The name is absent

11

To achieve robust results, both tests described so far require large samples. How-
ever, Harvey et al. (1997) recommend a modified test statistic in small samples:

The critical values for this test are taken from the t_N-1 distribution.

Forecast breakdown test

To evaluate the alternative inflation forecasts further, we also check the models
for a forecast breakdown (FB). This is defined as a situation in which the out-of-
sample forecasting performance of a forecast model is significantly worse than its
in-sample fit (Giacomini and Rossi 2006). To implement this check we compare
each model’s forecasting performance - measured by its mean squared forecast
error - to the expected forecast error based on its in-sample-fit.⁸ Analytically, a
“surprise loss” ( sl ) at time t is calculated as difference between the out-of-sample
loss and the average in-sample loss l_t ^jh ,

_sP^j = (_e^j )² _- l^jh
s t+h ⁼ (^et+h ) ^- t ^.

If forecast model j is reliable, the mean of the associated surprise losses sl ,
taken over all T forecasts, should be close to zero. The standard normally distrib-
uted forecast breakdown test statistic is
where γ^j is a Newey-West estimator of the variance of the weighted losses.
Clearly, the precision of the estimate of the forecast model depends on the length
of the sample that is used for estimation. The null hypothesis of a forecast break-
down is rejected at significance level α whenever the forecast breakdown test
statistic is larger than the (1-α) -th quantile of a standard normal distribution.

j-jh
sl

⁸ We only perform a one-sided test to reflect the assumption that a loss that is smaller than
expected is desirable and therefore does not constitute a forecast breakdown. The forecasting
scheme is recursive.

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