Generally a stationary model, which requires returns to be drawn from a single régime, cannot be viewed as an adequate description of the data generating process for value indices of commercial real estate in either the US or the UK. Linear regressions which require the parameters to be constant throughout the entire sample period, do not capture the non-stationary features of the data.
The Markov régime-switching model provides an alternative method of removing the restrictive assumption that financial returns are drawn from a single stationary régime with constant parameters. The model appears to fit the data well, and describes important features of the series.
The Markov model discussed here can be generalised to include the probability that xt = p is dependent on not only the value of xt-1, but also on a vector of observed variables - pre-emptive indicators of a switch in régime - to forecast future values of a series; see Diebold, Lee, & Weinbach . Thus, if the parameter estimates depend on cyclical factors, then the required parameter shift dates can be forecast and included in models that require parameters to be estimated without prior knowledge. The implication of these results is that it may be possible to forecast value indices of commercial real estate using régime-switching models.
The results obtained from the normality tests, and the existence of régime switching in value indices of commercial real estate, allow us to conclude that they are non-normal. Although considerably less likely to reject normality within the bounds of a régime, part of this may be due to a small sample effect. The results of recent papers11 that use annual or biannual data in order to avoid the problems of non-normality - rather than quarterly or monthly data - need to be interpreted accordingly.
These results also have several implications for theoretical models and empirical research in financial economics. For both multi-period asset pricing models and performance evaluation, the evidence of non-stationarity implies violations of model specification and estimation procedures. The assumptions inherent in the CAPM undermine the practicality of its application in the construction of multi-asset investment portfolios, in which the structure of individual asset classes vary widely. As seen in Chapter 2, the characteristics of the real estate differ substantially from those of equities and bonds. Also, as Chapter 6 has illustrated, the assumption that returns from real estate investment are normally distributed cannot be relied upon. This assumption is fundamental to the CAPM.
Taken together with the conclusions drawn from Chapter 5, the CAPM is thus inapplicable to investment decisions that include real estate. This necessarily leads us to attempt the definition of an alternative asset allocation model, to accommodate two of the shortcomings highlighted above, namely those of downside risk-aversion and the specification of a market proxy.
11See for example, Firstenberg, Ross & Zisler , Liu, Hartzell & Grissom [1992a], Myer & Webb  and Sanders, Pagliari & Webb .