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.     

关于多元Gauss—Weierstrass算子的一致逼近

本文利用一类 K—泛函和光滑模的等价性给出了二元 Gauss—weierstrass 算子在一致逼近意义的正定理、逆空理和特征性。     

中国数学史断代研究的一项新成果：—《明清数学史论文集》简介

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从尚艳到崇雅——论《御览诗》、《极玄集》在中晚唐诗风衍变历程中的座标意义

《御览诗》和《极玄集》分别编成于宪宗元和后期和文宗开成初年。前者喜尚轻艳,追摹齐梁;后者推崇清雅,回归大历。不同的风格特征、相异的审美追求,清晰地透现出中晚唐之际士人心态的变化及诗风衍变的动态历程,在唐诗发展史上极具座标意义。     

Erds 等人的一个定理的新证明

本文给出定理:“在2n—1个整数中,必有n 个数,它们的和被n 整除”的一个新的证明,它无需先讨论n 为素数。     

医院信息管理系统业务量估算与网络流量控制

本文介绍医院信息管理系统组成与设计要求;讨论了信息系统业务量估算,网络流量控制方法,保证信息管理系统数据有效性,快速存储,共享使用与安全可靠性。     

韶关大学男生身体素质现状研究

本文通过对韶关大学93和94级男生五项身体素质成绩的差异研究，并与全省同年级男生进行横向比较，以了解韶关大学男生身体素质现状，并为公共体育教学和为学校发展学生身体素质提供参考依据。     

上海民俗的泛化及其发展

民俗文化随社会历史的变化而发生变化。都市民俗文化的变迁主要表现“泛化”，泛化的根源在于历史原因、民风变革、心理原因、科技进步等。     

论陈三立诗歌的悲情

陈三立是戊戍维新党人,又是晚清民初杰出的"同光体"诗人之一。在他的诗歌中,有着对时代的自觉性省察,真实地再现他对家国、生命、文化的悲剧性反思。