kalman filter

November 1, 2004

Multivariate unobserved components (structural) time series models are fitted to annual post-war observations on real income per capita in countries in the euro zone. The aim is to establish stylized facts about convergence as it relates both to long-run income levels and to cycles. The analysis is based on a new model in which convergence components are combined with a common trend and similar cycles. These convergence components are formulated as a second-order error correction mechanism that ensures that the extracted components change smoothly, thereby giving a clearer decomposition into long-run movements and cycles.

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November 1, 2003

This Paper analyses the co-movement in activity, measured by GDP and industrial production, between the G7 countries for the period 1972-2002. For that purpose, a dynamic factor model is estimated using Kalman Filtering techniques. In addition to separating common and country-specific - idiosyncratic - developments of output, we try to identify the causes underlying the observed co-movement: to what extent is it driven by common shocks and to what extent can cross-country/cross-area spill-over effects account for the observed co-movement? We find that the output developments in G7 countries are driven to a substantial extent by common dynamics. A significant part of the co-movement, especially in the first half of the sample, can be explained by developments in the price of oil, an important and easily identifiable common shock. The analysis suggests that, in addition, area-specific common factors play an important role, separating the sample into a North American (US, Canada) and a continental European (France, Germany, Italy) area, with the UK and Japan being somewhat separate from these areas. We find that developments in the North American factor have a strong lagged impact on the continental European factor, while the reverse is not true. Furthermore, the strength of the cross-area spillovers from America to Europe appears to have become stronger over the sample period, suggesting that international linkages have increased in the process of globalization.

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October 1, 2004

Existing methods for data interpolation or backdating are either univariate or based on a very limited number of series, due to data and computing constraints that were binding until the recent past. Nowadays large datasets are readily available, and models with hundreds of parameters are fastly estimated. We model these large datasets with a factor model, and develop an interpolation method that exploits the estimated factors as an efficient summary of all the available information. The method is compared with existing standard approaches from a theoretical point of view, by means of Monte Carlo simulations, and also when applied to actual macroeconomic series. The results indicate that our method is more robust to model misspecification, although traditional multivariate methods also work well while univariate approaches are systematically outperformed. When interpolated series are subsequently used in econometric analyses, biases can emerge, depending on the type of interpolation but again be reduced with multivariate approaches, including factor-based ones.

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