Exponential smoothing: Behavior of the ex-post sum of squares near 0 and 1

When using simple exponential smoothing on a given time series the nature of the relationship between the optimal smoothing constant and the autocorrelation structure of the series remains an unresolved question. Although numerical search routines can easily be used to find optimal values of the smoothing constant, they offer little insight into the nature of the relationship between the estimated smoothing constant and the structure of the underlying time series. We suggest that renewed investigations of the ex-post sum of squares function may prove helpful in this pursuit. Results are presented that illustrate how the optimal smoothing constant depends upon the value used to initialize the smoothing and upon the sample autocorrelation coefficients of the observed series. These results are based on a new formula for the derivative of the ex-post sum of squares function. In particular, the derivative is examined near 0 and 1, where great simplifications occur in its form, thereby facilitating investigations near these points. A necessary and sufficient condition is stated for when the ex-post sum of squares must have a positive derivative at 0 and the autocorrelation coefficients of the differenced series are shown to affect the sign of the derivative near 1. Based on these results, a general algorithm is presented as an alternative to grid search routines for minimizing the ex-post sum of squares.     

几个数项级数求和的一般结论

通过一道求极限习题limx∞(1/ 2 + 3/ 2 2 +… + (2n - 1) / 2 n)的探讨 ,归纳总结出了几个数项级数求和的一般结论     

有限和式的积分放缩及应用

本文给出有限和式sum from k=1 to nf(k)的积分放缩的若干结论,并讨论其在求极限、证明不等式和无穷级数收敛性等问题中的应用。     

Riding on Tyvek-A Case Study about How a New Material Invented by Western Multinational Company Enters China

This paper is a case study about how a new product developed by Western multinational company enters new market ?the Mainland China. In this study, a new fabric ?DuPont's hi-technical Tyvek?PU Coating, is fashionized and developed into a new fashionable and functional casual-rainwear, using the approach of new product development method ( idea generation; screening; business analysis; development; evaluation and testing; commercialization).     

关于笛卡尔积码的广义Hamming重量的分析

在文献[1 0 ] 中 ,由旧码C1 、C2 构造了一类新码C1 C2 ———笛卡尔积码。本文根据文献[1 ]中提出的广义Hamming重量的定义 ,分析了笛卡尔积码与旧码C1 、C2 的广义Hamming重量的关系 ,给出了几个有意义的结果     

一类由Hadamard乘积定义的函数子类

设p为正整数,)(pA表示单位圆盘内形如+=+=1)(pkkkpzazzf的解析函数全体,对给定的复 常数p-l及)(zf )(pA, 用 )()()(zfzhzfJ*=ll 定义算子lJ,其中kpkzkpzhlll++==)(,文章得出当)()()(alpnRzfJ(p相似文献   

探索中总结经验创造中发展自我

文章论述教师在教学中帮助学生不断积累经验的重要性及必要性。     

Research on Digital Models for Product Design and Manufacture

CAD/CAM integrate technology has been drawn to much a ttention and becomes one of the focus of the international academic and commerci al research, Through efforts nearly 10 years, remarkable progress has been made in the 3-dimension feature parametric modeling. UG, SOLIDWORK and MDT apply the se technology with respective features. However, no distinct development has bee n made in the digital models from geometric feature to manufacture feature. Prod uct information expression and the basic model frame ...     

Research on Product Information Integrating and Sharing for Dynamic Colla boration

Dynamic Collaboration emerges as the new trend of n et working and collaborating work in manufacturing industry, in which product infor mation sharing among allied enterprises plays very important roles in collaborat ing product development. This thesis aims at studying the integrating, contr olling and sharing mode of product information among the heterogeneous and dispe rsed environments through Internet, and proposes the information integrating/sha ring architecture based on the Product Master Model (P...     

中国南海海绵化学成份研究Ⅱ—B·C

从中国南海西沙群岛永胜岛附近海域采集到的一种海绵(种属未定)分离到两种新的三羟基长链酰胺类化合物S—Ⅱ(C_(49)H_(99)NO_4,M=765,m.p.138-140℃)和S—Ⅲ(C_(45)H_(93)NO_4,M=723,m.p.92—93℃),通过对它们的IR,MS,~1HNMR,~(13)CNMR及~(13)CNMR DEPT等波谱数据分析,S—Ⅱ和S—Ⅲ的结构分别确定为N-(1-乙基-3,22-二羟基)二十二烷基-2-甲基-4-羟基二十四脂肪酸酰胺和N-(1-羟甲基-2-乙基-4-甲基-3,18-二羟基)十九烷基—二十三脂肪酸酰胺。