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Yet more on a stochastic economic model: Part 3B: stochastic bridging for retail prices and wages

Published online by Cambridge University Press:  21 November 2016

A. D. Wilkie  and
Şule Şahin
A. D. Wilkie*
Affiliation:
InQA Limited, Dennington, Ridgeway, Horsell, Woking GU21 4QR, UK
Şule Şahin
Affiliation:
Department of Actuarial Sciences, Hacettepe University, 06800 Ankara, Turkey
*
*Correspondence to: A. D. Wilkie, InQA Limited, Dennington, Ridgeway, Horsell, Woking GU21 4QR, UK. Tel. +441483 725984 or 01483 725984; E-mail: [email protected]
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Abstract

This is the second subpart of three in a long paper in which we consider stochastic interpolation for the Wilkie asset model, considering both Brownian bridges and Ornstein–Uhlenbeck (OU) bridges. In Part 3A, we developed certain properties for both these types of stochastic bridge, and we investigate the properties of many of our data series on the same lines. We have several economic or investment series, which all have their own peculiarities. In this paper, we cover only retail prices and wages. The other series are dealt with in Part 3C. We find that, although the annual series for the rate of inflation is generated by an AR(1) model, which is the discrete time equivalent of an OU process, an OU bridge is not suitable. We need to use a Brownian bridge on the logarithm of the Price Index. Further, the standard deviation of the monthly increments in any year is, as we find empirically from the data, a function of the change in the annual value, and further there is correlation between the monthly increments in successive years.

Keywords

Wilkie modelStochastic interpolationBridgingRetail pricesWages
Type
Papers
Information
Annals of Actuarial Science , Volume 11 , Issue 1 , March 2017 , pp. 100 - 127
Copyright
© Institute and Faculty of Actuaries 2016 

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References

Wilkie, A.D. (1986). A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341–381.Google Scholar
Wilkie, A.D. (1995). More on a stochastic asset model for actuarial use. British Actuarial Journal, 1, 777–964.Google Scholar
Wilkie, A.D. & Şahin, Ş. (2016). Yet more on a stochastic economic model: part 2: initial conditions, select periods and neutralising parameters. Annals of Actuarial Science, 10, 1–51.CrossRefGoogle Scholar
Wilkie, A.D., Şahin, Ş., Cairns, A.J.G. & Kleinow, T. (2011). Yet more on a stochastic economic model: part 1: updating and refitting, 1995 to 2009. Annals of Actuarial Science, 5, 53–99.Google Scholar