Subset vector autoregressions for listed property and oil markets using bootstrap model selection

Abstract

Subset Vector Autoregressive (SVAR) models are fitted to the International Listed Property Trust (LPT) market and the global oil market. A General-to-Specific (GetS) model selection algorithm and a Bootstrap model based resampling method are employed to determine the best fitting models from a set of candidate models.

Section One presents one of the largest studies to date of the effect of crises on diversification opportunities in the listed property context, spanning 12 markets{u2091}. The analysis demonstrates an application of alternative superior modelling of market integration. Much early research on the diversification benefits of securitised real estate markets uses correlations and/or a simple mean variance framework. These static descriptive statistics, while informative, cannot adequately capture the dynamic behaviour present in the data or information on how the two variables are related on a lead/lag basis. Autocorrelation analysis can give some insight into temporal relationships between the response and the covariates now and into the past, but the more complex (SVAR) model allows us to capture the behaviour of the data series more flexibly and, in particular, model all markets of interest simultaneously. Such an approach captures not only internal dependence, but also complex dependence structures involving multiple markets. This study covers the Asian market crisis and the current global credit crisis. Critically this study includes modelling of the potential for currency effects to impact the diversification environment. Diversification benefits evaporate during the crisis in both hedged and unhedged cases, perhaps a surprising result given the magnitude of the currency effects experienced during the Asian crisis. Interestingly, although diversification benefits vanish during the crisis in both hedged and unhedged cases, the markets that are significant in the model differ between the two cases.

While the analysis in Section One demonstrates that SVAR models can provide a superior insight into the diversification problem, model uncertainty was not addressed adequately. Financial market industry participants and researchers often fit statistical models to time series data without regard for the issues relating to purpose and model uncertainty. Often an inappropriate model is fitted, and even if an "appropriate" model is applied, the final model reported is treated as though there is no uncertainty with respect to size or significance of the coefficients, variables included or excluded. Section Two discusses model uncertainty.

In Section Three, the question, "Can you trust your model?" is asked. By applying a resampling method called the bootstrap, model uncertainty is quantified. The global oil market is modelled using an implementation of Subset Vector Autoregression with Exogenous Variables (SVARX). When fitting large models such as those in Section One and Section Three, coefficient and standard error estimates have been traditionally determined by conditioning on a single best model. Estimates from a single model ignore model uncertainty and result in under-estimated standard errors and over-estimated coefficients. The results of this study find under-estimation of standard errors of up to164% and over-estimation of coefficients of up to 37%. The bootstrap provides improved estimation of coefficients and their standard errors, and allows better identification of the relative importance of predictors. Using the bootstrap, this study shows how traditional methods for selecting predictors result in false positives (inclusion of unimportant/noise variables) and exclusion of important variables. Using daily log return time series, this exploratory study suggests the following predictors as the most important drivers of the global oil market:

US 10 Year Government Bond Yield (lags 0, 4 and 13)

US Inflation Rate (lags 0 and 11)

US Business Confidence (lags 8 and 11)

Given the set of predictors above, confirmatory out-of-sample analysis where models of size two, three and four or more are fitted and analysed should be conducted. A multi-model averaging based approach should be implemented to account for model uncertainty if the models are to be used for predictive purposes.

{u2091}Based on the work in Section One of this thesis, a journal article has been published. Ryan, L. (2011), Nowhere to hide: an analysis of investment opportunities in listed property markets during financial market crises, Journal of Property Research, Volume 28, Number 2, June 2011, pp. 97-131(35)