A new approach in multivariate time series specification

Within the study of multivariate time series, this work is centered on vector autoregressive moving average (VARMA) models, specifically on the specification stage. Until now, numerous procedures have been proposed to resolve the problem of identifying the dynamic behavior in a VARMA model framework. A new strategy is added to specify VARMA models justified by results within the field of matrix Padé approximation. Besides contributing a characterization of these models, alternative methods are added to those already in the literature to deal with the problems of identifiability and exchangeability. The obtained characterizations have the advantage of graphically presenting the results in tables for direct interpretation. The proposed technique is illustrated by means of a theoretical example, a simulated model, and data from economic variables (already dealt with by other authors) in order to compare results.     

VAR modelling and Haavelmo's probability approach to macroeconomic modelling

Some recent developments in the macroeconometric analysis of time series are discussed in the light of Haavelmo (1944). Experimental design in econometrics is discussed and related to the case of passive observation. The general ideas are illustrated with a analysis of the long-run and short-run structure in Danish monetary data.This paper has benefitted from useful comments from Søren Johansen, Claus Va strup and John Muellbauer, and in particular, from two unknown referees. Financial report from the joint committee of the Nordic Social Science Research Council is gratefully acknowledged.     

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.     

A structural time series approach to modelling multiple and resurgent meat scares in Italy

This paper exploits a structural time series approach to model the time pattern of multiple and resurgent food scares and their direct and cross-product impacts on consumer response. A structural time series Almost Ideal Demand System (STS-AIDS) is embedded in a vector error correction framework to allow for dynamic effects (VEC-STS-AIDS). Italian aggregate household data on meat demand is used to assess the time-varying impact of a resurgent BSE crisis (1996 and 2000) and the 1999 Dioxin crisis. The VEC-STS-AIDS model monitors the short-run impacts and performs satisfactorily in terms of residuals diagnostics, overcoming the major problems encountered by the customary vector error correction approach.     

A time series approach to g convergence

This paper applies time series analysis to study how the gap between a number of countries and the USA evolves through time. As other authors, it is found that time series analysis provides a better insight into the concept of convergence than the cross sectional one. The econometric results show that the stochastic behaviour of the output disparity varies considerably: neither the steady-state equilibrium nor the speed of convergence are unique and constant across countries and time. In general, there is catching up for European countries, convergence for East and South Asian countries, and neither of them for Latin American countries.     

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.     

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).     

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.      

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.     

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.     

A medium-N approach to macroeconomic forecasting

This paper considers methods for forecasting macroeconomic time series in a framework where the number of predictors, N, is too large to apply traditional regression models but not sufficiently large to resort to statistical inference based on double asymptotics. Our interest is motivated by a body of empirical research suggesting that popular data-rich prediction methods perform best when N ranges from 20 to 40. In order to accomplish our goal, we resort to partial least squares and principal component regression to consistently estimate a stable dynamic regression model with many predictors as only the number of observations, T, diverges. We show both by simulations and empirical applications that the considered methods, especially partial least squares, compare well to models that are widely used in macroeconomic forecasting.     

A macroeconomic approach to the income-tax work-effort relationship

In this paper, we analyse the dynamic relationship between hours worked per employee (per self-employed) and marginal income tax-rate shocks in terms of both a comparative-dynamics model and a stochastic general equilibrium econometric model. The econometric model is estimated for Germany, UK and USA over the post-1960 period using the GMM estimation technique. Estimates in both models show that increases in the marginal income-tax rate exert negative effects on hours worked by both employees and the self-employed, but the response of the employees who are subject to tax withholding is stronger than the response of the self-employed.     

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.     

On testing for nonlinearity in multivariate time series

This paper considers a multivariate extension of the test for neglected nonlinearity proposed by Tsay (1986) that uses principal components to overcome the problem of dimensionality that is common with tests of this type. Monte Carlo experiments reveal that the modified multivariate test provides a significant dimensional reduction without suffering from any systematic level distortion or power loss, and is more powerful than univariate nonlinearity tests.     

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.     

A multivariate time series analysis of the United States aggregate production function

This study examines the effects of hours of work per unit of private sector capital, the relative price of energy, government capital per unit of private sector capital, and inflation on private sector output per unit of capital in the U.S. over the period 1952–90. A small vector autoregressive model that comprises the variables typically employed in single-equation estimates of the aggregate production function is used. Variance decompositions and cumulative impulse response functions indicate that hours of work per unit of private sector capital, the relative price of energy, and the inflation rate have significant effects on private sector output per unit of capital over the 1952–90 period. However, there is no evidence of a significant effect for government capital per unit of private capital. An historical decomposition that begins in 1973 with the emergence of a “productivity slump” and continues through 1990 indicates that shocks to hours of work per unit of capital, the relative price of oil, and inflation appear important in explaining output per unit of capital but shocks to government capital are not important.     

Atheoretical and structural approaches to modelling Canadian-American macroeconomic interaction

Much recent work on Canadian-American macroeconomic interaction utilizes the vector autoregression methodology advocated by Sims (1980). Examples include Burbidge and Harrison (1985), Kusczak and Murray (1986) and Ambler (1988). The Sims' methodology is severely criticized by Cooley and Leroy (1985) and Leamer (1985) because, as it is generally implemented and interpreted, including in the studies cited above, the models contain strong implicit identifying assumptions. Bernanke (1986), Blanchard (1986) and Sims (1986) propose alternative estimation techniques which, while retaining some of the advantages of the vector autoregression approach, make the identifying assumptions explicit. This paper uses both approaches to estimate models of Canadian-American macroeconomic interaction. The results show the method adopted does affect the interpretation of the results. The vector autoregression methodology is not free of the imposition of untestable identifying assumptions.     

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.