This note gives a few practical guidelines for cointegration analysis. The focus is on testing the cointegration rank in a VAR model and on how an intercept and a trend should be incorporated in the model. Only two cases appear relevant for most economic data. There is no new material in this note, and all results have been derived elsewhere. The discussion of the two relevant cases should however be useful for those who use standard packages like for example EViews. I thank Marius Ooms for bringing this issue to my attention, and Peter Boswijk, Richard Paap and Dick van Dijk for helpful comments. y Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR, Rotterdam, The Netherlands, email: franses@few.eur.nl 1 Introduction Cointegration analysis is an important tool when modelling economic data with trends. Ever since its formal introduction in Engle and Granger (1987), it has been popular among practitioners and theorists. The current standard for analys...

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This paper reviews research issues in modeling panels of time series. Examples of this type of data are annually observed macroeconomic indicators for all countries in the world, daily returns on the individual stocks listed in the S&P500, and the sales records of all items in a retail store. A panel of time series usually concerns the case where the cross-section dimension and the time dimension are large. Usually, there is no a priori reason to select a few series or to aggregate the series over the cross-section dimension. In that case, however, the use of for example a vector autoregression or other types of multivariate systems becomes cumbersome. Panel models and associated estimation techniques are more useful. This paper discusses representation, estimation and inference in case the data have trends, seasonality, outliers, or nonlinearity. Various examples illustrate the various models.

Abstract. Since its first inception in the debate on the relationship between environment and growth in 1992, the Environmental Kuznets Curve has been subject of continuous and intense scrutiny. The literature can be roughly divided in two historical phases. Initially, after the seminal contributions, additional work aimed to extend the investigation to new pollutants and to verify the existence of an inverted-U shape as well as assessing the value of the turning point. The following phase focused instead on the robustness of the empirical relationship, particularly with respect to the omission of relevant explanatory variables other than GDP, alternative datasets, functional forms, and grouping of the countries examined. The most recent line of investigation criticizes the Environmental Kuznets Curve on more fundamental grounds, in that it stresses the lack of sufficient statistical testing of the empirical relationship and questions the very existence of the notion of Environmental Kuznets Curve. Attention is in particular drawn on the stationarity properties of the series involved – per capita emissions or concentrations and per capita GDP – and, in case of presence of unit roots, on the cointegration property that must be present for the Environmental Kuznets Curve to be a well-defined concept. Only at that point can the researcher ask whether the long-run relationship exhibits an inverted-U pattern. On the basis of panel integration and cointegration tests for sulphur, Stern (2002, 2003) and Perman and Stern (1999, 2003) have presented evidence and forcefully stated that the Environmental Kuznets Curve does not exist. In this paper we ask

Theatre historiography suggests that there has been a gradual change in audience behaviour in the period 1860-1914 in The Netherlands, where this change is towards a higher degree of receptivity of quality and taste. This would imply that ticket sales time series data show signs of long-memory. We test the gradual change hypothesis by tting long-memory time series models for weekly ticket sales series for the Grand Theatre, Coolsingel, Rotterdam for the period 1860-1881. We nd that, even after correcting for deterministic changes (due to changes in management) and for price eects, there is substantial evidence of long-memory. This nding holds for all ranks, expect for gallery. Hence, we nd supportive evidence for the gradual change hypothesis. Key words and phrases: Theatre ticket sales, gradual changes, long memory time series models Mailing address: Institute for Media and Representation, Kromme Nieuwe Gracht 29, NL3512 HD Utrecht, The Netherlands, email: henk.k.g...

Can neural network model selection be guided by statistical procedures such as hypothesis tests, information criteria and cross-validation? Recently, Anders and Kom (1999) proposed five neural network model specification strategies based on different statistical procedures. In this paper, we use and adapt the Anders-Koru framework to find appropriate neural network models for financial time series prediction. The most important new issue in this context is the specification of IIII. dynamic structure of the models, i.e. the selection ofthe lagged values ofthe input time series. A linear model is built with full dynamic structure, then its possihl« nonlinear extensions are tested using a statistical procedure inspired by thl' Anders-Kom approach. Promising results are obtained with an application 10 predict the monthly time series ofmortgage loans purchased in The Netherlands.

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The growing body of research focusing on real estate as an individual asset class puts the real estate cycle in the very center of strategic investment decisions and implications thereof. This article investigates if the non-structural definition of the cycle as defined by the Hodrick-Prescott (HP) filter can be used to construct indicators of the Swedish real estate cycle. The methodology of the HP-filter, which is to separate a time-series into a trend component and a growth component, is often used in analysis of aggregate economic growth (i.e., GDP). The article also evaluates the indicative characteristics of the indicator.

What are the drivers of retailers ' prices and what, if any, are their financial consequences? The results of a large-scale quantitative analysis show that retail prices are mainly driven by pricing history (50%), acquisition costs (25%) and demand feedback (12.5%). In contrast to pricing history, demand-based pricing is associated with higher retailer (and manufacturer) financial

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