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Empirical Economics

Erschienen in:

04.07.2019

Assessing distributional properties of forecast errors for fan-chart modelling

verfasst von: Marián Vávra

Erschienen in: Empirical Economics | Ausgabe 6/2020

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Abstract

This paper considers the problem of assessing the distributional properties (normality and symmetry) of macroeconomic forecast errors of G7 countries for the purpose of fan-chart modelling. Our results indicate that the assumption of symmetry of the marginal distribution of forecast errors is reasonable, whereas the assumption of normality is not, making symmetric prediction intervals clearly preferable.

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Hammond et al. (2012) survey the (inflation) reports of 27 central banks, out of which 20 banks provide prediction intervals officially.

The only exception, the author is aware of, is Reifschneider and Tulip (2019) where the appropriate Monte Carlo critical values are used when testing for normality of the US forecast errors.

It is only fair to note that the authors are aware of this shortcoming (see Reifschneider and Tulip 2007, pp. 19–20).

A MATLAB code is available to researchers upon request from the author.

Note that the null hypothesis can be alternatively stated as: \(\mathcal {H}_{0}^N: F = N(0,\sigma ^2)\) since the forecast errors should be zero-mean stochastic processes. However, empirical evidence suggests that the forecast errors are biased in small samples. The official forecasts are thus corrected for historically observed biases in forecast errors. Therefore, we inspect the stochastic properties of the errors beyond the first moment in this study.

Note that the null hypothesis can be alternatively stated as: \(\mathcal {H}_{0}^S: F(x) = 1 - F(- x)\) since the forecast errors should be zero-mean stochastic processes. See Footnote 4 for an explanation.

It is important to point out that, as discussed in Poskitt (2007), the autoregressive representation (6) provides a meaningful approximation even if \(\psi (z)\) has zeros in the unit disk \(\left| z\right| <1\).

While \(H^{*}\) is unknown, an approximation (of any desired accuracy) can be obtained by Monte Carlo simulation as \(B \rightarrow \infty \).

Theoretically, it would be more policy relevant to assess the distributional properties of the central banks’ forecast errors. Practically, it would be infeasible to compile a comparable dataset of central banks’ forecast errors with the one employed in the study.

Note that quarter-on-quarter percentage changes of economic variables are not considered here since they are available only for GDP but not for CPI.

An alternative way could be to use a Student t distribution with the estimated degrees of freedom which are very likely to be horizon/variable dependent as implied from Fig. 1c.

The Monte Carlo results for different sample sizes are available from the author upon request.

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Titel: Assessing distributional properties of forecast errors for fan-chart modelling
verfasst von: Marián Vávra
Publikationsdatum: 04.07.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Empirical Economics / Ausgabe 6/2020
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-019-01726-0

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