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 seasonal unit root structure in New Zealand Macroeconomic variables

ADF unit root tests are generally applied to macroeconomic data prior to testing theoritical models to ensure that all relevant variables are integrated of the same order. Not only is it important to test that these variables are integrated of the same order but also that a cointegrating relationship exists; failure to do so raise the specture of false inference associated with the spurious regression problem. The seasonal nature of quarterly data adds a further proplem which has generally been overcome by seasonally adjusting the data using procedure such as the census X-11 rather than suppressing it, have attempted to determine whether the seasonal component in each variable exhibits stochastic non-stationary. This paper analysisunit roots in a seasonal setting and compares the recently developed tests for seasonal unit roots as well as the standard augmented Dickey-Fuller zerop frequency unit root tests. Of the variables tested relatively few paper to be integrated at the seasonal frequenciues and, as other studies suggest,determinstic seasonal effects are typically more important than stochastic ones.     

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.

     

季节平稳过程间的虚假回归

本文推导了当数据生成过程是独立的季节平稳过程情形下,OLS参数估计及检验统计量的极限分布。发现序列中的自相关性会导致虚假回归现象的发生。     

The nature of Austrian macroeconomic time series unit root tests

It is still an open question in economic and econometric modelling whether the non-stationarity in a time series is captured by detrending or by differencing. We test thirrteen Austrian macroenconomic time series for difference versus trend stationarity using informal methods and formal procedures developed by Dickey-Fuller and Phillips-Perron. To eliminate the effects of seasonal adjustment on the tests we apply a third procedure to the unadjusted data, recently developed by Hylleberg-Engle-Granger-Yoo. Independent of the seasonal adjustment the empirical results indicate that these series are integrated of order 1.     

The order of integration for quarterly macroeconomic time series: A simple testing strategy

An empirical example and a simulation study show that much more attention should be devoted to the practical issue of selecting the maximum admissible order of integration for quarterly macroeconomic time series. In fact, it is shown that when that order is too high, one may get (spurious) evidence for an excessive number of unit roots, resulting in an overdifferenced series. Besides introducing a simple and intuitive definition for the order of integration of quarterly time series, this paper also presents a simple testing strategy to determine that order for the case of macroeconomic data.Helpful comments and suggestions from João Santos Silva and Paulo Rodrigues are gratefully acknowledged. I am also grateful to two anonymous referees, whose comments and suggestions helped improving this paper. Obviously, the usual disclaimer applies. This work has also benefited from financial support from Fundação para a Ciência e Tecnologia (FCT), through Programa POCTI (ECO/33778/2000). A previous version of this paper was presented at the Royal Economic Society Conference, March 2002, Warwick.     

Mechanical detrending by Hodrick-Prescott filtering: A note

The Hodrick-Prescott filter is widely used to extract cyclical movements about trend in macroeconomic time series. The filter is based on the assumption that nonstationary movements in time series are captured by smooth and slowly changing trends. This note shows that applying the Hodrick-Prescott filter to time series with stochastic trends may extract cyclical movements which are entirely spurious.     

Testing fractional integration with monthly data

Seasonal roots can help to explain the seasonal fluctuations in macroeconomic time series. In this paper we concentrate on monthly data and look at different versions of Robinson’s (1994) tests for testing unit roots and other fractionally integrated hypotheses when the root is located at zero and/or at the seasonal frequencies. A Monte Carlo experiment is carried out to check the power of these tests against different fractional alternatives, and an empirical application, using Spanish monthly data for the consumer price index, is also carried out in the article.     

Deterministic and Stochastic Methods for Estimation of Intra-day Seasonal Components with High Frequency Data

We introduce a model for the analysis of intra-day volatility based on unobserved components. The stochastic seasonal component is essential to model time-varing intra-day effects. The model is estimated with high frequency data for Deutsche mark–US dollar for 1993 and 1996. The model performs well in terms of coherence with the theoretical aggregation properties of GARCH models, it is effective in terms of both forecasting ability and describing reactions to macroeconomic news.
(J.E.L.: C14, C53, F31).     

Bayesian model averaging and identification of structural breaks in time series

Bayesian Model Averaging (BMA) is used for testing for multiple break points in univariate series using conjugate normal-gamma priors. This approach can test for the number of structural breaks and produce posterior probabilities for a break at each point in time. Results are averaged over specifications including: stationary; stationary around trend and unit root models, each containing different types and number of breaks and different lag lengths. The procedures are used to test for structural breaks on 14 annual macroeconomic series and 11 natural resource price series. The results indicate that there are structural breaks in all of the natural resource series and most of the macroeconomic series. Many of the series had multiple breaks. Our findings regarding the existence of unit roots, having allowed for structural breaks in the data, are largely consistent with previous work.     

Seasonal fluctuations and equilibrium models of exchange rate

Most of the evidence on dynamic equilibrium exchange rate models is based on seasonally adjusted consumption data. Equilibrium models have not worked well in explaining the actual exchange rate. However, the use of seasonally adjusted data might be responsible for the spurious rejection of the model. This article presents a new equilibrium model for the exchange rates that incorporates seasonal preferences. The fit of the model to the data is evaluated for five industrialized countries using seasonally unadjusted data. Our findings indicate that a model with seasonal preferences can generate monthly time series of the exchange rate without seasonality even when the variables that theoretically determine the exchange rate show clear seasonal behaviours. Further, the model can generate theoretical exchange rates with the same order of integration than actual exchange rates, and in some cases, with the same stochastic trend.     

Inflation and financial development: Evidence from Brazil

We examine the impact of inflation on financial development in Brazil, and the data available permit us to cover the period between 1985 and 2004. The results—based initially on time series and then on panel time series and panel data and analyses—suggest that inflation presented deleterious effects on financial development during the period investigated here. The main implication of the results is that poor macroeconomic performance has detrimental effects to financial development, a variable that is important for affecting, (e.g., economic growth and income inequality). Therefore, low and stable inflation, and all that it encompasses, is a necessary first step to achieve a deeper and more active financial sector with all its attached benefits.     

A finite mixture analysis of structural breaks in the G-7 gross domestic product series

In this paper we apply a clustering procedure to detect trend changes in macroeconomic data, focusing on the GDP time series for the G-7 countries. A finite mixture of regression models is considered to show different patterns and changes in GDP slopes over time in the long-trend component. Two popular trend-cycle decompositions (i.e., Beveridge and Nelson Decomposition and Hodrick and Prescott filter) are considered in a preliminary step of the analysis to stress the differences between the two methods in terms of the inferred clustering, if any. This approach can be used also to detect structural breaks or change points and it is an alternative to existing approaches in a probabilistic framework. We also discuss international changes in the GDP distribution for the G-7 countries, highlighting similarities, e.g., in break dates, aiming at adding more insights on the economic integration among countries. Our findings suggest that by looking at changes in slope over time a mixture of regression models is able to detect change points, also compared with alternative procedures.     

Radial basis functions neural networks for nonlinear time series analysis and time-varying effects of supply shocks

I propose a flexible Radial Basis Functions (RBFs) Artificial Neural Networks method for studying the time series properties of macroeconomic variables. To assess the validity of the RBF approach, I conduct a Monte Carlo experiment using the data generated from a nonlinear New Keynesian (NK) model. I find that the RBF estimator can uncover the structure of the NK model from the simulated data of 300 observations. Finally, I apply the RBF estimator to the quarterly US data and show that the positive supply shocks have significantly weaker expansionary effects during the periods of passive monetary policy regimes.     

Inflation,real economic growth and unemployment expectations: an empirical analysis based on the ECB survey of professional forecasters

Expectations are at the centre of modern macroeconomic theory and policymakers. In this article, we examine the predictive ability and the consistency properties of macroeconomic expectations using data of the European Central Bank (ECB) Survey of Professional Forecasters (SPF). In particular, we provide evidence on the properties of forecasts for three key macroeconomic variables: the inflation rate, the growth rate of real gross domestic product and the unemployment rate.     

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.     

The HUMP-shaped behavior of macroeconomic fluctuations

We analyze the nature of persistence in macroeconomic fluctuations. The current view is that shocks to macroeconomic variables (in particular realGNP) have effects that endure over an indefinite horizon. This conclusion is drawn from the presence of a unit root in the univariate time series representation. Following Perron (1989), we challenge this assessment arguing that most macroeconomic variables are better construed as stationary fluctuations around a breaking trend function. The trend function is linear in time except for a sudden change in its intercept in 1929 (The Great Crash) and a change in slope after 1973 (following the oil price shock). Using a measure of persistence suggested by Cochrane (1988) we find that shocks have small permanent effects, if any. To analyze the effects of shocks at finite horizon, we select a member of theARMA(p, q) class applied to the appropriately detrended series. For the majority of the variables analyzed the implied weights of the moving-average representation have the once familiar humped shape.     

Unit and Fractional Roots at the Long Run and the Seasonal Frequencies in Macroeconomic Time Series

In this article, we show that macroeconomic time series may contain unit and fractional roots at both, at zero and at zero and at the seasonal frequencies. The importance of the root at the long run or zero frequency requires in many cases to consider this root at both, separately in an independent polynomial, and also included in the seasonal one. Several Monte Carlo experiments are conducted to examine cases when the root at the zero frequency is not appropriately considered. An empirical application based on the tests of Robinson, Peter M. “Efficient Tests of Nonstationary Hypotheses,” Journal of the American Statistical Association, 89, 1994, pp. 1420–37 is also carried out at the end of the article.The author gratefully acknowledges financial support from the Government of Navarra (“Ayudas de Formación e Investigación y Desarrollo”).     

Estimating ‘gamma’ for tail-hedge discount rates when project returns are cointegrated with GDP

Martin Weitzman has suggested a method for calculating social discount rates for long-term investments when project returns are covariant with consumption or other macroeconomic variables, so-called ‘tail-hedge discounting’. This method relies on a parameter called ‘real project gamma’ that measures the proportion of project returns that is covariant with the macroeconomic variable. We compare two approaches for estimation of this gamma when the project returns and the macroeconomic variable are cointegrated. First, we use Weitzman’s own approach, and second a simple data transformation that keeps gamma within the zero to one interval. In a Monte-Carlo study, we show that the method of using a standardized series is better and robust under different data-generating processes. Both approaches are examined in a Monte-Carlo experiment and applied to Swedish time-series data from 1950–2011 for annual time-series data for rail freight (a measure of returns from rail investments) and GDP.     

Analysis on structural changes in the macroeconomic data series with the empirical evidence from China

Analysis on structural changes in macroeconomic data series has been the key issue for studying data quality. This paper studies the structural changes in China’s 36 macroeconomic time series using joint estimation model, and we find out the characteristics and movement pattern for the outliers. Our results show that most outliers show up more or less in groups, indicating that there is a significant correlation between them. The isolated outliers are not the main characteristic of China’s macroeconomic time series. Nearly all the original series contain the obvious skewness and kurtosis; hence, the hypothesis of normality is significantly rejected. Most original and outlier correction series show the non-autoregressive conditional heteroskedasticity (ARCH) characteristic, but the p value for ARCH2, ARCH4, and ARCH8 is very different. __________ Translated from Economic Research Journal (经济研究), 2005, (1) (in Chinese)