Holt-Winters Forecasting: An Alternative Formulation Applied to UK Air Passenger Data

This paper provides a formulation for the additive Holt-Winters forecasting procedure that simplifies both obtaining maximum likelihood estimates of all unknowns, smoothing parameters and initial conditions, and the computation of point forecasts and reliable predictive intervals. The stochastic component of the model is introduced by means of additive, uncorrelated, homoscedastic and Normal errors, and then the joint distribution of the data vector, a multivariate Normal distribution, is obtained. In the case where a data transformation was used to improve the fit of the model, cumulative forecasts are obtained here using a Monte-Carlo approximation. This paper describes the method by applying it to the series of monthly total UK air passengers collected by the Civil Aviation Authority, a long time series from 1949 to the present day, and compares the resulting forecasts with those obtained in previous studies.     

An Application of Vector Time Series Techniques to Macroeconomic Forecasting

A wide variety of time series techniques are now used for generating forecasts of economic variables, with each technique attempting to summarize and exploit whatever regularities exist in a given data set. It appears that many researchers arbitrarily choose one of these techniques. The purpose of this article is to provide an example for which the choice of time series technique appears important; merely choosing arbitrarily among available techniques may lead to suboptimal results.     

基于传递函数的产品价格预测模型

对多变量时间序列进行预测,单变量ARIMA模型和普通多元回归分析并不适用,这种情况下应用多变量ARIMA即传递函数模型是很好的选择。以一种受原油和原材料多种因素影响的合成化纤产品为例,说明利用传递函数模型对其价格进行预测的建模过程中,如何进行模型识别、参数估计及诊断的有关问题。     

Inference and prediction with arma processes

An essential ingredient of any time series analysis is the estimation of the model parameters and the forecasting of future observations. This investigation takes a Bayesian approach to the analysis of time series by making inferences of the model parameters from the posterior distribution and forecasting from the predictive distribution.

The foundation of the approach is to approximate the condi-tional likelihood by a normal-gamma distribution on the parameter space. The techniques illustrated with many examples of ARMA processes.     

Modeling Interval Time Series with Space–Time Processes

We consider interval-valued time series, that is, series resulting from collecting real intervals as an ordered sequence through time. Since the lower and upper bounds of the observed intervals at each time point are in fact values of the same variable, they are naturally related. We propose modeling interval time series with space–time autoregressive models and, based on the process appropriate for the interval bounds, we derive the model for the intervals’ center and radius. A simulation study and an application with data of daily wind speed at different meteorological stations in Ireland illustrate that the proposed approach is appropriate and useful.     

Non-Gaussian Conditional Linear AR(1) Models

This paper gives a general formulation of a non-Gaussian conditional linear AR(1) model subsuming most of the non-Gaussian AR(1) models that have appeared in the literature. It derives some general results giving properties for the stationary process mean, variance and correlation structure, and conditions for stationarity. These results highlight similarities with and differences from the Gaussian AR(1) model, and unify many separate results appearing in the literature. Examples illustrate the wide range of properties that can appear under the conditional linear autoregressive assumption. These results are used in analysing three real datasets, illustrating general methods of estimation, model diagnostics and model selection. In particular, the theoretical results can be used to develop diagnostics for deciding if a time series can be modelled by some linear autoregressive model, and for selecting among several candidate models.     

Book Reviews

Books reviewed:
Janice Derr, Statistical Consulting: A Guide to Effective Communication
Helmet Lütkepohl, Handbook of Matrices
J.Y. Campbell, A.W. Lo & A.C. MacKinlay, The Econometrics of Financial Markets
Bo-Cheng Wei, Exponential Family Nonlinear Models
V. Ionescu & N. Limnios (eds.), Statistical and Probabilistic Models in Reliability
M. Bramson & R. Durrett (eds.), Perplexing Problems in Probability: Festschrift in Honor of Harry Kesten
John I. Marden, Analysing and Modeling Rank Data     

Missing data and forecasting in multivariate time series: An application of the common components dynamic linear model

Summary The paper deals with missing data and forecasting problems in multivariate time series making use of the Common Components Dynamic Linear Model (DLMCC), presented in Quintana (1985), and West and Harrison (1989). Some results are presented and discussed: exploiting the correlation between series, estimated by the DLMCC, the paper shows as it is possible to update state vector posterior distributions for the unobserved series. This is realized on the base of the updating of the observed series state vectors, for which the usual Kalman filter equations can be applied. An application concerning some Italian private consumption series provides an example of the model capabilities.     

Subsampling confidence intervals for parameters of atmospheric time series: block size choice and calibration

Problems of practical implementation of the computer intensive subsampling methodology are addressed by Monte Carlo simulations of a situation typical for atmospheric time series. The motivating data were collected under Lake-Effect Snow Studies Project in the winter of 1983–1984 over Lake Michigan. Certain enhancements of subsampling methodology are suggested specifically on the issue of optimal block size choice.     

Exact bootstrap confidence intervals for regression coefficients in small samples

ABSTRACT

Regression analysis is one of the important tools in statistics to investigate the relationships among variables. When the sample size is small, however, the assumptions for regression analysis can be violated. This research focuses on using the exact bootstrap to construct confidence intervals for regression parameters in small samples. The comparison of the exact bootstrap method with the basic bootstrap method was carried out by a simulation study. It was found that on a very small sample (n ≈ 5) under Laplace distribution with the independent variable treated as random, the exact bootstrap was more effective than the standard bootstrap confidence interval.     

Polynomial trends in time series

The J^* test which was previously proposed by the present author for the detection of a trend in a time series does not depend on any quantitative assumptions, but in the case of a polynomial trend it depends on its degree; if this degree is too high, the test cannot be applied. The author finds a bound of the significance level at which the test can be applied when the sample size, as well as a bound of the degree of the trend, are given. Asymptotic results are used only when we trust the asymptotic distribution of J^* under the null hypothesis.     

基于小波分析的基金净值预测模型

基于小波分析提出了一种基金净值预测模型。此模型利用小波分析理论用改进的小波阈值去噪方法对基金净值数据进行去噪处理,再对经过去噪处理后得到的较为平稳的数据,利用计量经济学中时间序列自回归模型进行短期预测。研究证明：该预测模型能较好地预测基金净值的短期趋势,预测结果优于传统的基金净值预测模型。     

Statistical Issues in Weather Forecasting*

Research and operational applications in weather forecasting are reviewed, with emphasis on statistical issues. It is argued that the deterministic approach has dominated in weather forecasting, although weather forecasting is a probabilistic problem by nature. The reason has been the successful application of numerical weather prediction techniques over the 50 years since the introduction of computers. A gradual change towards utilization of more probabilistic methods has occurred over the last decade; in particular meteorological data assimilation, ensemble forecasting and post‐processing of model output have been influenced by ideas from statistics and control theory.     

Transparency in Structural Research

Abstract

We propose a formal definition of transparency in empirical research and apply it to structural estimation in economics. We discuss how some existing practices can be understood as attempts to improve transparency, and we suggest ways to improve current practice, emphasizing approaches that impose a minimal computational burden on the researcher. We illustrate with examples.     

经济预测中的Monte Carlo模拟及方差控制——以国际石油价格预测为例

从MDnte Carlo模拟的实现过程入手，首先通过对Monte Carlo方法原理的阐述来介绍该种方法。进一步结合具体的实例通过计算机进行模拟来解释Monte Carlo方法的具体实现过程。重点讨论在选择合理的数据生成过程的前提下，如何在Monte Carlo方法中减少模拟方差，从而提高估计精度，更好地应用这种方法来进行经济预测。     

The Prediction of Time Series With Trends and Seasonalities

A maximization of the expected entropy of the predictive distribution interpretation of Akaike's minimum AIC procedure is exploited for the modeling and prediction of time series with trend and seasonal mean value functions and stationary covariances. The AIC criterion best one-step-ahead and best twelve-step-ahead prediction models can be different. The different models exhibit the relative optimality properties for which they were designed. The results are related to open questions on optimal trend estimation and optimal seasonal adjustment of time series.     

Age,Trend, and Cohort Effects in a Macro Model of Canadian Expenditure Patterns

A quadratic almost ideal demand system allowing for age, cohort, and trend effects is developed at the macro level. The model is estimated by maximum likelihood, using a three-tier iterative/search method applied to pooled 1961–1992 time series for five regions of Canada and six categories of expenditure. Hypothesis tests indicate support for the model specification. Elasticities are compared with those reported in other studies, with special attention to food. Effects of demographic and trend variables on elasticities and expenditure shares are investigated. An overall conclusion is that such effects can be very important in a macro demand system.     

国内删失数据统计研究状况综述

研究了国内在线性回归模型、非线性回归模型、半参数回归、非参数回归、单指标回归、生存分析、时间序列分析、密度估计等领域删失数据统计研究状况。     

On time-irreversibility and other non-linear features in time series

Time-irreversibility, asymmetry of the distribution, and the occurrence of sudden bursts are considered, amongst others, as non-linear features in time series modeling. The implication is often made that time series showing these features must be analyzed using non-linear models. In contrast, this paper shows that time-irreversible asymmetric time series showing certain types of sudden bursts may be generated by linear models with adequate input sequences. Thus some non-linear time series features may be caused by the pattern in the input sequence rather than by non-linearity in the model. Examples are considered to illustrate the situation.     

时间分层组合预测法的改进及其在进口贸易中的应用

针对现有时间分层组合预测法中协方差估计存在的不足,提出一种Shrinkage方法对协方差进行修正,以增强协方差估计的稳定性。Monte Carlo模拟结果表明:Shrinkage时间分层组合预测法的预测准确性较现有方法有所提高,且对季节因素不敏感;将该方法应用于中国进口贸易的预测中,结果显示新方法可显著提升各层预测效果,且对较高层序列的调整效果更佳;Shrinkage分层组合预测法能为海关等相关部门提供一种可针对不同时间维度进行同时性预测的新思路。