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 the identification problem for the model of Lee and Carter (1992).  The parameters of this model are known only to be identified up to certain transformations.  Forecasts from the model may therefore depend on the arbitrarily chosen identification scheme.  A condition for...

The paper by Atkinson, Riani and Ceroli, henceforth ARC, is concerned with detection of outliers and unsuspected structures which is rather important in practice.  This is done through a Forward Search Algorithm.  The statistical analysis of such algorithms poses many challenging problems, and...

Estimated characteristic roots in stationary autoregressions are shown to give rather noisy information about their population equivalents.  This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes.  In the asymptotic analysis the problems...

The Forward Search is an iterative algorithm concerned with detection of outliers and other unsuspected structures in data.  This approach has been suggested, analysed and applied for regression models in the monograph Atkinson and Riani (2000).  An asymptotic analysis of the Forward Search is...

It has long been known that maximum likelihood estimation in a Poisson model reproduces the chain-ladder technique.  We revisit this model.  A new canonical parametrisation is proposed to circumvent the inherent identification problem in the parametrisation.  The maximum likelihood estimators...