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 for...

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...

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 forecast...

Johansen derived the asymptotic theory for his cointegration rank test statisic for a vector autoregression where the parameters are restricted so the process is integrated of order one. It is investigated to what extent these parameter restrictions are binding. The eigenvalues of Johansen’s...

The log normal reserving model is considered. The contribution of the paper is to derive explicit expressions for the maximum likelihood estimators. These are expressed in terms of development factors which are geometric averages. The distribution of the estimators is derived. It is shown that...

It is of considerable interest to forecast future mesothelioma mortality. No measures for exposure are available so it is not straight forward to apply a doseresponse model. It is proposed to model the counts of deaths directly using a Poisson regression with an age-period-cohort structure, but...

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...

We review recent asymptotic results on some robust methods for multiple regres- sion. The regressors include stationary and non-stationary time series as well as polynomial terms. The methods include the Huber-skip M-estimator, 1-step Huber-skip M-estimators, in particular the Impulse Indicator...

Age-period-cohort models for Lexis diagrams are considered. The identi- cation problem is addressed by reparametrizing the models in terms of freely varying parameters. The reparametrisation covers all three Lexis diagrams. A new plot of the unidentied time eects is suggested and interpreted....