Seasonal adjustment perspectives on “Damping seasonal factors: shrinkage estimators for the X-12-ARIMA program”

We examined the shrinkage methods of Miller and William from the perspective of seasonal adjustment rather than forecasting, restricting attention to their performance on the approximately 500 of the 1428 M3 series that are seasonal and have multiplicative seasonality. Local shrinkage improved the quality of the seasonal adjustment of enough of these series that almost 50% have acceptable automatic X-12-ARIMA adjustments, instead of 40% with no shrinkage. For a few series, global shrinkage produced demonstrably incorrect results, and for some of these series and also others improved by local shrinkage, the SEATS seasonal adjustment provided by an experimental version of X-12-ARIMA offered still greater improvements. No benefits were observed from global shrinkage.     

Damping seasonal factors: Shrinkage estimators for the X-12-ARIMA program

We examine the effect of damping X-12-ARIMA's estimated seasonal variation on the accuracy of its seasonal adjustments of time series. Two methods for damping seasonals are proposed. In a simulation experiment, we generated time series data for each of 90 distinct experimental conditions that, in aggregate, characterize the variety of monthly series in the M3-competition. X-12-ARIMA consistently overestimated the actual seasonal variation by an amount consistent with statistical theory. Damping seasonals reduced X-12-ARIMA's estimation error by as much as 79% and under no conditions was estimation error increased beyond a trivial amount. Improvement depended primarily on the degree to which random variation in a series dominated seasonal variation. When the multiplicative X-12-ARIMA model did not match the data-generating model, overestimation was less for trend series than for series with no trend; otherwise the presence of trend had no discernible effect. One of the proposed methods was somewhat more accurate and robust, but more complex, than the other. In an analysis of real data—the 1428 monthly series of the M3-competition-damping X-12-ARIMA seasonals prior to forecasting (1) reduced the average forecasting MAPE by 4.9–1.4% and (2) improved forecasting accuracy for 59–65% of the series, depending on the forecasting horizon. This research suggests that damping X-12-ARIMA seasonals leads to more accurate seasonal adjustments of time series, thus providing a more reliable basis for policy-making, forecasting, and the evaluation of forecasting methods by researchers.     

X-12-ARIMA中调整类似春节效应的模型研究及应用

由于X-12-ARIMA只根据美国的假日情况设定了复活节、劳动节和感恩节三种移动假日效应的调整,其调整方法不适用中国特有的类似春节效应的调整。因此,本文针对中国现有的类似春节效应调整模型中存在的局限性,构建了扩展的L-Z模型体系,并与X-12-ARIMA程序相结合,形成了一套具有中国特色的调整方案。同时利用新的调整方案对中国工业增加值中存在的类似春节效应进行了有效调整,得到的经季节调整数据可以更好地满足经济分析的要求。对X-12-ARIMA进行本地化改造后,不但应用效果更好,而且应用范围也更加广泛。     

如何对中国CPI进行季节调整——基于X-12-ARIMA方法的改进

本文基于X-12-ARIMA方法,针对中国CPI存在的类似春节等移动假日效应调整问题,得到改进的X-12-ARIMA-BHG和X-12-ARIMA-LZ方法,利用改进的方法进行季节调整可更加准确地反映中国CPI的基本发展趋势。同时利用改进的方法对2010年12月至2011年6月份的中国CPI进行预测,得到了具有指导意义的预测结果。     

Empirical evidence on individual, group and shrinkage seasonal indices

This paper provides empirical evidence on forecasting seasonal demand using both individual and group seasonal indices methods. The findings show that the group seasonal indices methods outperform the individual seasonal indices method. This paper also offers empirical results from comparing two shrinkage methods with the group seasonal indices methods. The theoretical rules developed by the authors for choosing between group seasonal indices and individual seasonal indices produce more accurate forecasts than do published rules for choosing between shrinkage methods, when measured by the MSE, and are competitive when measured by the symmetric MAPE.     

Shrinkage estimators of time series seasonal factors and their effect on forecasting accuracy

This paper shows that forecasting accuracy can be improved through better estimation of seasonal factors under conditions for which relatively simple methods are preferred, such as relatively few historical data, noisy data, and/or a large number of series to be forecasted. In such situations, the preferred method of seasonal adjustment is often ratio-to-moving-averages (classical) decomposition. This paper proposes two shrinkage estimators to improve the accuracy of classical decomposition seasonal factors. In a simulation study, both of the proposed estimators provided consistently greater accuracy than classical decomposition, with the improvement sometimes being dramatic. The performances of the two estimators depended on characteristics of the series, and guidelines were developed for choosing one of them under a given set of conditions. For a set of monthly, M-competition series, greater forecasting accuracy was achieved when either of the proposed methods was used for seasonal adjustment rather than classical decomposition, and the greatest accuracy was achieved by following the guidelines for choosing a method.     

Time Series Analysis of Repeated Surveys: The State–space Approach

Cross sectional estimates from repeated surveys form a time series { y_t }. These estimates can be viewed as the sum y _t = Y _t + e _t of two processes, { Y _t }, the population process and { e _t }, the survey error process. Serial correlations in the latter series are usually present, mainly due to sample overlap. Other sources of data such as censuses, administrative records and demographic population counts are also available. The state–space modelling approach to the analysis of repeated surveys allows combining information from different sources, incorporating benchmarking constraints in a natural way. Results from these methods seem to compare favourably with those from X-11-ARIMA in filtering out survey errors.     

Comparison of seasonal estimation methods in multi-item short-term forecasting

This paper addresses the issue of estimating seasonal indices for multi-item, short-term forecasting, based upon both individual time series estimates and groups of similar time series. This development of the joint use of individual and group seasonal estimation is extended in two directions. One class of methods is derived from the procedures developed for combining forecasts. The second employs the general class of Stein Rules to obtain shrinkage estimates of seasonal components. A comparative evaluation has been undertaken of several versions of these methods, based upon a sample of retail sales data. The results favour these newly developed methods and provide some interesting insights for practical implementation.     

How does(n't) Urban Shrinkage get onto the Agenda? Experiences from Leipzig,Liverpool, Genoa and Bytom

This article discusses the question of how urban shrinkage gets onto the agenda of public‐policy agencies. It is based on a comparison of the agenda‐setting histories of four European cities, Liverpool (UK), Leipzig (Germany), Genoa (Italy) and Bytom (Poland), which have all experienced severe population losses but show very different histories with respect to how local governments reacted to them. We use the political‐science concepts of ‘systemic vs. institutional agendas’ and ‘policy windows’ as a conceptual frame to compare these experiences. The article demonstrates that shrinkage is hardly ever responded to in a comprehensive manner but rather that policies are only implemented in a piecemeal way in selected fields. Moreover, it is argued that variations in institutional contexts and political dynamics lead to considerable differences with regard to the chances of making shrinkage a matter of public intervention. Against this background, the article takes issue with the idea that urban shrinkage only needs to be ‘accepted’ by policymakers who would need to overcome their growth‐oriented cultural perceptions, as has been suggested in a number of recent writings, and calls for a more differentiated, context‐sensitive view.     

Outlier‐Robust Bayesian Multinomial Choice Modeling

A Bayesian method for outlier‐robust estimation of multinomial choice models is presented. The method can be used for both correlated as well as uncorrelated choice alternatives and guarantees robustness towards outliers in the dependent and independent variables. To account for outliers in the response direction, the fat‐tailed multivariate Laplace distribution is used. Leverage points are handled via a shrinkage procedure. A simulation study shows that estimation of the model parameters is less influenced by outliers compared to non‐robust alternatives. An analysis of margarine scanner data shows how our method can be used for better pricing decisions. Copyright © 2015 John Wiley & Sons, Ltd.     

汽车用改性聚丙烯收缩率的影响因素探讨

本文重点研究弹性体,PE,无机刚性粒子填料,成核剂以及注塑工艺对聚丙烯(PP)成型收缩率的影响。结果表明添加改性剂可大幅度降低聚丙烯成型收缩率,随着添加量的增加收缩率逐渐减小,另外无机刚性粒子的添加对聚丙烯成型收缩率影响最明显,弹性体、PE及成核剂的添加也能降低聚丙烯的收缩率;改变注塑工艺可以调整聚丙烯成型收缩率,降低注射温度、延长注射时间、提高注塑压力和速率可降低聚丙烯成型收缩率。     

Measurement errors and outliers in seasonal unit root testing

Seasonal and non-seasonal data are frequently observed with noise. For instance, the time series can have irregular abrupt changes and interruptions following as a result of additive or temporary change outliers caused by external circumstances. Equally, the time series can have measurement errors. In this paper we analyse the above types of data irregularities on the behavior of seasonal unit root tests. Outliers and measurement errors can seriously affect seasonal unit root inference and it is shown how the distortion of the tests will depend upon the frequency, magnitude, and persistence of the outliers as well as on the signal to noise ratio associated with measurement errors. Some solutions to the implied inference problems are suggested and shown to work in practice.     

Instrumental variable estimation in the presence of many moment conditions

This paper develops shrinkage methods for addressing the “many instruments” problem in the context of instrumental variable estimation. It has been observed that instrumental variable estimators may behave poorly if the number of instruments is large. This problem can be addressed by shrinking the influence of a subset of instrumental variables. The procedure can be understood as a two-step process of shrinking some of the OLS coefficient estimates from the regression of the endogenous variables on the instruments, then using the predicted values of the endogenous variables (based on the shrunk coefficient estimates) as the instruments. The shrinkage parameter is chosen to minimize the asymptotic mean square error. The optimal shrinkage parameter has a closed form, which makes it easy to implement. A Monte Carlo study shows that the shrinkage method works well and performs better in many situations than do existing instrument selection procedures.     

Cross Validation Calibration Based Shrinkage – Revisited for the Construction of Prognostic Indices

The use of shrinkage methods for the construction of prognostic indices has been paid increasing attention in the literature on medical statistics in the last years. One approach for the construction of a shrinkage factor is cross validation calibration as suggested by van H ouwelingen and le C essie (1990). We investigate this approach in more detail. First we try to clarify why shrinkage factors constructed by cross validation calibration tend to be smaller than 1. Second we explain why use of this shrinkage factor can result in an improvement of the average prediction error. Third we investigate the possible gain for constellations relevant in medical research by means of a simulation study, focusing on the dilemma, that the improvement on average has to be paid by distinct deteriorations for some patients. Finally we conclude that it is necessary to rethink the choice of loss functions in constructing prognostic indices before recommendations about the use of shrinkage methods can be made.     

Shrinkage estimation of semiparametric multiplicative error models

Within models for nonnegative time series, it is common to encounter deterministic components (trends, seasonalities) which can be specified in a flexible form. This work proposes the use of shrinkage type estimation for the parameters of such components. The amount of smoothing to be imposed on the estimates can be chosen using different methodologies: Cross-Validation for dependent data or the recently proposed Focused Information Criterion. We illustrate such a methodology using a semiparametric autoregressive conditional duration model that decomposes the conditional expectations of durations into their dynamic (parametric) and diurnal (flexible) components. We use a shrinkage estimator that jointly estimates the parameters of the two components and controls the smoothness of the estimated flexible component. The results show that, from the forecasting perspective, an appropriate shrinkage strategy can significantly improve on the baseline maximum likelihood estimation.     

Bayesian doubly adaptive elastic-net Lasso for VAR shrinkage

We develop a novel Bayesian doubly adaptive elastic-net Lasso (DAELasso) approach for VAR shrinkage. DAELasso achieves variable selection and coefficient shrinkage in a data-based manner. It deals constructively with explanatory variables which tend to be highly collinear by encouraging the grouping effect. In addition, it also allows for different degrees of shrinkage for different coefficients. Rewriting the multivariate Laplace distribution as a scale mixture, we establish closed-form conditional posteriors that can be drawn from a Gibbs sampler. An empirical analysis shows that the forecast results produced by DAELasso and its variants are comparable to those from other popular Bayesian methods, which provides further evidence that the forecast performances of large and medium sized Bayesian VARs are relatively robust to prior choices, and, in practice, simple Minnesota types of priors can be more attractive than their complex and well-designed alternatives.     

Shrinkage Estimation Strategies in Generalised Ridge Regression Models: Low/High-Dimension Regime

In this study, we suggest pretest and shrinkage methods based on the generalised ridge regression estimation that is suitable for both multicollinear and high-dimensional problems. We review and develop theoretical results for some of the shrinkage estimators. The relative performance of the shrinkage estimators to some penalty methods is compared and assessed by both simulation and real-data analysis. We show that the suggested methods can be accounted as good competitors to regularisation techniques, by means of a mean squared error of estimation and prediction error. A thorough comparison of pretest and shrinkage estimators based on the maximum likelihood method to the penalty methods. In this paper, we extend the comparison outlined in his work using the least squares method for the generalised ridge regression.     

An extended review of the X11ARIMA seasonal adjustment package

The revised version of X11ARIMA, Statistics Canada's seasonal adjustment package, is reviewed. The 1988 package, available for PCs as well as mainframes, is easy to use and more flexible than the 1980 version. New features reflecting research by Estela Dagum and her colleagues are highlighted. Comparisons are made with some other available X-11 programs.     

混凝土的自缩性研究

混凝土的自干燥必将引起混凝土宏观体积的减小,这种现象被称为混凝土的自缩(self-desiccation shrinkage or autogenous shrinkage)。由于混凝土的自缩与混凝土的早期开裂现象关系紧密,因此有必要对混凝土的自缩性能加以研究。     

The effect of seasonal adjustment on the properties of business cycle regimes

We study the impact of seasonal adjustment on the properties of business cycle expansion and recession regimes using analytical, simulation and empirical methods. Analytically, we show that the X‐11 adjustment filter both reduces the magnitude of change at turning points and reduces the depth of recessions, with specific effects depending on the length of the recession. A Monte Carlo analysis using Markov‐switching models confirms these properties, with particularly undesirable effects in delaying the recognition of the end of a recession. However, seasonal adjustment can help to clarify the true regime when this is well underway. These results continue to hold when a seasonally non‐stationary process with regime‐dependent mean is misspecified as one with deterministic seasonal effects. The empirical findings, based on four coincident US business cycle indicators, reinforce the analytical and simulation results by showing that seasonal adjustment leads to the identification of longer and shallower recessions than obtained using unadjusted data. Copyright © 2008 John Wiley & Sons, Ltd.