Issues Involved With the Seasonal Adjustment of Economic Time Series

In the first part of this article, we briefly review the history of seasonal adjustment and statistical time series analysis in order to understand why seasonal adjustment methods have evolved into their present form. This review provides insight into some of the problems that must be addressed by seasonal adjustment procedures and points out that advances in modem time series analysis raise the question of whether seasonal adjustment should be performed at all. This in turn leads to a discussion in the second part of issues involved in seasonal adjustment. We state our opinions about the issues raised and review some of the work of other authors. First, we comment on reasons that have been given for doing seasonal adjustment and suggest a new possible justification. We then emphasize the need to define precisely the seasonal and nonseasonal components and offer our definitions. Finally, we discuss criteria for evaluating seasonal adjustments. We contend that proposed criteria based on empirical comparisons of estimated components are of little value and suggest that seasonal adjustment methods should be evaluated based on whether they are consistent with the information in the observed data. This idea is illustrated with an example.     

Issues Involved With the Seasonal Adjustment of Economic Time Series

In the first part of this article, we briefly review the history of seasonal adjustment and statistical time series analysis in order to understand why seasonal adjustment methods have evolved into their present form. This review provides insight into some of the problems that must be addressed by seasonal adjustment procedures and points out that advances in modern time series analysis raise the question of whether seasonal adjustment should be performed at all. This in turn leads to a discussion in the second part of issues invloved in seasonal adjustment. We state our opinions about the issues raised and renew some of the work of our authors. First, we comment on reasons that have been given for doing seasonal adjustment and suggest a new possible justification. We then emphasize the need to define precisely the seasonal and nonseasonal components and offer our definitions. Finally, we discuss our criteria for evaluating seasonal adjustments. We contend that proposed criteria based on empirical comparisons of estimated components are of little value and suggest that seasonal adjustment methods should be evaluated based on whether they are consistent with the information in the observed data. This idea is illustrated with an example.     

我国居民消费季节调整和节日效应测算

Bayes季节调整方法因有坚实的理论基础,调整效果优于其它方法等,目前正日益受到广泛的重视与应用。本文将Bayes季节调整模型引入国内,同时在模型中补充贸易日和闰年的影响。用R软件的Timsac包中的Bayesian程序实现对社会消费品零售额的季节调整和环比增长率测算,表明长期我国社会消费品零售总额具有稳定的指数增长趋势和U型季节特征,得到的月环比增长率反应灵敏。通过季节指数抛物线拟合,得到“五一”和“十一”节日经济效应和比例。总体上“五一”的节日效应显著,“十一”仍有正面效应,但影响不显著。     

中国季度GDP的季节调整：结构时间序列方法

 内容提要：本文利用结构时间序列方法讨论了中国季度GDP的季节调整问题,从季节单位根、季节自相关、周期自相关等多个方面对不同季节模式的调整结果进行了比较。结论认为,随机虚拟变量形式和三角函数形式得到的调整结果非常相似;结构时间序列方法更好地捕捉到了时变季节特征,明显优于X-11和SEATS方法;非高斯稳健季节调整的结果表明,高斯结构时间序列方法具有较好的稳定性。     

Maximum entropy extreme‐value seasonal adjustment

Some economic series in small economies exhibit meagre (i.e. non‐positive) values, as well as seasonal extremes. For example, agricultural variables in countries with a distinct growing season may exhibit both of these features. Multiplicative seasonal adjustment typically utilises a logarithmic transformation, but the meagre values make this impossible, while the extremes engender huge distortions that render seasonal adjustments unacceptable. To account for these features, we propose a new method of extreme‐value adjustment based on the maximum entropy principle, which results in replacement of the meagre values and extremes by optimal projections that utilise information from the available time series dynamics. This facilitates multiplicative seasonal adjustment. The method is illustrated in the New Zealand agricultural series.     

Multivariate Seasonal Adjustment,Economic Identities,and Seasonal Taxonomy

This article extends the methodology for multivariate seasonal adjustment by exploring the statistical modeling of seasonality jointly across multiple time series, using latent dynamic factor models fitted using maximum likelihood estimation. Signal extraction methods for the series then allow us to calculate a model-based seasonal adjustment. We emphasize several facets of our analysis: (i) we quantify the efficiency gain in multivariate signal extraction versus univariate approaches; (ii) we address the problem of the preservation of economic identities; (iii) we describe a foray into seasonal taxonomy via the device of seasonal co-integration rank. These contributions are developed through two empirical studies of aggregate U.S. retail trade series and U.S. regional housing starts. Our analysis identifies different seasonal subcomponents that are able to capture the transition from prerecession to postrecession seasonal patterns. We also address the topic of indirect seasonal adjustment by analyzing the regional aggregate series. Supplementary materials for this article are available online.     

A Survey of Recent Developments in Seasonal Adjustment

In recent years there have been notable advances in the methodology for analyzing seasonal time series. This paper summarizes some recent research on seasonal adjustment problems and procedures. Included are signal-extraction methods based on autoregressive integrated moving average (ARIMA) models, improvements in X–11, revisions in preliminary seasonal factors, regression and other model-based methods, robust methods, seasonal model identification, aggregation, interrelating seasonally adjusted series, and causal approaches to seasonal adjustment.     

基于平衡轮换样本调查的季节调整方法研究

传统季节调整方法对时间序列数据进行季节调整时,往往假定误差项为白噪声,不考虑其序列相关关系。为了进行更准确地季节调整分析,本文从连续性抽样调查的角度出发,研究基于平衡轮换样本调查的抽样误差对季节调整的影响,建立一般化的季节调整模型,利用卡尔曼滤波进行参数估计,并从预测误差、误差方差等角度评价模型精度。最后以中国城镇住户调查采用的12～0平衡轮换模式为例,对考虑抽样误差结构特征的季节调整模型进行实证分析,验证这套季节调整方法的有效性。     

季节异方差序列的季节调整问题研究

季节调整是从经济序列中剔除季节成分的重要方法。季节异方差的存在,使经典的季节调整方法无法彻底分离出季节成分,致使季节调整失败。本文针对季节异方差问题提出用于季节调整的改进的HS模型,并定义改进的HS模型构造季节异方差检验LR统计量,通过蒙特卡洛模拟方法分析该检验的检验尺度和检验功效。最后,利用我国税收总额月度序列给出实证分析,并通过对比考察了改进的HS模型方法季节调整的有效性。     

Time Series Properties of the German Production Index

Summary: The production index is an important indicator for assessing the cyclical state of the economy. Unfortunately, the monthly time series is contaminated by many noisy components like seasonal variations, calendar and vacation effects. Only part of those nuisance components are explicitly considered in the seasonal adjustment procedures used by statistical agencies. In this paper, we propose a more flexible specification for the seasonal and working day effects and introduce an indicator for the summer vacations effect. We allow for time-varying parameters and show that the resulting Unobserved Components Model delivers more reliable results for the trend and cycle components of the production index. * I am grateful to a referee and the participants of the ifo Lunchtime Seminar, the Pfingstkonferenz of the Deutsche Statistische Gesellschaft and the annual conference of the Verein für Socialpoltik for helpful comments.     

Seasonal Adjustment of Time Series Using One-Sided Filters

This article presents a model-based signal extraction seasonal adjustment procedure to extract estimates of the independent unobserved seasonal and nonseasonal components from an observed time series. The decomposition yields a one-sided filter that is optimal for adjusting the most recent observation under the assumption of using only the past observed series. Some advantages of this procedure are that no forecasts are required for implementation and there are no problems of revision of estimates or questions of concurrent adjustment. Comparisons are made with existing procedures using two-sided filters.     

The Surrogate Henderson Filters in X-11

This paper explains the surrogate Henderson filters that are used in the X-11 variant of the Census Method II seasonal adjustment program to obtain trends at the ends of time series. It describes a prediction interpretation for these surrogate filters, justifies an approximation to the filters, proposed by Kenny & Durbin (1982), and proposes a further interpretation of the results. The starting point for the paper is unpublished work by Musgrave (1964a, 1964b). His work has continuing relevance to current seasonal adjustment practice. This paper makes that work generally available for the first time, and reviews and extends it.     

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.     

On the nearly nonstationary seasonal time series

A time series is said to be nearly nonstationary if some of its characteristic roots are close to the unit circle. For a seasonal time series, such a notion of near-nonstationarity is studied in a double-array setting. This approach not only furnishes a natural transition between stationarity and nonstationarity, but also unifies the corresponding asymptotic theories in a seasonal-time-series context. The general theory is expressed in terms of functionals of independent diffusion processes. The asymptotic results have applications to estimation and testing in a nearly nonstationary situation and serve as a useful alternative to the common practice of seasonal adjustment.     

A Method for Seasonally Adjusting Time Series With Variation in the Seasonal Amplitude

The official seasonally adjusted figures of the unemployment series in the Netherlands proved to be unsatisfactory in the years 1976 until 1980 because of the occurrence of a residual seasonal pattern in the adjusted series. There is indication that this failure is due to the presence of variations in the seasonal amplitude of the unemployment series. To improve this unsatisfactory state of affairs further research on methods of seasonal adjustment was undertaken at the Netherlands Central Bureau of Statistics. The outcome, method CPBX11, combines features of two methods that have been used officially, CENSUS X-11 and CPB-1. Since December 1980 the Netherlands Central Bureau of Statistics has used CPBX11 to compute seasonally adjusted labor market series. In this article we review in short the literature on seasonal adjustment and compare the performance of the three procedures referred to above in adjusting the series Unemployment in Construction and Live Births (per 1,000 of the mean population) for the Netherlands. The CPBX11 method yields more satisfactory results, especially for the first series.     

Adjustment of provisional mortality series: the dynamic linear model with structured measurement errors

The authors "consider the problem of adjusting provisional time series using a bivariate structural model with correlated measurement errors. Maximum likelihood estimators and a minimum mean squared error adjustment procedure are derived for a provisional and final series containing common trend and seasonal components. The model also includes measurement errors common to both series and errors that are specific to the provisional series. [The authors] illustrate the technique by using provisional data to forecast ischemic heart disease mortality."     

Seasonal Adjustment Using Structural Time Series Models: An Application and a Comparison With the Census X-11 Method

This article makes the method of seasonal adjustment operational using suitable structural time series models (STM). This so-called STM method is applied to several relevant Dutch macro- economic quarterly and monthly time series. The results are compared with those of the Census X-11 method using several formal criteria as yardsticks. The STM method proves to compete well with the Census X-11 method in this respect.     

中国月度数据的季节调整：一个新方案

 本文针对中国特定的节假日效应和交易日效应对季节调整问题提出了新的方案,包括移动节假日效应（如春节、中秋节、清明节、端午节等）、黄金周效应、五天工作制效应等;论文利用新的调整方案对我国社会消费品零售总额的月度数据进行了季节调整,诊断结果表明,新方案能比较充分地提取各种季节特征;论文对我国季节调整问题提出了针对性建议。     

A comparison of indicators for evaluating x-11-arima seasonal adjustment

Summary The evaluation of the performance of seasonal adjustment procedures is an issue of practical importance in view of the unobservable nature of the components. Looking at just one indicator when judging the overall quality of a procedure may be misleading, even though this is common practice when many series are involved. The main purpose of this paper is to compare the information content of different synthetic indicators with reference to the X-11-ARIMA procedure. Sixty-six different types of monthly seasonal series are generated and the seasonal component then extracted by carrying out X-11-ARIMA with standard options. The correlation between the pseudo-true error for each series and various synthetic indicators allows us to compare the latter's reliability, under both the hypotheses of minimum and maximum variance of the pseudo-true seasonal component. We show that the overall quality indexQ-the indicator most commonly adopted by users of the X-11-ARIMA-is always outperformed by the simpler diagnostics based on the stability of the estimates. In particular, the “sliding-spans” indicator, proposed by Findley et al. (1990) and included in the diagnostics of the new X-12 procedure, shows a much stronger correlation with the pseudo-true error in the seasonal adjustment. We also show that the total forecasting errors in the one-year-ahead extrapolation of the seasonal component have a good informative power and perform almost as well as the “sliding-spans” indicator.     

Measures of Variability for Model-Based Seasonal Adjustment Procedures

An algorithm is derived that develops measures of variability for the estimates of the nonseasonal component computed from a model-based seasonal adjustment procedure. The measures of variability are developed from signal extraction theory. Properties of components of the variance are developed, and the behavior of the variance is investigated for one popular time series model. The results are illustrated by using real data.