Mathematical and Statistical Methods for Actuarial Sciences and Finance

240 Marcella Niglio and Cira Perna

nonstationarity of the seriesXt, which can be empirically appreciated by observing
the correlogram in Figure 2, which presents a very slow decay.

Fig. 1.Weekly 90-day US T-bill secondary market rates: 4 January 1957–17 December 1993

Fig. 2.ACF plot of the weakly 90-day US T-bill

In Table 4 the nonlinearity ofrtis further investigated through the likelihood ratio
(LR) test proposed in [6] and [7], where the linearity of the process is tested against
threshold nonlinearity. In particular, the test statistic with the correspondingp-value
is presented when the null autoregressive model of orderpand the threshold delay
d(of the alternative hypothesis) allow refusal of the linearity of the data-generating
process.