  This paper addresses short term forecast of ultra short AR(1) sequences (4 to
6 terms only) with a single structural break at an unknown time and of unknown
sign and magnitude. As prediction of autoregressive processes requires
estimated coefficients, the efficiency of which relies on the large sample
properties of the estimator, it is a common perception that prediction is
practically impossible for such short series with structural break. However, we
obtain a heuristic result that some universal predictors represented in the
frequency domain allow certain predictability based on these ultra short
sequences. The predictors that we use are universal in a sense that they are
not oriented on particular types of autoregressions and do not require explicit
modelling of structural break. The shorter the sequence, the better the
one-step-ahead forecast performance of the smoothed predicting kernel. If the
structural break entails a model parameter switch from negative to positive
value, the forecast performance of the smoothed predicting kernel is better
than that of the linear predictor that utilize AR(1) coefficient estimated from
the ultra short sequence without taking the structural break into account
regardless whether the innovation terms in the learning sequences are
constructed from independent and identically distributed random Gaussian or
Gamma variables, scaled pseudo-uniform variables, or first-order
auto-correlated Gaussian process.
