Mathematical and Statistical Methods for Actuarial Sciences and Finance

Nonparametric prediction in time series analysis: some

empirical results

Marcella Niglio and Cira Perna

Abstract.In this paper a new approach to select the lagpfor time series generated from

Markov processes is proposed. It is faced in the nonparametric domain and it is based on

the minimisation of the estimated risk of prediction of one-step-ahead kernel predictors. The

proposed procedure has been evaluated through a Monte Carlo study and in empirical context

to forecast the weakly 90-day US T-bill secondary market rates.

Key words:kernel predictor, estimated risk of prediction, subsampling

1 Introduction

One of the aims in time series analysis is forecasting future values taking advantage

of current and past knowledge of the data-generating processes. These structures

are often summarised with parametric models that, based on specific assumptions,

define the relationships among variables. In this parametric context a large number

of models have been proposed (among others, [3], [20], [4], and, more recently, [11],

which discusses parametric and nonparametric methods) and for most of them the

forecast performance has been evaluated.

To overcome the problem of prior knowledge about the functional form of the

model, a number of nonparametric methods have been proposed and widely used

in statistical applications. In this context, our attention is focused on nonparametric

analysis based on kernel methods which have received increasing attention due to

their flexibility in modelling complex structures.

In particular, given a Markov process of orderp, in this paper a new approach to

select the lagpis proposed. It is based on the minimisation of the risk of prediction,

proposed in [13], estimated for kernel predictors by using the subsampling.

After presenting some results on the kernel predictors, we discuss, in Section 2,

how they can be introduced in the proposed procedure.

In Section 3 we further describe the algorithm whose performance has been dis-

cussed in a Monte Carlo study. To evaluate the forecast accuracy of thenonparametric

predictor in the context of real data, in Section 4 we present some results on the weekly

M. Corazza et al. (eds.), Mathematical and Statistical Methodsfor Actuarial Sciencesand Finance
© Springer-Verlag Italia 2010