Mathematical and Statistical Methods for Actuarial Sciences and Finance

Nonparametric prediction in time series analysis 243

The selection ofpis obtained from the minimisation of a quadratic loss function
that makes use of the subsampling estimate of the one-step-ahead forecasts as shown
in Procedure 1.
The simulated and empirical results show the good performance of the proposed
procedure that can be considered, in the context of model selection, an alternative to
more consolidated approaches given in the literature.
Much remains to be done: to investigate the properties ofpˆ; to generalise the
procedure to the case with lead time>1; to consider more complex data-generating
processes that belong to the Markov class. Further, the procedure could be extended
to parametric and/or semiparametric predictors that can be properly considered to
minimizeˆT,b.
All these tasks need proper evaluation of the computational effort that is requested
when computer-intensive methods are selected.

Acknowledgement.The authors would like to thank two anonymous referees for their useful
comments.

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