International Statistical Review (2010), 78, 2, 218–239 doi:10.1111/j.1751-5823.2010.00114.x Comparison of Classical and Bayesian Approaches for Intervention Analysis Thiago R. Santos 1 , Glaura C. Franco 1 and Dani Gamerman 2 1 Department of Statistics,Federal University of Minas Gerais, Av. Antonio Carlos 6627, Belo Horizonte, MG 31270-901, Brazil 2 Department of Statistical Methods, Federal University of Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro RJ 21945-970, Brazil E-mails: thiagors@ufmg.br, glauraf@ufmg.br, dani@im.ufrj.br Summary Intervention analysis has been recently the subject of several studies, mainly because real time series present a wide variety of phenomena that are caused by external and/or unexpected events. In this work, transfer functions are used to model different forms of intervention to the mean level of a time series. This is performed in the framework of state-space models. Two canonical forms of intervention are considered: pulse and step functions. Static and dynamic explanation of the intervention effects, normal and non-normal time series, detection of intervention, and study of the effect of outliers are also discussed. The performance of the two approaches is compared in terms of point and interval estimation through Monte Carlo simulation. The methodology was applied to real time series and showed satisfactory results for the intervention models used. Key words: State space models; dynamic linear models; prediction; transfer function; bootstrap; MCMC. 1 Introduction Time series are frequently affected by external events, known as interventions, that can change the structure of the series (such as strikes, policy changes, etc.). The first proposals of intervention analysis seem to have arisen in the Social Sciences with the work of Campbell & Stanley (1968), but the term intervention was first introduced by Glass (1972). However, it was only in 1975 that Box and Tiao developed the theory of intervention analysis to study structural changes in time series (Box & Tiao, 1975). At the same time, Box & Jenkins (1976) introduced the transfer function (TF) models in the context of the Autoregressive Integrated Moving Average (ARIMA) process. TF models were designed to measure the relationship between an output series and one or more input series. For example, in the case of an output series y t and an input series x t , the TF relates the variables through a linear filter of the form y t = ϑ ( B )x t + ǫ t , where ϑ ( B ) = ∑ ∞ j =−∞ ϑ j B j , B is the backshift operator B k y t = y t −k and the error series ǫ t is possibly time-correlated. The coefficients ϑ j in the TF model are called impulse response function. C  2010 The Authors. Journal compilation C  2010 International Statistical Institute. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.