Choosing the Best Volatility Models: The Model Confidence Set Approach

Peter Reinhard Hansen, Asger Lunde, and James M. Nason
Working Paper 2003-28
October 2003

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This paper applies the model confidence sets (MCS) procedure to a set of volatility models. A MSC is analogous to a confidence interval of parameter in the sense that the former contains the best forecasting model with a certain probability. The key to the MCS is that it acknowledges the limitations of the information in the data. The empirical exercise is based on fifty-five volatility models, and the MCS includes about a third of these when evaluated by mean square error, whereas the MCS contains only a VGARCH model when mean absolute deviation criterion is used. We conduct a simulation study that shows the MCS captures the superior models across a range of significance levels. When we benchmark the MCS relative to a Bonferroni bound, this bound delivers inferior performance.

JEL classification: C12, C19, C44, C52, C53

Keywords: forecasting, model selection, multiple comparison, data mining

The authors thank Mark Kamstra and seminar pariticpants at the Federal Reserve Bank of Atlanta for useful comments. Financial support from the Danish Research Agency, grant no. 24-00-0363, and the Salomon Research Award at Brown University is gratefully acknowledged. This paper also owes much to the Federal Reserve Bank of Atlanta, which provided. support and hospitality to the first and third authors. The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’ responsibility.

Please address questions regarding content to Peter Reinhard Hansen, Department of Economics, Box B, Brown University, Providence, Rhode Island 02912,; Asger Lunde, The Aarhus School of Business, Department of Information Science, Fuglesangs Alle 4 DK-8210, Aarhus V, Denmark,, or James M. Nason, Federal Reserve Bank of Atlanta, Research Department, 1000 Peachtree Street, N.E., Atlanta, Georgia 30309, 404-498-8891,