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.     

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.     

Minimum Mean Squared Error Estimation of the Noise in Unobserved Component Models

In model-based estimation of unobserved components, the minimum mean squared error estimator of the noise component is different from white noise. In this article, some of the differences are analyzed. It is seen how the variance of the component is always underestimated, and the smaller the noise variance, the larger the underestimation. Estimators of small-variance noise components will also have large autocorrelations. Finally, in the context of an application, the sample autocorrelation function of the estimated noise is seen to perform well as a diagnostic tool, even when the variance is small and the series is of relatively short length.     

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.     

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.     

Concurrent Seasonal Adjustment With Census X-11

Much investigative effort is being expended worldwide toward improving seasonally adjusted estimates from the Census X-11 program. Several recent investigations have resulted in a recommendation to obtain the most recent month's adjustment by applying X-11 to data through that month (concurrent adjustment), rather than relying on projected factors obtained from an earlier run. Although there are theoretical arguments supporting the applicaton of X-11 concurrently, a comprehensive study documenting the results of concurrent adjustment with X-11 on U.S. economic series has not previously been undertaken. This study evaluates the effect of applying X-11 concurrently to a set of selected Census Bureau economic time series. The accuracy of concurrent estimates, in terms of mean absolute deviations from historical estimates, is examined. The results obtained are generally favorable to concurrent adjustment.     

Seasonal Adjustment of the Weekly Monetary Aggregates: A Model-Based Approach

A procedure is developed for seasonally adjusting weekly time series, based on a composite of regression and time series models. The procedure is applied to some weekly U.S. money supply series currently seasonally adjusted by the Federal Reserve.     

季节调整新方法及其原理研究

本文的主要工作是从频域的角度对季节调整中“季节滤子”的设计及估计问题进行研究。通过将直接信号提取（DSEF）方法引入到季节调整的应用之中,突破现有季节调整方法中仅能处理季度或月度数据的限制,且该方法下季节调整后的序列是理论季节调整后序列的“均方误差”最小估计。将DSEF方法应用于对中国季度进出口总额序列的季节调整分析中。分析结果显示,相比于X-11和SEATS方法,DSEF方法季节调整结果的离差较小且稳健性较好。     

Seasonal Adjustment of the Monetary Aggregates: Summary of the Federal Reserve's Committee Report

The Committee of Experts on Seasonal Adjustment Techniques was formed by the Federal Reserve Board to examine and make recommendations concerning the Board's procedures for seasonally adjusting the money supply and related series. This article summarizes the report of that committee.     

The Seasonal Adjustment Procedures for the Consumer Price Indexes: Some Empirical Results

Beginning with January of 1987, the consumer price indexes (CPI's) have been seasonally adjusted by the X-11 autoregressive integrated moving average (ARIMA) procedure. This modification of the X-11 procedure was introduced following an empirical investigation into three aspects of seasonal adjustment methodology as applied to several CPI series—the choice of ARIMA models to fit and forecast those series, the improvements made by the ARIMA modification in terms of revision and smoothness of the seasonally adjusted series, and the effect on the quality of seasonal adjustment and the identifiability of seasonality due to the ARIMA modification. This article reports the results of that investigation, in addition, a brief account is given of the U.S. Bureau of Labor Statistics procedures relating to the projected seasonal factors, seasonally adjusted aggregate series, and the revisions of the seasonally adjusted series.     

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.     

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.     

The Performance of Periodic Autoregressive Models in Forecasting Seasonal U.K. Consumption

The parameters of a periodic model are allowed to vary according to the time at which observations are made. Periodic autoregressive models are fitted to the quarterly values of seasonally unadjusted real nondurable consumers' expenditure for the United Kingdom and its components. The periodic model offers no improvement over conventional specifications if the aggregate is modeled directly. On the other hand, periodic models generally perform well for the components, which contain additional seasonal information. The choice between a periodic or nonperiodic specification is also shown to have an important influence on the resulting dynamic properties.     

Diagnostic Checking of Unobserved-Components Time Series Models

Diagnostic checking of the specification of time series models is normally carried out using the innovations—that is, the one-step-ahead prediction errors. In an unobserved-components model, other sets of residuals are available. These auxiliary residuals are estimators of the disturbances associated with the unobserved components. They can often yield information that is less apparent from the innovations, but they suffer from the disadvantage that they are serially correlated even in a correctly specified model with known parameters. This article shows how the properties of the auxiliary residuals may be obtained, how they are related to each other and to the innovations, and how they can be used to construct test statistics. Applications are presented showing how residuals can be used to detect and distinguish between outliers and structural change.     

季节调整方法的历史演变及发展新趋势

本文梳理了季节调整方法的历史演变过程,深入分析了当前季节调整方法的理论、实践的最新发展趋势,找出我国在季节调整理论研究和实践应用方面存在的差距,提出加强我国季节调整理论研究和实践应用的建议。     

基于季节调整的CPI统计环比指数研究

本文首先阐述了季节调整与统计环比指数的必要性,简要介绍了X-12-ARIMA与TRAMO/SEATS季节调整原理,然后运用X-12-ARIMA程序对中国1997年1月至2010年5月CPI月度数据进行季节调整,再运用TRAMO/SEATS方法解决季节调整程序中中国春节因素问题。接着由季节调整后的数据计算得到月环比CPI,对月环比CPI和同比增加率进行了比较,结果显示月环比CPI领先同比CPI。最后利用TRAMO/SEATS程序建立ARIMA模型（210）（011）进行了24个月的预测,预测结果显示,未来24个月内我国消费者物价指数温和上升,不会发生大的通货膨胀,但是存在一定的通胀压力。     

基于频域的X-13ARIMA-SEATS季节调整过滤器诊断

本文从频域角度对X-13ARIMA-SEATS季节调整程序的对称和并行过滤器进行研究,考察不同的模型非季节和季节移动平均参数和不同过滤器长度对平方增益函数和相位延迟函数的影响,并以中国采购经理人指数（PMI）和居民消费价格指数（CPI）季节序列诊断为例,从频域角度比较X-11和以ARIMA为基础的（AMB）方法的平方增益函数和相位延迟函数来选择更优的季节调整方法。得出的结论：①非季节移动平均参数增大时,两种过滤器平方增益函数有下降趋势,季节移动平均参数增大时,平方增益函数有上升趋势。长度较短的过滤器波动更剧烈,季节频率上波谷宽度更宽;②季节移动平均参数越大时,相位延迟函数震荡越剧烈,非季节移动平均参数越大时,季节频率上的相位延迟增大。单个非季节频率区间内相位延迟函数与平方增益函数有反向关系;③AMB方法在非季节频率区间上的增益函数比X-11方法更趋于1,过滤器的凹槽比X-11方法更窄,且频率分量的相位失真更小,在PMI季节调整中更好;X-11方法对称过滤器的平方增益函数更小且更趋于1,在非频率区间上的相位延迟函数比AMB方法更小,更适用CPI的季节调整。④与传统季节调整质量诊断相比,频域诊断在估计季节成分的稳定性和过滤器的延迟特性方面具有优势,在季节调整方法选择时可综合两方面的结论。     

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.     

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.     

Basic Issues on the Seasonal Adjustment of the Canadian Consumer Price Index

This study is mainly concerned with basic issues that arise in connection with the seasonal: adjustment of the Canadian Consumer Price Index when used as a current indicator of inflation. It analyzes the seasonal characteristics of the series and evaluates whether a direct or an indirect adjustment is preferred from the viewpoint of the degree of smoothness of the monthly rate of change. The use of ARIMA extrapolations versus no ARIMA extrapolations and the application of concurrent versus year-ahead seasonal factors are also discussed. The selection of the optimal procedure is made according to the degree of smoothness and size of the revisions of the seasonally adjusted monthly rate of change.