Some comments on the initialization of exponential smoothing

It is shown that the traditional choice for the initial smoothed statistics in general exponential smoothing leads to the same forecasts as the equivalent ARIMA model, provided that one uses zero starting values for the initial shocks. In addition, an initialization which uses ‘backforecasts’ as initial smoothed statistics is considered, and its relationship to unconditional least squares is explored.     

SMOOTHING AND CURVE-FITTING OF THE MEASURED DATA OF PLANE CAM PROFILE

The necessary continuity of the second order derivative or curvature of the cam profile has been analyzed. In order to guarantee the smoothness of the cam radius data, a proper method with which it could be possible to revise directly the first and the second order difference coefficients as well as the slope has been proposed. This method, applicable to different cam mechanisms by using a unified formula of correction, possesses the characteristics of simplicity, intuition and precision. Meanwhile, a cubic spline function for fitting the cam profile has also been described.     

均匀分划下S_(n,λ,l)的表达式和性质

本文给出在均匀分划下S_(n,λ,1)(f_Δ)的表达式和讨论有界函数f(x)的S_(n,λ,1)(f_Δ)的收敛性。     

Causal forces: Structuring knowledge for time-series extrapolation

This paper examines a strategy for structuring one type of domain knowledge for use in extrapolation. It does so by representing information about causality and using this domain knowledge to select and combine forecasts. We use five categories to express causal impacts upon trends: growth, decay, supporting, opposing, and regressing. An identification of causal forces aided in the determination of weights for combining extrapolation forecasts. These weights improved average ex ante forecast accuracy when tested on 104 annual economic and demographic time series. Gains in accuracy were greatest when (1) the causal forces were clearly specified and (2) stronger causal effects were expected, as in longer-range forecasts. One rule suggested by this analysis was: ‘Do not extrapolate trends if they are contrary to causal forces.’ We tested this rule by comparing forecasts from a method that implicitly assumes supporting trends (Holt's exponential smoothing) with forecasts from the random walk. Use of the rule improved accuracy for 20 series where the trends were contrary; the MdAPE (Median Absolute Percentage Error) was 18% less for the random walk on 20 one-year ahead forecasts and 40% less for 20 six-year-ahead forecasts. We then applied the rule to four other data sets. Here, the MdAPE for the random walk forecasts was 17% less than Holt's error for 943 short-range forecasts and 43% less for 723 long-range forecasts. Our study suggests that the causal assumptions implicit in traditional extrapolation methods are inappropriate for many applications.     

汉字的平滑放大技术

介绍一项在点阵汉字字模显示或打印中进行平滑放大的技术－三角形填充法，论述了该方法的特点、原理、实现过程及其局限性，并讨论了点阵汉字放大输出的有关问题。     

指数平滑系数的优化研究

通过对指数平滑系数的研究,提出了平滑系数的优化确定方法;并将优化后的指数平滑系数在我国煤炭产量的预测中得以验证.     

ORLICZ函数空间k严格凸与k光滑

本文给出了赋Luxemberg范数与Orlicz范数的Orlicz函数空间的k-端点，k-光滑点的判据，从而得到了k严格凸与k光滑性的充要条件．     

电力系统中长期负荷预测的模糊算法

介绍了用模糊指数平滑法和模糊线性回归法进行电力系统中长期负荷预测的方法，以实际预测为例，给出预测结果，实践证明了上述2种方法虽然以传统预测方法为基础，但具有算法简单，计算速度快，预测精度高，预测误差小，并能提供负荷的一个预测区间等优点，尤其在原始数据存在不确定性和模糊性时，更有着常规预测方法无可比拟的优越性。     

关于单整时间序列非线性变换的研究

文献［１］提出了单整序列的非线性变换问题,并对变换序列的统计性质进行了分析．文献［２］也对单整序列的非线性变换问题进行了比较深入的研究,他们都得出结论：一般情况下,一个Ｉ（１）序列的非线性变换会产生一个长期记忆序列,但是变换后的序列未必是一个Ｉ（１）序列．本文讨论了文献［１,２］关于单整序列非线性变换问题的研究方法和基本结论,同时提出了一个新的问题：如果｛Ｘｔ｝和｛Ｙｔ｝都是Ｉ（１）序列,并且它们之间不存在协整关系,那么在什么条件下存在｛Ｘｔ｝和｛Ｙｔ｝的非线性变换,使得变换后的序列是协整的？论文首先根据ＡＣＥ算法,提出了最优非线性变换函数的估计方法,然后对估计后的残差序列进行单位根的检验,从而检验变换后序列｛ｆ（Ｙｔ）｝和｛ｇ（Ｘｔ）｝之间协整关系的存在性     

一种特征保持的自适应三角网格模型光顺算法

提出了一个基于双边滤波器的特征保持的自适应三角网格模型光顺算法，该算法为了加强保持特征的效果．结合网格局部顶点一阶邻域的几何特征并将改进后的双边滤波算子应用于顶点的位置更新操作．在光顺过程中有效地避免了三角网格模型的过度光顺现象．给出了几个实验实例来说明该算法在去除网格噪音的同时保留特征的有效性．