  In this paper we propose some novel non-parametric prediction methods to
perform short- and long-term aggregated forecasting for the log-returns of
econometric datasets. The previous works in the regime of NoVaS model-free
prediction are restricted to short-term forecasting only. Often practitioners
and traders want to understand the future trend for a longer time into the
future. This article serves two purposes. First it explores robustness of
existing model-free methods for long-term predictions. Then it introduces, with
systematic justification, some new methods that improve the existing ones for
both short- and long-term predictions. We provide detailed discussions of the
existing and new methods and challenge the new ones with extensive simulations
and real-life data. Interesting features of our methods are that these entail
significant improvements compared to existing methods for a longer horizon,
strong volatile movements and shorter sample size.
