In Defence of Model-Based Seasonal Adjustment: An Illustration Using Australian Data

It is argued that the X-11 seasonal adjustment procedure suffers from severe drawbacks, and so it should be abandoned in favour of model-based seasonal adjustment. Furthermore, it is argued that Harvey's structural time series model is superior to the conventional seasonal ARIMA models for the purpose of model-based seasonal adjustment. It is shown, with the help of a large number of Australian time series, that the nature of seasonality differs from one series to another, and this is why model selection is crucial for seasonal adjustment. It is further shown that model-based seasonal adjustment could produce results that are significantly different from those obtained by applying the X-11 procedure. Since the X-11 procedure is not based on an explicit model and in view of its other serious drawbacks, it is concluded that the procedure should be abandoned in favour of model-based seasonal adjustment.     

实际经济时间序列的计算、季节调整及相关经济含义

本文首先讨论了计算中国实际经济时间序列的不同做法 ,并分析了其对季节调整的影响 ,指出通过同比增长率计算实际变量并进行季节调整是一个可以接受的做法 ,可以得到非常接近真实的季调后序列 ,并且在中国现有数据资源的限制下拥有一些特别的优势。然后本文具体讨论了对几个不同经济变量进行季节调整的方法 ,并给出了一些在经济数据分析与预测中的简单应用。方法的关键是采用regARIMA模型 ,从而可以对工作日变化、放长假、春节因素等作出一个估计和调整。作为一个副产品 ,本文引荐了一个相对较新的季节调整程序 (方法 ) ,TRAMO SEATS ,简单介绍了它的原理和优势 ,希望今后能得到更广泛的应用。     

Seasonal adjustment,demography, and GDP growth

Seasonal adjustment removes the predictable seasonal variation in GDP. If there is seasonal variation in factor inputs, then seasonal adjustment factors may be correlated with those inputs. This correlation can obscure statistically the importance of those inputs for GDP. This effect is apparent for the demographic composition of the labour force for Canada. Seasonal adjustment also changes the time‐series properties of GDP. Accounting for the seasonal pattern and trend change in demography suggests that the period of reduced volatility in GDP growth for Canada, the ‘Great Moderation,’ can be traced to the changing demographic structure of the labour force.     

Outlier detection and seasonal adjustment

By analysing three macroeconomic time series, namely retail sales, purchases of durables and of cars, we show the consequences of the presence of outliers in the data on the outcome of model-based seasonal adjustment. For all three series, we detect substantial negative effects for the resulting seasonally adjusted figures.In a recent paper,Thury — Wüger (1992) demonstrated that the presence of outliers in economic data has serious negative effects for time series modelling. Poorly estimated ARIMA models with an unsatisfactory forecasting performance are the consequence. Beyond that, we suspect that outliers may also cause problems for seasonal adjustment. Since seasonally adjusted data play a prominent role in applied economic research, it seems worthwhile to investigate this problem more deeply. Analysing the same three series as in the above mentioned paper, namely retail sales, purchases of durables and of cars which, as we know, are severely contaminated by outliers, we try to derive the consequences of the existence of outliers in the data for seasonal adjustment. Where monthly observations of our considered data exist, we also enclose calendar effects in the modelbased seasonal adjustment procedure.

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Zusammenfassung Die Existenz von Ausreißern in ökonomischen Zeitreihen führt zu schlecht spezifizierten Zeitreihenmodellen mit verzerrten Parameterschätzwerten. Verwendet man solche Modelle als Ausgangspunkt für eine auf Modellansatz basierende Saisonbereinigung, so erhält man sehr unverläßliche, mit starken Zufallsschwankungen behaftete Ergebnisse.

     

Masking of volatility by seasonal adjustment methods

We report that the X-12 ARIMA and TRAMO–SEATS seasonal adjustment methods consistently underestimate the variability of the differenced seasonally adjusted series. We show that underestimation is due to a non-zero estimation error in estimating the seasonal component at each time period, which is the result of the use of low order seasonal filter in X12-ARIMA for estimating the seasonal component. Hence, we propose the use of high order seasonal filter for estimating the seasonal component, which helps reducing the estimation error noticeably, helps amending the underestimation problem, and helps improving the forecasting accuracy of the series. In TRAMO–SEATS, Airline model is found to deliver the best seasonal filter among other ARIMA models.     

Seasonality in macroeconomic time series

Recently, the seasonal characteristics of macroeconomic time series have drawn a lot of attention. It has been argued that the seasonal component of many macroeconomic time series constitutes a major part of the series measured as a proportion of the variance. In addition it has been found that the seasonal component of most macroeconomic time series is constant and best “explained” by seasonal dummies. Specifically it is often found that a Christmas boom is followed by a beginning of the year trough. Based on quarterly and monthly macroeconomic time series from a large number of countries this paper shows that many macroeconomic time series have seasonal components that are changing over time. Furthermore, the Christmas boom and especially the 1st quarter trough is not found nearly as often as one might expect.     

The use of ARIMA models in seasonal adjustment

This paper compares the traditional Census X-11 method for seasonal adjustment with two recent alternative methods using ARIMA models, viz. X-11 ARIMA and Burman's signal extraction method. No strong preference results for one of these methods when applied to a number of macro-economic time series for the Netherlands.     

"假日经济"与居民消费——来自季节调整的证据

本文采用季节调整的方法,通过考察"五一"、"十一"长假制度实施前后季节模式的变迁,定量测算了"假日经济"对居民消费的影响以及春节的移动假日效应,结果显示"假日经济"实际上更多的是有限的消费在不同时期间的转移和替代.居民收入增长缓慢,以及未来预期的不确定性是制约居民消费的关键因素.     

Testing for Seasonal Stability in Unemployment Series: International Evidence

Recently, it has been shown that seasonal and business cycles are related and a similar economic mechanism is at work in producing both types of cycles (Miron 1996). Thus, an analysis of seasonal fluctuations sheds light on the nature of the business cycle. This paper uses the classical test developed by Hylleberg et al. and the LM-type tests proposed by Canova and Hansen (1995) to investigate seasonal behavior in the unemployment series of Australia, Canada, Japan, New Zealand, the US and a number of OECD countries. The main findings are that the Australian, Austrian and Canadian series are non-stationary at all seasonal frequencies, French, Japan, the NZ and the UK series are stationary at all seasonal frequencies and the USA series is stationary only at the annual frequency. The test results for other series are mixed, suggesting that further analysis is required to reach a definite conclusion. The series, except for France, Japan, New Zealand and the UK, appear to possess unstable seasonal patterns, indicating changing business cycle conditions.     

季节时间序列理论发展综述

随着社会的进步,统计数据由过去的年度数据变为如今的季度、月度和日度数据,有些以实时交易为基础的超高频金融数据达到了按秒为间隔的频率,这些数据被称为季节时间序列。季节时间序列研究已经成为近十年来经济计量学和统计学中的热点,Joumal of Econometrics（1993,volume 55）就此问题进行了专题讨论。本文按照历史发展顺序对季节性时间序列理论进行了系统地介绍,并对这一领域的前沿热点问题进行了评述和展望。     

Seasonality and Markov switching in an unobserved component time series model

It is generally acknowledged that the growth rate of output, the seasonal pattern, and the business cycle are best estimated simultaneously. To achieve this, we develop an unobserved component time series model for seasonally unadjusted US GDP. Our model incorporates a Markov switching regime to produce periods of expansion and recession, both of which are characterized by different underlying growth rates. Although both growth rates are time-varying, they are assumed to be cointegrated. The analysis is Bayesian, which fully accounts for all sources of uncertainty. Comparison with results from a similar model for seasonally adjusted data indicates that the seasonal adjustment of the data significantly alters several aspects of the full model. First Version Received: January 2001/Final Version Received: February 2002 Send offprint requests to: Rob Luginbuhl?Correspondence to: Rob Luginbuhl     

Modelling trigonometric seasonal components for monthly economic time series

The basic structural time series model has been designed for the modelling and forecasting of seasonal economic time series. In this article, we explore a generalization of the basic structural time series model in which the time-varying trigonometric terms associated with different seasonal frequencies have different variances for their disturbances. The contribution of the article is two-fold. The first aim is to investigate the dynamic properties of this frequency-specific Basic Structural Model (BSM). The second aim is to relate the model to a comparable generalized version of the Airline model developed at the US Census Bureau. By adopting a quadratic distance metric based on the restricted reduced form moving-average representation of the models, we conclude that the generalized models have properties that are close to each other compared to their default counterparts. In some settings, the distance between the models is almost zero so that the models can be regarded as observationally equivalent. An extensive empirical study on disaggregated monthly shipment and foreign trade series illustrates the improvements of the frequency-specific extension and investigates the relations between the two classes of models.     

Intertemporal nonseparability,liquidity constraints,and seasonality of aggregate consumer expenditures: An empirical investigation

The paper proposes a simple framework for intertemporal nonseparability in consumer preferences. It relies on the distinction between consumption and expenditures. As only the latter are observable, a technology is postulated which gives current consumption as a weighted sum of current and past expenditures. The Euler equations of the modified maximization problem place restrictions on the autoregressive process of consumption and the real interest rate. Superimposing this model with an explicit seasonal model, results in a bivariate ARMA representation. Having investigated the issue of identification, the model is tested empirically by time series data on Austria. The main results of this investigation are. First, nonseparability is indeed an important element in characterizing aggregate expenditure behaviour. Current behaviour of households is therefore not exclusively forward looking but is committed by past expenditures. Second, this nonseparability is not due to habit formation but to a strong “durable component”. Third, Hall's orthogonality test presents no evidence for the presence of liquidity constrained households. Fourth, the misleading role of seasonal adjustment is documented. This raises serious doubts on the “excess sensitivity” and “smoothness” results which have been obtained with seasonally adjusted data.     

An Investigation of the Effects of Data Transformation on Nonlinearity

This paper investigates the effects of data transformation on nonlinearity by means of a simulation analysis based on empirical threshold models for the unemployment rate. Unemployment rate series are particularly suitable because they exhibit a number of interesting features: business cycle asymmetries, persistence, long memory and seasonality. The main finding is that evidence of nonlinearity is not independent of the form in which data are analysed and that most data transformations result in a loss of nonlinearity. This is particularly the case for seasonal adjustment transformations, which remove not only seasonality but also nonlinear features, as shown for the commonly applied Census X12 method.     

The impact of information signals on market prices when agents have non-linear trading rules

Several methods have been developed for filtering seasonal influences and extreme returns in financial and economic time series. The theoretical support for these approaches is rather questionable since it focuses on the effects of shocks on prices and not on their sources. Removing such effects modifies the true generating system of market dynamics because of the non-proportional character of non-linearity. Thus, taking into account that the underlying process of economic time series is highly non-linear we cannot be certain a priori what the impact of new information will be on the dynamic structure of a system. The main contribution of this paper is to demonstrate using the methodology of simulations the eventual distortions in time series data arising from the arrival of news when agents follow non-linear trading strategies. We argue that if news can really modify the dynamical behaviour of a system, then the methodology of filtering exogenous distortions needs to be re-examined.     

Seasonality, Cointegration, and Forecasting UK Residential Energy Demand

Much of the short‐run movement in energy demand in the UK is seasonal, and the contribution of long‐run factors to short‐run forecasts is slight. Nevertheless, using a variety of techniques, including a recently developed estimation procedure that is applicable irrespective of the orders of integration of the data, we obtain a long‐run income elasticity of demand of about one third, and we are unable to reject a zero price elasticity. An econometric model is shown to provide superior short‐run forecasts to well‐known seasonal time series models ex post , but is inferior to Box‐Jenkins SARMA models when the determinants themselves have to be forecast. However, the relatively short data sample and small number of forecasts suggest caution in generalising these results.     

Forecasting business and consumer surveys indicators–a time-series models competition

The objective of this article is to compare different time-series methods for the short-run forecasting of Business and Consumer Survey Indicators. We consider all available data taken from the Business and Consumer Survey Indicators for the Euro area between 1985 and 2002. The main results of the forecast competition are offered not only for raw data but we also consider the effects of seasonality and removing outliers on forecast accuracy. In most cases, the univariate autoregressions were not outperformed by the other methods. As for the effect of seasonal adjustment methods and the use of data from which outliers have been removed, we obtain that the use of raw data has little effect on forecast accuracy. The forecasting performance of qualitative indicators is important since enlarging the observed time series of these indicators with forecast intervals may help in interpreting and assessing the implications of the current situation and can be used as an input in quantitative forecast models.     

On the (mis)specification of seasonality and its consequences: An empirical investigation with US data

It is well known that mis-specification of a trend leads to spurious cycles in detrended data (see, e.g., Nelson and Kang (1981)). Seasonal-adjustment procedures make assumptions, either implicitly or explicitly, about roots on the unit circle both at the zero and seasonal frequencies. Consequently, seasonal-adjustment procedures may produce spurious seasonal variation and other statistically undesirable effects. In this paper we document for a large class of widely used US quarterly macroeconomic series the effects of competing seasonal-adjustment procedures on the univariate time-series properties of the adjusted series. We also investigate which procedures are most appropriate given the properties of the data. Overall, we find very significant differences and evidence that several U.S. macroeconomic time series contain a mixture of deterministic and stochastic seasonal components.     

Seasonal fractional components in macroeconomic time series

Seasonal fractional models are shown in this article to be alternative credible ways of modelling the seasonal component in macroeconomic time series. A testing procedure that allows one to test different orders of integration at zero and at each of the seasonal frequencies is described. This procedure is then applied to the Italian consumption and income series, the results being very sensitive to the way of modelling the I(0) disturbances.     

A STATE‐LEVEL ANALYSIS OF BUSINESS CYCLE ASYMMETRY

This paper provides a comprehensive examination of asymmetry in US state‐level business cycles. We consider two different types of asymmetry in the adjustment process of a stationary time series: deepness and steepness. The data used in the study are a comparable set of state‐level coincident indexes (SCIs) developed by the Federal Reserve Bank of Philadelphia. Specifically, results from using the momentum‐threshold autoregressive model provide evidence of asymmetry in the growth rate of 23 SCIs as well as the equivalent national coincident index.