This paper provides a means of accurately simulating explosive autoregressive processes, and uses this method to analyse the distribution of the likelihood ratio test statistic for an explosive second order autoregressive process. Nielsen (2001) has shown that for the asymptotic distribution of...

We undertake a generalization of the cumulative sum of squares (CUSQ) test to the case of non-stationary autoregressive distributed lag models with quite general deterministic time trends.  The test may be validly implemented with either ordinary least squares residuals or standardized...

In this paper, we consider the identification problem arising in the age-period-cohort models, as well as in the extended chain ladder model.  We propose a canonical parametrization based on the accelerations of the trends in the three factors.  This parametrization is exactly identified.  It...

The classical Chow (1960) test for structural instability requires strictly exogenous regressors and a break-point specified in advance.  In this paper we consider two generalisations, the 1-step recursive Chow test (based on the sequence of studentized recursive residuals) and its supremum...

A vector autoregression is singular when explosive characteristic roots have geometric multiplicity larger than one.  The singular component is a mixingale.  Martingale decompositions are constructed for sample moments involving the singular component.  This permits weak and strong analysis...

Reserving in general insurance is often done using chain-ladder-type methods.  We propose a method aimed at situations where there is a sudden change in the economic environment affecting the policies for all accident years in the reserving triangle.  It is shown that methods for forecasting...

During extreme hyper-inflations productivity tends to fall dramatically.  Yet, in models of money demand in hyper-inflation variables such as real income has been given a somewhat passive role, either assuming it exogenous or to have a negligible role.  In this paper we use an empirical...

We consider forecasting from age-period-cohort models, as well as from the extended chain-ladder model.  The parameters of these models are known only to be identified up to linear trends.  Forecasts from such models may therefore depend on arbitrary linear trends.  A condition for invariant...