In this paper we adopt the multiple time-series modelling approach suggested by Tiao & Box (1981) to construct a stochastic investment model for price inflation, share dividends, share dividend yields and long-term interest rates in the United Kingdom. This method has the advantage of being direct and transparent. The sequential and iterative steps of tentative specification, estimation and diagnostic checking parallel those of the well-known Box-Jenkins method in the univariate time-series analysis. It is not required to specify any a priori causality as compared to some other stochastic asset models in the literature.

This paper reviews the stochastic asset model described in Wilkie (1995) and previous work on refining this model. The paper then considers the application on non-linear modelling to investment series, considering both ARCH techniques and threshold modelling. The paper suggests a threshold autoregressive (TAR) system as a useful progression from the Wilkie (1995) model. The authors are making available (on compact disk) a collection of spreadsheets, which they have used to simulate the stochastic asset models which are considered in this paper.

In this paper we review the Wilkie asset model for a variety of UK economic indices, including the Retail Prices Index, both without and with an ARCH model, the wages index, share dividend yields, share dividends and share prices, long term bond yields, short term bond yields and index-linked bond yields, in each case by updating the parameters to June 2009. We discuss how the model has performed from 1994 to 2009 and estimate the values of the parameters and their confidence intervals over various sub-periods to study their stability. Our analysis shows that the residuals of many of the series are much fatter-tailed than in a normal distribution. We observe also that besides the stochastic uncertainty built into the model by the random innovations there is also parameter uncertainty arising from the estimated values of the parameters.