霍特指数平滑法参数的优选

霍特指数平滑方法是一种高级的指数平滑方法,它有两个平滑参数需要确定.用霍特指数平滑方法进行预测时,最重要、而且最因难的工作是确定平滑参数α、β的取值问题.笔者利用EXCEL模拟运算表的功能很容易实现了在离差平方和最小(或绝对离差和最小)条件下的参数估计.为霍特指数平滑方法在实际中的广泛应用提供一种有效的途径.     

指数平滑预测公式与平滑系数

文章探讨了使用不同的平滑预测公式会有不同的最佳平滑系数的问题，提出了一种预测误差更小、适用范围更广又更加简单的指数平滑短中期预测公式，并提出直接平滑系数和间接平滑系数的概念，推导出计算最佳间接平滑系数的近似计算公式。     

怎样推导指数平滑法预测模型的参数计算公式

指数平滑法是较为常用的一种趋势预测方法.但令人遗憾的是,有些统计学著作在介绍指数平滑法的参数推导过程时,往往过于简单,且前提条件不够充分.本文将给出有关指数平滑法多项式预测模型的参数计算公式以及这一公式的证明.设指数平滑法多项式预测模型为:     

基准动态指数平滑的预测模型

指数平滑法在实际应用中,由于其平滑参数和初值是静态的且主要靠使用者的经验来选择,极易导致系统偏差问题,因此,预测结果往往不够理想。本文在对传统指数平滑预测方法局限性分析的基础上,引出准动态平滑参数和准动态平滑初值的概念,并提出一种能自动适应预测进程的新模型。先依据统计学原理对指数平滑预测模型的精度特性进行分析;再以最小预测误差平方和(SSE)为优化目标,建立准动态指数平滑参数和初值的动态优化模型,该模型能随着新观测值的加入而自动调整;最后,基于最速梯度法基本原理,给出该优化模型的一个可行求解方法,客观地求取最优的准动态指数平滑参数和初值。将该模型作为关键技术应用到加工质量预测补偿控制领域,并与时序AR模型、灰色GM模型及传统指数平滑模型的结果进行对比,表明本文方法具有一定的优越性。     

Excel变量与三次指数平滑模拟预测方法

指数平滑法是对预测对象的全部历史序列数据,通过加权平均从而进行预测的一种方法.在进行指数平滑预测时一般要通过对加权系数α取不同的值,经过多次模拟运算并比较预测误差,从而选择适当的预测结果.然而,当采用二次或三次指数平滑模型,进行预测分析时,由于计算公式较为复杂,模拟运算过程参数的改变就非常繁琐.本文以我国肉类产量三次指数平滑预测为例,利用Excel变量和工作表相结合,建立数据、图表间的链接关系,从而实现了方便、快捷的模拟运算预测分析.     

系统安全数据预测方法综述

据不完全统计,现有的各类预测方法达300种之多,而通常用于系统安全数据预测的方法主要有回归分析法、德尔菲法、趋势外推法、马尔可夫预测、齐次泊松过程模型、指数平滑线、残差辩识法、模型法和灰色预测法等。这些预测方法可分成3类:前5种是统计型的;指数平滑与残差辩识属递推型;灰色预测与模型法则属于连续型。现就这几种预测方法作一简要评述。一、统计型的预测方法1、回归分析法这是一种传统的分析、预测方法,长期以来作为一种经典方法而广泛应用,且种类较多。在系统安全数据的预测上,目前运用较多的为单元线性回归和单元指数回归。由于…     

经济预测中的指数平滑法

指数平滑法是回归分析和时间序列相结合的一种预测方法。华伯泉同志在《统计研究》1986年第2期中介绍了这种方法,但没有解决平滑常数和初始统计量的合理确定问题,也没有提到模型和实际数据是否适合的检验问题;并且以普通回归方程中y的预测区间代替指数平滑法中Z的预测区间,这是不合适的。本文试图解决这些问题,并研究K个观测值总和的预测区间。 -、以时间为独立变量的回归模型 设Z_(n j)表示在时间n j的观测值,考虑如下形式的模型:     

确定平滑系数的新方法

文章利用最小平方法导出了确定平滑系数α的近似计算公式，并通过３个例子讨论了用该种方法确定的平滑系数进行统计预测的误差情况     

季节性指数平滑法参数的优选

一、季节性指数平滑法 季节性指数平滑法是20世纪60年代初由温特(Winters)研究制定出来的一种较高级形式的指数平滑方法.这种方法最突出的优点是对具有趋势变动和季节变动两种因素的时间数列,分别对每种因素进行指数平滑,然后将各种因素的平滑结果结合起来,对原时间数列进行预测.这就扩大了指数平滑方法的应用范围,提高了对兼有趋势和季节变动两种因素时间数列预测的准确性.     

指数平滑法预测信息业实例分析

随着信息产业的迅速崛起,其研究方法日益丰富多彩,特别是相关学科的交叉和渗透,数理方法在这里得到长足应用。诸如在信息产业的投入产出、规模结构、信息化水平和前景预测等方面,自２０世纪８０年代中期以来,陆续出现了一些量化研究的范例。本文试以勃朗三次指数平滑方法对河北省信息产业规模结构进行预测分析。 一、指数平滑法的模型特点 指数平滑法属趋势外推预测,它的数学特性是历史统计数据的大致平滑,是趋势外延。也就是说,它假定过去的发展规律还将继续进行下去。指数平滑又是一种自适应的数学模型,分为一次指数平滑、二次指…     

Understanding exponential smoothing via kernel regression

Exponential smoothing is the most common model-free means of forecasting a future realization of a time series. It requires the specification of a smoothing factor which is usually chosen from the data to minimize the average squared residual of previous one-step-ahead forecasts. In this paper we show that exponential smoothing can be put into a nonparametric regression framework and gain some interesting insights into its performance through this interpretation. We also use theoretical developments from the kernel regression field to derive, for the first time, asymptotic properties of exponential smoothing forecasters.     

Nonparametric regression estimators in complex surveys

In this article, we extend smoothing splines to model the regression mean structure when data are sampled through a complex survey. Smoothing splines are evaluated both with and without sample weights, and are compared with local linear estimator. Simulation studies find that nonparametric estimators perform better when sample weights are incorporated, rather than being treated as if iid. They also find that smoothing splines perform better than local linear estimator through completely data-driven bandwidth selection methods.     

Fast covariance estimation for sparse functional data

Smoothing of noisy sample covariances is an important component in functional data analysis. We propose a novel covariance smoothing method based on penalized splines and associated software. The proposed method is a bivariate spline smoother that is designed for covariance smoothing and can be used for sparse functional or longitudinal data. We propose a fast algorithm for covariance smoothing using leave-one-subject-out cross-validation. Our simulations show that the proposed method compares favorably against several commonly used methods. The method is applied to a study of child growth led by one of coauthors and to a public dataset of longitudinal CD4 counts.     

Boundary corrected cubic smoothing splines

Smoothing splines are known to exhibit a type of boundary bias that can reduce their estimation efficiency. In this paper, a boundary corrected cubic smoothing spline is developed in a way that produces a uniformly fourth order estimator. The resulting estimator can be calculated efficiently using an O(n) algorithm that is designed for the computation of fitted values and associated smoothing parameter selection criteria. A simulation study shows that use of the boundary corrected estimator can improve estimation efficiency in finite samples. Applications to the construction of asymptotically valid pointwise confidence intervals are also investigated .     

Automatic repeated-loess decomposition of data consisting of sums of oscillatory curves

Repeated loess is a nonparametric procedure that uses progressive smoothing and differencing to decompose data consisting of sums of curves. Smoothing is by locally weighted polynomial regression. Here the procedure was developed so that the decomposition into components was controlled automatically by the number of maxima in each component. The level of smoothing of each component was chosen to maximize the estimated probability of the observed number of maxima. No assumptions were made about the periodicity of components and only very weak assumptions about their shapes. The automatic procedure was applied to simulated data and to experimental data on human visual sensitivity to line orientation.An erratum to this article can be found at     

An algorithm for generalized monotonic smoothing

In this paper, an algorithm for Generalized Monotonic Smoothing (GMS) is developed as an extension to exponential family models of the monotonic smoothing techniques proposed by Ramsay (1988, 1998a,b). A two-step algorithm is used to estimate the coefficients of bases and the linear term. We show that the algorithm can be embedded into the iterative re-weighted least square algorithm that is typically used to estimate the coefficients in Generalized Linear Models. Thus, the GMS estimator can be computed using existing routines in S-plus and other statistical software. We apply the GMS model to the Down's syndrome data set and compare the results with those from Generalized Additive Model estimation. The choice of smoothing parameter and testing of monotonicity are also discussed.     

Using recursive algorithms for the efficient identification of smoothing spline ANOVA models

In this paper we present a unified discussion of different approaches to the identification of smoothing spline analysis of variance (ANOVA) models: (i) the “classical” approach (in the line of Wahba in Spline Models for Observational Data, 1990; Gu in Smoothing Spline ANOVA Models, 2002; Storlie et al. in Stat. Sin., 2011) and (ii) the State-Dependent Regression (SDR) approach of Young in Nonlinear Dynamics and Statistics (2001). The latter is a nonparametric approach which is very similar to smoothing splines and kernel regression methods, but based on recursive filtering and smoothing estimation (the Kalman filter combined with fixed interval smoothing). We will show that SDR can be effectively combined with the “classical” approach to obtain a more accurate and efficient estimation of smoothing spline ANOVA models to be applied for emulation purposes. We will also show that such an approach can compare favorably with kriging.     

Smoothing spline Gaussian regression: more scalable computation via efficient approximation

Summary.  Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O ( n ³), n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approximations that are asymptotically as efficient. A simple algorithm is presented and the Bayes model that is associated with the approximations is derived, with the latter guiding the porting of Bayesian confidence intervals. The practical choice of the dimension of the approximating space is determined through simulation studies, and empirical comparisons of the approximations with the exact solution are presented. Also evaluated is a simple modification of the generalized cross-validation method for smoothing parameter selection, which to a large extent fixes the occasional undersmoothing problem that is suffered by generalized cross-validation.     

Smoothing spline estimation in varying-coefficient models

Summary.  Smoothing spline estimators are considered for inference in varying-coefficient models with one effect modifying covariate. Bayesian 'confidence intervals' are developed for the coefficient curves and efficient computational methods are derived for computing the curve estimators, fitted values, posterior variances and data-adaptive methods for selecting the levels of smoothing. The efficacy and utility of the methodology proposed are demonstrated through a small simulation study and the analysis of a real data set.     

Nearest neighbor hazard estimation with left-truncated duration data

Duration data often suffer from both left-truncation and right-censoring. We show how both deficiencies can be overcome at the same time when estimating the hazard rate nonparametrically by kernel smoothing with the nearest-neighbor bandwidth. Smoothing Turnbull’s estimator of the cumulative hazard rate, we derive strong uniform consistency of the estimate from Hoeffding’s inequality, applied to a generalized empirical distribution function. We also apply our estimator to rating transitions of corporate loans in Germany.