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.     

Loss aversion in aggregate macroeconomic time series

Prospect theory has been the focus of increasing attention in many fields of economics. However, it has scarcely been addressed in macroeconomic growth models—neither on theoretical nor on empirical grounds. In this paper we use prospect theory in a stochastic optimal growth model. Thereafter, the focus lies on linking the Euler equation obtained from a prospect theory growth model of this kind to real macroeconomic data. We will use generalized method of moments (GMM) estimation to test the implications of such a non-linear prospect utility Euler equation. Our results indicate that loss aversion can be traced in aggregate macroeconomic time series.     

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 performance of unit root tests under level-dependent heteroskedasticity

Several financial variables exhibit level-dependent conditional heteroskedasticity. This may cause severe distortions in conventional unit root tests. Given the absence of theoretical results, we conduct Monte Carlo investigation to assess the performance of the standard Dickey–Fuller tests, a nonparametric alternative, and a heteroskedastic-robust extension of the Dickey–Fuller t-test. While these procedures have approximately correct size, we find strong distortions in the power of the standard Dickey–Fuller tests.     

Multivariate time series models for Austrian interest rates

Zusammenfassung Fünf monatliche österreichische Zinszeitreihen, die Habenzinsen, die Sollzinsen sowie die Zinssätze für Dreimonatsgelder, der täglich fälligen Gelder und der Anleihen (i. w. S.) werden für den Zeitraum 1972 bis 1980 mit Hilfe multivariater (oder vektor-)autoregressiver (AR) Prozesse untersucht.Nachdem die Zeitreihen mittels der Methode vonKitagawa-Akaike (1982) auf Ausreißer geprüft und korrigiert wurden, zeigt sich, daß die korrigierte Zeitreihe der Sollzinsen bessere Prognoseeigenschaften erzielt. Obwohl die Stationaritätsvoraussetzungen für alle Zeitreihen etwas problematisch sind, bringen auch einfache Transformationen wie Differenzenbildung keine Hilfe bezüglich Stationarität. Die Schätzung eines simultanen fünfdimensionalen AR-Prozesses allerZinsreihen ergibt, daß ein Aufbrechen dieses Systems in zwei Blöcke das beste Resultat im Sinne des InformationskriteriumsAIC ergibt. Der erste Block wird durch die Habenzinsen und die (korrigierten) Sollzinsen gebildet, die eine wechselseitige Dynamik bis zum Lag 2 aufweisen. Der zweite Block wird durch die Zinssätze für Dreimonatsgelder, täglich fällige Gelder und Anleihen gebildet. Als Nebenprodukt dieser multivariaten Zeitreihenanalyse können temporale Kausalitäts- (oder Feedback-)maße berechnet werden. Es wird jedoch gezeigt, daß das Zusammenwirken von bestimmten Schätzprozeduren mit dem InformationskriteriumAIC die Schätzung dieser Kausalitätsmaße nicht immer ermöglicht. Allgemein läßt sich sagen, daß die instantane Kausalität in den Modellen dominiert, was teilweise durch nichtstationäre Einflüsse und Ausreißer erklärt werden kann.     

No unit root conditions for bivariate series when a component univariate series has a unit root

The root-locus method is used to derive conditions under which a bivariate series does not possess a unit root when a component univariate series does have a unit root. The bivariate series composed of the U.S. real GNP and civilian unemployment rate (1948.I–1973.IV) does not have a unit root.     

On business cycle fluctuations in USA macroeconomic time series

This study employs eighteen USA macroeconomic time series variables to investigate possible existence of asymmetries in business cycle fluctuations in the series. Detection of asymmetric fluctuations in economic activity is important for policymakers since effective monetary policy relies on asymmetric business cycle fluctuations in all the series. The asymmetric deviations from the long-term growth trend in each of the series are modeled using regime switching models and artificial neural networks. The results based on nonlinear switching time series models reveal strong evidence of business cycle asymmetries in most of the series. The results based on in-sample approximations from artificial neural networks show statistically significant evidence of asymmetries in all the series. Similar results are obtained when jackknife out-of-sample approximations from artificial neural networks are used. Thus, the study results show statistically significant evidence of asymmetries in all the series which indicates that business cycle fluctuations in the series are asymmetric, thus alike. Therefore, the impact of monetary policy shocks on the output and the other macroeconomic variables can be anticipated using nonlinear models only. The results on asymmetric business cycle fluctuations in real GDP are in line with recent studies but in sharp contrast with Balke and Fomby (1994).     

A multivariate time series approach to modelling macroeconomic sequences

In this paper we discuss a multivariate generalization of autoregressive integrated moving average models. A methodology for constructing multivariate time series models is developed and the derivation of forecasts from such models is considered. A bivariate model for Austrian macroeconomic sequences is constructed. Furthermore it is discussed whether multivariate time series methods can be expected to lead to a significant increase in prediction accuracy when forecasting macroeconomic series.     

The Phillips unit root tests for polynomials of integrated processes

In this paper, we derive the limiting distributions of the first order serial correlation coefficient and its t-statistic, which are the basis for the non-parametric unit root tests of Phillips (1987), for polynomials of integrated processes. The resulting limiting distributions depend upon nuisance parameters and in general the modification proposed by Phillips (1987), to achieve a nuisance parameter free limiting distribution, is not feasible for polynomials of integrated processes. For the special case of serially uncorrelated innovations, the limiting distributions are nuisance parameter free and are simulated. The distributions shift to the left with increasing variance for increasing polynomial orders.     

Testing for deterministic and stochastic cycles in macroeconomic time series

In this paper we use a statistical procedure which is appropriate to test for deterministic and stochastic (stationary and nonstationary) cycles in macroeconomic time series. These tests have standard null and local limit distributions and are easy to apply to raw time series. Monte Carlo evidence shows that they perform relatively well in the case of functional misspecification in the cyclical structure of the series. As an example, we use this approach to test for the presence of cycles in US real GDP.      

Evidence for common features in G7 macroeconomic time series

Systems of economic data potentially exhibit a number of common features, which aid both econometric modelling and economic interpretation. This paper surveys a variety of common features and applies the corresponding testing and estimation techniques to systems of macroeconomic time series in the G7 countries. Strong evidence is found of common trends and common or co-dependent cycles in the data, and, for two countries, empirical support for common non-linearities.     

On smoothing macroeconomic time series using the modified HP filter

In business-cycle research, smoothing data is an essential first step to evaluate the extent to which model-generated moments stand up to their empirical counterparts. We put to test McDermott’s (1997) modified version of Hodrick and Prescott’s (1997) smoothing filter. On the one hand, our simulations suggest that relative to other filters, the modified HP-filter replicates better artificially generated series with known properties. On the other hand, using true data we find that autoregressive properties of smoothed series are not affected by the choice of smoothing HP filters, but the same does not hold when it comes to multivariate analysis. The later result is especially strong for annual data. We report results for a large set of countries.     

The behaviour of seasonal unit root tests under neglected local drifts

This paper analyses the limit distributions of the seasonal unit root test procedures proposed by Dickey, Hasza and Fuller (1984) and Hylleberg, Engle, Granger and Yoo (1990), when local trends at different frequencies are present in data generation processes, but ignored in the test regressions used. The findings presented explicitly show that neglected deterministic trends have negative effects on the distributions of the test statistics. Analytical observations and Monte Carlo simulations reveal that seasonal unit root test statistics become severely undersized as the values of standardized local trends increase. Hence, failure to consider local trends may often bear the undesirable effect of biasing decisions towards non-rejection of unit roots.Received: February 2001, Accepted: September 2001, JEL Classification: C12, C22Paulo M. M. Rodrigues: I am thankful to two anonymous referees for their detailed and useful comments and suggestions.     

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.     

Relationships between macroeconomic time series in a fixed-exchange-rate economy: The case of Italy

This paper presents an empirical analysis that is useful for the task of characterizing the dynamic structure and causal orderings of the underlying macroeconomic model of a fixed-exchange-rate economy. Particular emphasis is given to the formulation and testing of versions of the ‘natural-rate’ hypothesis, the ‘small open economy’ hypothesis, and the ‘non-sterilization’ hypothesis. These issues are examined on the basis of quarterly time series for Italy (1956 1970)     

Forecast content and content horizons for some important macroeconomic time series

Abstract.  The information content of statistical forecasts of approximately stationary quantities tends to decline as the forecast horizon increases, and there exists a maximum horizon beyond which forecasts cannot provide discernibly more information about the variable than is present in the unconditional mean (the content horizon ). The pattern of decay of forecast content (or skill) with increasing horizon is well known for many types of meteorological forecasts; by contrast, little generally accepted information about these patterns or content horizons is available for economic variables. In this paper we estimate content horizons for a variety of macroeconomic quantities; more generally, we characterize the pattern of decay of forecast content as we project farther into the future. We find a wide variety of results for the different macroeconomic quantities, with models for some quantities providing useful content several years into the future, for other quantities providing negligible content beyond one or two months or quarters.     

Further application of Narayan and Liu (2015) unit root model for trending time series

In this paper, we further subject the new GARCH-based unit root test for trending time series proposed by Narayan and Liu (NL) (2015) to empirical scrutiny. We utilize daily, weekly, and monthly data of 10-year bond yield for seventeen countries across the regions of America, Asia, and Europe. We find that the unit root test for sovereign bond yield data is better modeled in the presence of structural breaks, conditional heteroscedasticity, and time trend. More importantly, it may be necessary to pre-test for the existence of these statistical features when modeling with the bond yield data.     

The power of asymmetric unit root tests under threshold and consistent-threshold estimation

The asymmetric unit root tests of Enders and Granger (Journal of Business and Economic Statistics, 16, 304–11, 1998) are examined using consistent threshold estimation and the original two-step procedure. In contrast to earlier studies, the ability of the tests to jointly reject the unit root and symmetry hypotheses is examined, thus permitting a fuller analysis of the tests' properties. Whilst the threshold autoregressive test is found to have little power in either its consistent or original forms, the consistent momentum-threshold autoregressive test is found to exhibit high power against a range of plausible alternatives when using newly derived critical values.     

Business cycle asymmetries and non-linearities in U.K. macroeconomic time series

This paper empirically tests for and models non-linearities in a selection of U.K. macroeconomic time series. Attention is focused first on business cycle asymmetry, using Markov chain models to investigate whether cycles in macroeconomic time series display symmetric behaviour on both sides of a peak or trough. Next, a selection of statistical tests of non-linearity are employed to investigate formally the presence of departures from the linearity assumption. A variety of specific non-linear models of the business cycle that have been proposed recently are then fitted to ascertain how useful they are in explaining any non-linearities that have been observed in the series. Finally, the results are brought together in an extended discussion of their implications for business cycle research and policy analysis.     

Long run time series tests of constant steady-state growth

We propose a new methodology to study the stability of steady-state growth. Long-run GDP per capita can be characterized by: (1) the linear trend hypothesis, where there are no long-run changes in GDP levels or growth rates, (2) the level shift hypothesis, where there are long-run level shifts, but not changes in growth rates, and (3) the growth shift hypothesis, where there are long-run changes in both GDP levels and growth rates. We formally test these hypotheses using time series techniques with over 139 years of data. The results are not favorable to the hypothesis of constant steady-state growth. While we find evidence supporting the linear trend hypothesis for the United States and Canada and the level shift hypothesis for three additional OECD countries, the growth shift hypothesis is supported for seven OECD and four Asian countries. The results are not driven by transition dynamics.