Seasonal Adjustment and Volatility Dynamics

Abstract

Nous étudions l'effet de filtre sur l'estimation de processus de type GARCH. Le cas du filtre linéaire est analysé dans un contexte général pour des processus GARCH faibles. Plusieurs cas spéciaux sont discutés, notamment ce-lui du filtre d'ajustement X-11 pour les effets saisonniers. Nous trouvons que ce filtre produit un effet de persistance saisonnière au niveau de la volatilité. Nous abordons ensuite le filtrage non linéaire dans le cas du filtre X-11. Une étude de Monte Carlo démontre qu'il y a des différences très importantes entre la représentation linéaire du filtre et le programme non linéaire appliqué aux données réelles.

In this paper we try to enhance our understanding of the effect of filtering, particularly seasonal adjustment filtering, on the estimation of volatility models. We focus exclusively on ARCH models as a specific class of models and examine the effect of both linear and nonlinear filters on (seasonal) volatility dynamics. The case of linear filters is treated in a general abstract setting applicable to seasonal adjustment as well as various other linear filters often applied to transform raw data. Next we focus on specific cases like the first and seasonal differencing filters as well as the X-11 filter, both its linear representation and the (nonlinear) procedure implemented in practice. We uncover surprising features regarding the linear X-11 filter, e.g. it introduces a small seasonal pattern in volatility. More interestingly, we show that the linear X-11 and the actual procedure produce serious downward biases in ARCH effects and their persistence. Finally, we uncover important differences between the linear version of X-11 and the actual procedure.