skip to content

Faculty of Economics

Journal Cover

Harvey, A. C. and Luati, A.

Filtering with heavy tails

Journal of the American Statistical Association

Vol. 109 pp. 1112-1122 (2014)

Abstract: An unobserved components model in which the signal is buried in noise that is non-Gaussian may throw up observations that, when judged by the Gaussian yardstick, are outliers. We describe an observation driven model, based on a conditional Student t-distribution, that is tractable and retains some of the desirable features of the linear Gaussian model. Letting the dynamics be driven by the score of the conditional distribution leads to a specification that is not only easy to implement, but which also facilitates the development of a comprehensive and relatively straightforward theory for the asymptotic distribution of the maximum likelihood estimator. The methods are illustrated with an application to rail travel in the UK. The final part of the article shows how the model may be extended to include explanatory variables.

Keywords: Outlier, Robustness, Score, Seasonal, t-distribution, trend

JEL Codes: C22

Author links: Andrew Harvey  

Publisher's Link: https://doi.org/10.1080/01621459.2014.887011

Keynes Fund Project(s):
Dynamic Models for Volatility and Heavy Tails (JHLC)  
Dynamic Models for Volatility and Heavy Tails (JHLH)  



Cambridge Working Paper in Economics Version of Paper: Filtering with heavy tails, Harvey, A. C. and Luati, A., (2012)

Papers and Publications



Recent Publications


Faraglia, E., Marcet, A., Oikonomou, R. and Scott, A. Government Debt management: the Short and the Long of it Review of Economic Studies [2019]

Onatski, A. and Wang, C. Alternative Asymptotics for Cointegration Tests in Large VARs Econometrica [2018]

Corsetti, G., Mavroeidi, E., Thwaites, G. and Wolf, M. Step away from the zero lower bound: small open economies in a world of secular stagnation Journal of International Economics [2019]

Lee, Y-Y. and Bhattacharya, D. Applied welfare analysis for discrete choice with interval-data on income Journal of Econometrics [2019]