Empirical Simultaneous Confidence Regions for Path-Forecasts

51 Pages Posted: 19 May 2010

See all articles by Oscar Jorda

Oscar Jorda

Federal Reserve Banks - Federal Reserve Bank of San Francisco; University of California, Davis - Department of Economics

Malte Knüppel

Deutsche Bundesbank - Research Centre

Massimiliano Giuseppe Marcellino

Bocconi University - Department of Economics; Centre for Economic Policy Research (CEPR)

Date Written: April 2010

Abstract

Measuring and displaying uncertainty around path-forecasts, i.e. forecasts made in period T about the expected trajectory of a random variable in periods T+1 to T+H is a key ingredient for decision making under uncertainty. The probabilistic assessment about the set of possible trajectories that the variable may follow over time is summarized by the simultaneous confidence region generated from its forecast generating distribution. However, if the null model is only approximative or altogether unavailable, one cannot derive analytic expressions for this confidence region, and its non-parametric estimation is impractical given commonly available predictive sample sizes. Instead, this paper derives the approximate rectangular confidence regions that control false discovery rate error, which are a function of the predictive sample covariance matrix and the empirical distribution of the Mahalanobis distance of the path-forecast errors. These rectangular regions are simple to construct and appear to work well in a variety of cases explored empirically and by simulation. The proposed techniques are applied to provide confidence bands around the Fed and Bank of England real-time path-forecasts of growth and inflation.

Keywords: forecast uncertainty, path forecast, Scheffe;'s S-method, simultaneous confidence region

JEL Classification: C32, C52, C53

Suggested Citation

Jorda, Oscar and Knüppel, Malte and Marcellino, Massimiliano, Empirical Simultaneous Confidence Regions for Path-Forecasts (April 2010). CEPR Discussion Paper No. DP7797, Available at SSRN: https://ssrn.com/abstract=1611493

Oscar Jorda (Contact Author)

Federal Reserve Banks - Federal Reserve Bank of San Francisco ( email )

101 Market Street
San Francisco, CA 94105
United States
4159742691 (Phone)

HOME PAGE: http://www.frbsf.org/economic-research/economists/oscar-jorda/

University of California, Davis - Department of Economics ( email )

One Shields Drive
Davis, CA 95616-8578
United States
530-5549382 (Phone)

HOME PAGE: http://old.econ.ucdavis.edu/faculty/jorda/

Malte Knüppel

Deutsche Bundesbank - Research Centre ( email )

Wilhelm-Epstein-Str. 14
D-60431 Frankfurt/Main
Germany

HOME PAGE: http://sites.google.com/view/malteknueppel-research/home

Massimiliano Marcellino

Bocconi University - Department of Economics ( email )

Via Gobbi 5
Milan, 20136
Italy

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom