经济时间序列的灰色模型研究

经济时间序列的灰色模型研究广东商学院王泽日一、基本理论与方法对于实测的时间序列｛Ｘ（０）ｉ（ｔ）｝，（ｉ＝１，２，…，ｎ；ｔ＝１，２，…，ｍ），一般为随机的，将其累加处理，可获得新序列｛Ｘ（１）ｉ（ｔ）｝，其中｛Ｘ（１）ｉ（ｔ）｝＝ｔｋ＝１Ｘ（０）...     

自适应滤波在经济预测中的应用

自适应滤波在经济预测中的应用高健绪,顾岚一、自适应滤波及预测方法设｛Ｘｔ｝（ｔ＝１,２,．．．,Ｎ）是一个实际观测到的经济序列,不失一般性,可以认为它具有趋势性和季节性,我们可用长自回归模型ＡＲ（ｎ）对其进行拟合。式（１）中误差项｛εｔ｝是零均值白噪...     

区间赋值确定权数的方法

区间赋值确定权数的方法□东北财经大学博士白雪梅生活一点通金、银首饰可用烟灰或浓的热米汤擦试，使其恢复光亮这ｎ个子集叠加在一起，则形成覆盖在估计值轴上的一种分布，这种分布可用下式描述：Ｘ（Ｕｉ）＝１ｎ∑ｎｋ＝１Ｘ〔Ｕ（ｋ）１ｉ），Ｕ（ｋ）２ｉ〕（Ｕｉ）...     

关于期望寿命的估计

一、引言期望寿命又叫平均剩余寿命。设寿命 (或生存时间 )为Ｘ ,则在Ｘ >ｔ的条件下Ｘ -ｔ的期望ｅ =Ｅ(Ｘ -ｔ|Ｘ >ｔ)是期望寿命。设Ｘ的分布函数Ｆ(ｘ)是未知的 ,如何估计ｅｔ,这是保险精算、可靠性工程及生存分析等实际工作中很关心的问题。随机考察ｎ个个体 ,这些个体的寿命分别是ｘ1 ,ｘ2 ,… ,ｘｎ,他们被看作随机变量 ,相互独立 ,有相同的分布函数Ｆ(ｘ)。我们分别在一列时刻ａ0 =0 <ａ1<ａ2 <… <ａｍ 观测其寿命。令ａｍ + 1 =∞ ,Ｉｋ=(ａｋ,ａｋ + 1 ](ｋ =0 ,1,2 ,… ,ｍ)。考虑等距分组 ,即每个区间的长度都为ｈ ,ｈ =ａｋ +…     

折扣系数法在建立回归预测模型中的应用

一、折扣最小二乘法 在时间序列预测中，预测变量ｙ的变化主要依赖时间变量ｔ，它们之间具有相关关系 ｙ＝ｆ（ｔ）＋（此处，ｆ（ｔ）一般为ｔ的线性函数或可线性化的函数）。在确定它们之间的回归方程时，一般用最小二乘法。即对于给定的观测值（ｙＴ，ｔ）（ｔ＝１，２，…，ｎ），ｙｔ与ｔ之间满足关系式ｙｔ＝ｆ（ｔ）＋ｔ，需要确定ｆ（ｔ）中的参数，使Ｑ＝取到最小值。这里Ｑ＝对所有的观测点是同等对待的，为了体现近期观测值对未来预测值的影响大，远期观测值对未来预测值的影响小的特点，将不同观测值的误差平方给予不同的权重。…     

保险风险评估的一个模型

一、引言保险人对自身所经营风险的正确和全面的认识是保障稳健经营的前提。早在本世纪初 ( 190 3 )年 ,ＦｉｌｉｐＬｕｎｄｂｅｒｇ就奠定了古典风险分析理论的基础 ,但直到 1955年才由ＨａｒａｌｄＣｒａｍｅｒ[1]等人所完善。其古典风险模型可用如下的公式描述 :Ｓ(ｔ) =ｕ ｃｔ-ΣＮ (ｔ)ｋ =1Ｘｋ,其中ｕ是保险人为某一种或某一类风险的所准备的初始准备金 ,ｃ是费率 ,Ｎ (ｔ)是ｔ年之前的索赔个数 ,Ｘｋ 表示第ｋ次索赔的索赔额 ,因此Ｓ(ｔ)就表示ｔ年时保险人的盈余额。一个衡量保险公司经营好坏的重要指标就是盈余额Ｓ(ｔ)会不会达…     

“几个正数的算术平均数不小于它们的几何平均数”的证明

命题“几个正数的算术平均数不小于它们的几何平均数”在高中课本证明不等式时不可缺少的内容。可是课本上没有证明过程。下面我们利用数学归纳法来说明它。我们利用两种方法来证明命题“几个正数的算术平均数不小于它们的几何平均数”。 第一数学归纳法的内容： 设ｐ（ｎ）是一个含有自然数ｎ的命题，如果 （１）ｐ （ｎ）为ｎ＝ｎ０（ｎ０是命题成立的第一值）时成立． （２）在Ｐ（ｋ）成立的假定下，可以证明Ｐ（ｋ＋１）成立。那么Ｐ（ｎ）对任意自然数ｎ都成立。 下面我们利用此法来证明命题“ｎ个正数的算术平均数不小于它们的几何平…     

论多元函数全增量的统计分析

论多元函数全增量的统计分析杨启梓一、多元函数全增量统计分析的基本方法设Ｓ为一总指标,其值取决于ｎ个因素指标Ｘ１,Ｘ２,…,Ｘｎ,或者从数学上说,已知Ｓ是以ｘ１,ｘ２,…,ｘｎ为自变量的多元函数Ｓ＝ｆ（Ｘ１,Ｘ２,…,Ｘｎ）＝ｆ（Ｍ）当诸自变量由原值点...     

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:     

马氏链点值预测方法和时序分析预测方法的统计试验研究

基于绝对分布的马尔可夫链预测(ADMCP)方法、叠加马尔可夫链预测(SPMCP)方法和加权马尔可夫链预测(WMCP)方法在各种水文序列预测理论中得到了广泛的应用。然而,实际生活中仅仅预测出状态区间是不够的,文章给出了一种基于马氏链状态预测方法的点值预测方法,并将其与普遍接受的时间序列分析预测方法进行了基于统计试验的比较分析,得出了该方法在水文序列预测中较优的结论。     

Comparison of data analysis procedures for real-time nanoparticle sampling data using classical regression and ARIMA models

Real-time monitoring is necessary for nanoparticle exposure assessment to characterize the exposure profile, but the data produced are autocorrelated. This study was conducted to compare three statistical methods used to analyze data, which constitute autocorrelated time series, and to investigate the effect of averaging time on the reduction of the autocorrelation using field data. First-order autoregressive (AR(1)) and autoregressive-integrated moving average (ARIMA) models are alternative methods that remove autocorrelation. The classical regression method was compared with AR(1) and ARIMA. Three data sets were used. Scanning mobility particle sizer data were used. We compared the results of regression, AR(1), and ARIMA with averaging times of 1, 5, and 10?min. AR(1) and ARIMA models had similar capacities to adjust autocorrelation of real-time data. Because of the non-stationary of real-time monitoring data, the ARIMA was more appropriate. When using the AR(1), transformation into stationary data was necessary. There was no difference with a longer averaging time. This study suggests that the ARIMA model could be used to process real-time monitoring data especially for non-stationary data, and averaging time setting is flexible depending on the data interval required to capture the effects of processes for occupational and environmental nano measurements.     

Random Level-Shift Time Series Models,ARIMA Approximations,and Level-Shift Detection

The main purpose of this article is to assess the performance of autoregressive integrated moving average (ARIMA) models when occasional level shifts occur in the time series under study. A random level-shift time series model that allows the level of the process to change occasionally is introduced. Between two consecutive changes, the process behaves like the usual autoregressive moving average (ARMA) process. In practice, a series generated from a random level-shift ARMA (RLARMA) model may be misspecified as an ARIMA process. The efficiency of this ARIMA approximation with respect to estimation of current level and forecasting is investigated. The results of examining a special case of an RLARMA model indicate that the ARIMA approximations are inadequate for estimating the current level, but they are robust for forecasting future observations except when there is a very low frequency of level shifts or when the series are highly negatively correlated. A level-shift detection procedure is presented to handle the low-frequency level-shift phenomena, and its usefulness in building models for forecasting is demonstrated.     

Stationary persistent time series misspecified as nonstationary arima

Long-memory processes, such as Autoregressive Fractionally Integrated Moving-Average processes—ARFIMA—are likely to lead the observer to make serious misspecification errors. Nonstationary ARFIMA processes can easily be misspecified as ARIMA models, thus confusing a fractional degree of integration with an integer one. Stationary persistent ARFIMA processes can be misspecified as nonstationary ARIMA models, thus leading to a serious increase of out-of-sample forecast errors. In this paper, we discuss three prototypical misspecification cases and derive the corresponding increase in mean square forecasting error for different lead times.     

Predictive Accuracy Gain From Disaggregate Sampling in ARIMA Models

We compare the forecast accuracy of autoregressive integrated moving average (ARIMA) models based on data observed with high and low frequency, respectively. We discuss how, for instance, a quarterly model can be used to predict one quarter ahead even if only annual data are available, and we compare the variance of the prediction error in this case with the variance if quarterly observations were indeed available. Results on the expected information gain are presented for a number of ARIMA models including models that describe the seasonally adjusted gross national product (GNP) series in the Netherlands. Disaggregation from annual to quarterly GNP data has reduced the variance of short-run forecast errors considerably, but further disaggregation from quarterly to monthly data is found to hardly improve the accuracy of monthly forecasts.     

Statistical analysis of error for fourth-order ordinary differential equation solvers

We develop an autoregressive integrated moving average (ARIMA) model to study the statistical behavior of the numerical error generated from three fourth-order ordinary differential equation solvers: Milne's method, Adams–Bashforth method and a new method that randomly switches between the Milne and Adams–Bashforth methods. With the actual error data based on three differential equations, we desire to identify an ARIMA model for each data series. Results show that some of the data series can be described by ARIMA models but others cannot. Based on the mathematical form of the numerical error, other statistical models should be investigated in the future. Finally, we assess the multivariate normality of the sample mean error generated by the switching method.     

国债回购利率预测模型研究

以国债回购利率为研究对象，分别建立ARIMA及GARCH模型，并比较这两种模型的预测能力。研究结果表明：使用传统ARIMA模型，模型ARIMA（0，1，1）配适较好；使用GARCH模型，模型GARCH（2，3）配适效果较好。此外，虽然GARCH模型的预测置信区间的波动性比ARIMA模型要小，但ARIMA模型的预测置信区间更小一些，因此其预测能力比GARCH模型更强。     

A Bootstrap Test for Circular Data

In this article, variance stabilizing filters are discussed. A new filter with nice properties is proposed which makes use of moving averages and moving standard deviations, the latter smoothed with the Hodrick-Prescott filter. This filter is compared to a GARCH-type filter. An ARIMA model is estimated for the filtered GDP series, and the parameter estimates are used in forecasting the unfiltered series. These forecasts compare well with those of ARIMA, ARFIMA, and GARCH models based on the unfiltered data. The filter does not color white noise.     

Selection between models through multi-step-ahead forecasting

We develop and show applications of two new test statistics for deciding if one ARIMA model provides significantly better h-step-ahead forecasts than another, as measured by the difference of approximations to their asymptotic mean square forecast errors. The two statistics differ in the variance estimates used for normalization. Both variance estimates are consistent even when the models considered are incorrect. Our main variance estimate is further distinguished by accounting for parameter estimation, while the simpler variance estimate treats parameters as fixed. Their broad consistency properties offer improvements to what are known as tests of Diebold and Mariano (1995) type, which are tests that treat parameters as fixed and use variance estimates that are generally not consistent in our context. We show how these statistics can be calculated for any pair of ARIMA models with the same differencing operator.     

Forecasting Economic Time Series With Structural and Box-Jenkins Models: A Case Study

The basic structural model is a univariate time series model consisting of a slowly changing trend component, a slowly changing seasonal component, and a random irregular component. It is part of a class of models that have a number of advantages over the seasonal ARIMA models adopted by Box and Jenkins (1976). This article reports the results of an exercise in which the basic structural model was estimated for six U.K. macroeconomic time series and the forecasting performance compared with that of ARIMA models previously fitted by Prothero and Wallis (1976).     

Spectral properties of the concurrent and forecasting seasonal linear filters of the X-11-ARIMA method

This study analyzes the properties of the linear filters of the X-11-ARIMA seasonal adjustment method applied for current seasonal adjustment. It provides the general formula for the combined weights that result from the ARIMA model extrapolation filters with the X-11 seasonal-adjustment filters. The three cases studied correspond to the three ARIMA models automatically tested by the X-11-ARIMA program, namely, (0, 1, 1)(0, 1, 1), (0, 2, 2)(0, 1, 1), and (2, 1. 2)(0, 1,1). The parameter values chosen reflect different degrees of flexibility of the trend-cycle and seasonal components. It is shown that the X-11-ARIMA linear filters for current seasonal adjustment are very flexible; they change with both the ARIMA extrapolation model and its parameter values, contrary to those of the X-11 program, which are fixed for a given set of options.