

Adaptive Order Selection for Spline Smoothing

Computational methods are presented for spline smoothing that make it practical to compute smoothing splines of degrees other than just the standard cubic case. Specifically, an order n algorithm is developed that has conceptual and practical advantages relative to classical methods. From a conceptual standpoint, the algorithm uses only standard programming techniques that do not require specialized knowledge about spline functions, methods for solving sparse equation systems or Kalman filtering. This allows for the practical development of methods for adaptive selection of both the level of smoothing and degree of the estimator. Simulation experiments are presented that show adaptive degree selection can improve estimator efficiency over the use of cubic smoothing splines. Run-time comparisons are also conducted between the proposed algorithm and a classical, band-limited, computing method for the cubic case.     

时间序列指数平滑模型新体系及算法

本文提出了动态平滑参数的概念，由此建立了一类不需选取平滑初值、带有动态平滑参数的指数平滑新模型体系，包括差分一指数平滑模型；又以预测误差平方和SSE最小为目标，构造了优选并自动生成最佳平滑参数使平滑模型得以优化的最速下降算法，增强了指数平滑模型对时间序列的适应能力．从而较完整的解决了指数平滑预测中，平滑参数靠经验确定且为静态、平滑初值难以确定并易导致预测偏差等问题．     

Progressive Tuning of Simple Exponential Smoothing Forecasts

The paper outlines a finite sample version of exponential smoothing, and proposes a formula for estimating the smoothing parameter. The resulting method, which can be implemented on a recursive basis over time, is compared with alternative approaches, such as progressive numerical optimization of the smoothing parameter and adaptive forecasting on both synthetic and real data.     

Algorithms with Adaptive Smoothing for Finite Minimax Problems

We present a new feedback precision-adjustment rule for use with a smoothing technique and standard unconstrained minimization algorithms in the solution of finite minimax problems. Initially, the feedback rule keeps a precision parameter low, but allows it to grow as the number of iterations of the resulting algorithm goes to infinity. Consequently, the ill-conditioning usually associated with large precision parameters is considerably reduced, resulting in more efficient solution of finite minimax problems.The resulting algorithms are very simple to implement, and therefore are particularly suitable for use in situations where one cannot justify the investment of time needed to retrieve a specialized minimax code, install it on one's platform, learn how to use it, and convert data from other formats. Our numerical tests show that the algorithms are robust and quite effective, and that their performance is comparable to or better than that of other algorithms available in the Matlab environment.     

A Multiple Exponential Smoothing Scheme For Quality Control

1. INTRODUCTIONRoberts (1959) first introduced the exponentially weighted movingaverage (EWMA) control scheme. Such a scheme is useful for detectingsmall shifts in the mean of a process. Like Shewhart and cumulativesum (CUSUM) control schemes, an EWMA control scheme is easy toimplement and interpret. For the purpose of providing signals the clas-sical Shewhart chart has no memory, i. e. it ignores the immediate history. The CUSUM chart, however, has too much memory, giving equalwe…     

On Solving Large-Scale Finite Minimax Problems Using Exponential Smoothing

This paper focuses on finite minimax problems with many functions, and their solution by means of exponential smoothing. We conduct run-time complexity and rate of convergence analysis of smoothing algorithms and compare them with those of SQP algorithms. We find that smoothing algorithms may have only sublinear rate of convergence, but as shown by our complexity results, their slow rate of convergence may be compensated by small computational work per iteration. We present two smoothing algorithms with active-set strategies and novel precision-parameter adjustment schemes. Numerical results indicate that the algorithms are competitive with other algorithms from the literature, and especially so when a large number of functions are nearly active at stationary points.     

An Application of Double Exponential Smoothing Technique to Quality Control

休哈特控制图和ＳＵＳＵＭ控制图技术，在制造业得到广泛应用．Ｊ．Ｓ．Ｈｕｎｔｅｒ提出用指数加权滑动平均（ＥＷＭＡ）作为质量管理工具．然而，众所周知存在趋势项的情况下，用ＥＷＭＡ预测往往不是过低就是过高．本文的目的是表明利用双指数平滑（ＤＥＳ）技术可以减少此缺点．文中给出一个例子，它表明双指数平滑法比单指数平滑法，能更好地监控对于目标的偏离．     

可修复人机系统的指数稳定性

研究了两相同部件温储备可修的人机系统,运用C_0半群的相关理论,对系统主算子的谱界进行估值.估算系统的算子产生的半群的增长界,然后运用了共尾的概念及相关的理论,得到了系统算子A+B的谱界与系统算子产生的半群的增长界相同.进而运用相关代数知识证得,0为系统算子的简单本征值,并分析了系统算子的谱分布,得到系统的指数稳定性.并研究了系统算子预解式的特性.对任意给定的δ0,γ=a+bi,-μ+δa_1≤a≤a_2,得到lim|b|→∞‖R(γ;A+B)‖=0.进而得到在~sRγ≥a_1的右半平面内相应于系统算子A+B的谱点由有限个本征值组成.     

A Simple Graphical Method of Exponential Smoothing with a Linear Trend

A very simple graphical method is described for successively modifying a fitted trend line in the light of each fresh observation on a time series. The method is shown to be equivalent to the well-established method of exponential smoothing described by Holt. The graphical method is of some interest in its own right and also adds insight into the workings of Holt's method.     

Adaptive Estimation of Distributions Using Exponential Sub-Families

Abstract

An algorithm is presented that, for a large-dimensional exponential family G, finds a lower dimension exponential sub-family of G which contains distributions best fitting groups of identically distributed observations within a set of data. The data are therefore fitted to a family of distributions that has been adaptively chosen as representative of them. The algorithm is implemented in the special case in which G is a logspline family of distributions. An example data set is analyzed using the method.     

一类具有储备部件的可修复人机系统的指数稳定性

研究了具有储备部件的可修复人机系统.运用Banach空间上的线性算子半群理论,证明了严格占优本征值的存在性,并通过分析系统本质谱界经过扰动后的变化,进一步表明在一定的条件下,系统动态解以指数形式收敛于系统的稳态解.     

定时截尾场合指数分布表决系统产品的统计分析

本文针对指数分布2/3(G)表决系统产品,在截尾样本场合下给出了参数的拟矩估计、极大似然估计和近似区间估计,并通过大量的Monte-Carlo模拟分别考察了点估计和区间估计的精度。     

自适应逐步II型混合截尾恒加寿命试验下广义指数分布的统计分析

在自适应逐步II型混合截尾恒定应力加速寿命试验下,讨论了两参数广义指数分布的统计分析。利用EM算法和最小二乘法相结合的新方法推导出未知参数与可靠度函数的点估计,通过信息缺失原则得到了观测Fisher信息阵和尺度参数的渐近无偏估计。利用估计的渐近正态性和参数bootstrap方法构造了参数的置信区间。最后运用Monte-Carlo方法分别对得到的点估计和区间估计的精度进行研究,结果表明尺度参数的渐近无偏估计优于相应的两步估计, Boot-p置信区间比相应的渐近置信区间更精确。     

一个完全双曲相场系统的指数吸引子

本文研究一个非线性双曲微分积分系统,它由H.G.Rotstein等人于2001年提出,用来描述某种特殊的相位转换现象.该系统刻画了相对温度(?)和序参数(或相场)x的变化规律.对(?)和x分别赋予Dirichlet和Neumann边界条件下,该问题生成一个耗散的动力系统,Grasselli和Pata证明了该系统整体吸引子的存在性,随后,Grasselli证明了该系统的指数吸引集的存在性.本文进一步证明其指数吸引子的存在性,在得到指数吸引子有有限的分形维数的同时得到整体吸引子的分形维数的有限性.     

一类自适应控制系统的稳定性分析

对一类模型参考自适应控制映射进行了稳定性分析,通过使用中心流形简化和范式方法以及计算机辅助计算讨论了该类系统在参数空间内的所有1-余维和2-余维分岔行为及其性质,全面了解了系统在不同参数区域内的动态.从而为如何选取此类控制系统的参数以避免导致控制失效的多吸引子共存或长期存在的瞬态等动力学行为提供了方法和理论依据,并为在线调整参数以避免控制失效指明了方向.