Forecasting time series with increasing seasonal variation

Four options for modeling and forecasting time series data containing increasing seasonal variation are discussed, including data transformations, double seasonal difference models and two kinds of transfer function-type ARIMA models employing seasonal dummy variables. An explanation is given for the typical ARIMA model identification analysis failing to identify double seasonal difference models for this kind of data. A logical process of selecting one option for a particular case is outlined, focusing on issues of linear versus non-linear increasing seasonal variation, and the level of stochastic versus deterministic behavior in a time series. Example models for the various options are presented for six time series, with point forecast and interval forecast comparisons. Interval forecasts from data-transformation models are found to generally be too wide and sometimes illogical in the dependence of their width on the point forecast level. Suspicion that maximum likelihood estimation of ARIMA models leads to excessive indications of unit roots in seasonal moving-average operators is reported.     

Forecasting demand in international markets: The case of correlated time series

In this paper a data analysis tool for analyzing highly correlated time series data is suggested. The main objective is to unify multiple time series into a single series and then apply a univariate method for the purpose of prediction. This method is essentially efficient for analyzing multiple time series with sparse data. Several time series data of relative demand for black and white television receivers in various countries are analyzed and quite accurate predictions are obtained.     

Applications of time-series analysis in accounting: A review

This paper reviews research that makes use of one of the most popular forecasting methods applied in accounting: time-series analysis using the Box-Jenkins methodology. It organizes the research in the area, surveys recent applications of time-series analysis in accounting, and discusses the potential for the methodology in addressing future research issues. The emphasis is on those aspects of the accounting system that possibly cause difficulties in applying time-series methods in accounting.     

Forecasting system energy demand

This paper presents the results of the Electric Power Research Institute Short Range Forecasting Project (EPRI-SRF) performed by the Load Forecasts Department, Economics and Forecasts Division of Ontario Hydro, Ontario, Canada. In this study a variety of short-range forecasting techniques are applied to Ontario Hydro monthly data on total system energy demand. These techniques are available in a software package (FORECAST MASTER) developed for EPRI by two consultants—Scientific Systems, Inc. (SSI) and Quantitativ Economic Research, Inc. (QUERI). The methods used for this study were the univariate Box-Jenkins method, the multivariate state-space method, Bayesian vector autoregression and autoregress ve econometric regression. A comparison of the models developed show that the econometric models perform the best overall. The state-space models are more suitable for very short-term (one-step ahead) forecasts. Although the Box-Jenkins method has the advantage of simplicity in terms of estimation and data requirement, its performance was not as good as that of the others. Bayesian vector autoregresson results indicate that this program needs some modification for monthly data.     

民航客运量的ARIMA模型与预测

介绍了求和自回归移动平均(ARIMA)模型的一般表达方式,并提供了使用该模型进行建模和预报的一般过程,最后以某条航线的实测数据为例,进行实证分析,得到了8步的短期预报结果,其相对误差为0．08．     

乘积季节模型在储蓄存款预测中的应用

运用SPSS软件和SAS软件系统中的时间序列建模方法建立了我国城乡居民储蓄存款模型,并认为用最大似然估计法(ML)对结果进行短期预测,用无约束最小二乘估计法(ULS)对结果进行中长期预测,可得到较高的预测精度.     

Exponential smoothing: Estimation by maximum likelihood

In this paper several forecasting methods based on exponential smoothing with an underlying seasonal autoregressive-moving average (SARIMA) model are considered. The relations between the smoothing constants and the coefficients of the autoregressive and moving average polynomials are used. On that basis, a maximum likelihood procedure for parameter estimation is described. The approach rules out the need for initial smoothed values. Prediction intervals are also obtained as a by-product of the approach and a fast algorithm for implementing the method is outlined.     

A Comparison of Box—Jenkins and objective methods for determining the order of a non-seasonal ARMA Model

This paper evaluates different procedures for selecting the order of a non-seasonal ARMA model. Specifically, it compares the forecasting accuracy of models developed by the personalized Box-Jenkins (BJ) methodology with models chosen by numerous automatic procedures. The study uses real series modelled by experts (textbook authors) in the BJ approach. Our results show that many objective selection criteria provide structures equal or superior to the time-consuming BJ method. For the sets of data used in this study, we also examine the influence of parsimony in time-series forecasting. Defining what models are too large or too small is sensitive to the forecast horizon. Automatic techniques that select the best models for forecasting are similar in size to BJ models although they often disagree on model order.     

沪深A股综合指数的时间序列分析建模与预测

通过基于Box-Jenkins方法的时间序列分析技术,对中国沪、深A股综合指数的2000～2009年月收盘数据序列进行建模分析,验证了沪、深A股综合指数月收盘数据的时间序列特性,研究并选择了这两个序列的最佳ARMA模型,本文也通过模型对2010年的综合指数进行了预测.模型实证分析的结果表明：在股市综合指数时间序列分析建模与预测方面,Box-Jenkins方法及其模型是一种精度较高且切实有效的方法模型.     

基于时间序列模型的青藏铁路路基变形预测

为分析青藏铁路路基高程不规则变形,通过建立高程—时间响应模型,基于Box-Jenkins建模方法,确定时间序列模型阶数,根据AIC准则,选取适合的时间序列模型,最后给出批量预测全部路基测点高程的算法步骤。研究了青藏铁路路基高程随时间变形规律问题。结果表明：以2010年—2018年每月青藏铁路K1425+050处左侧路基高程数据为例,建立了ARMA(2,1,1)模型,并以2019年数据作为验证集,模型通过了模型适应性检验,证明了模型的有效性和准确性;总结了青藏铁路沿线各测点至2023年12月预测值中可能出现重大变形以及测点左右两侧路基高程差值出现较大差值的10个危险点;在测点K1476+600附近,路基两侧出现明显长距离的差异。可见本模型能准确预测青藏铁路路基高程的变化,对于工程养护维修具有一定借鉴意义。