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A method for modeling shocks in time series is derived. The method is based on state-space forms and allows all statistics for interventions to be generated from a single run of the Kalman filter smoother. It can also be refitted when aberrant behavior is identified to account for the additional structure. An analysis of shocks in structural component models and autoregressive integrated moving average models are discussed., 1. INTRODUCTION Many time series are subject to external influences. Our interest lies with sudden or unexpected events such as natural disasters, strikes, wars, the introduction of new legislation, or [...]

A new type of retirement bond is proposed called an SM bond. SM bonds are long dated government bonds divisible into two parts: a survivorship (S) part and a mortality (M) part. Each SM bond is associated with a particular age. SM bonds associated with a particular age are only purchasable by (originators) of that age. The SM bond is then splittable into an S and M component. The S part must be retained by the originator, who receives the face value of the bond if he/she is alive at maturity. For originators who die prior to the maturity date, the maturity value of the SM bond is assigned to a mortality pool. The holder of the M part of the bond receives the annual bond coupon, and at maturity a pro rata share of the mortality pool. M bonds are tradable: holders can sell their M bonds to anyone, at any time. It is envisaged different age bonds are issued every year for ages say 30–64 each with say a 35‐year term. The market will be regularly informed about the mortality experience, and the market price of the M bonds will vary over time to reflect that experience. [ABSTRACT FROM AUTHOR]