A Similarity Based Approach to Modelling and Forecasting Time-Varying Correlations

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Abstract

Component DCC models differentiate between the conditional correlation process and the long-run correlation process, which is time-varying and to which the former is attracted to. This thesis introduces the Sim-DCC model, which belongs to this class of models and is similar to the influential DCC-MIDAS model in that the long-run correlation is modelled as a weighted average of past realised correlations. The innovation presented in this thesis is that we alter the specification of the component DCC model in such a way that it allows for the long-run correlation to be a function of some variables, exogenous to the DCC model. A similar feature has been introduced elsewhere (DCC-MIDAS-X), but the approach adopted here has the advantage of retaining the use of past realised correlations to determine the long-run correlation and offering a route to extending this approach to higher dimensional models without a proliferation of model parameters.Specifically we will introduce exogenous variables that influence the weights for past realised correlations in the long-run correlation function. Higher weights are given to those periods in which the exogenous variables are similar to the current period.Multivariate volatility models, in particular high dimensional ones, are almost certainly misspecified. In particular relationships between exogenous variables and correlation processes are likely to be highly complex and non-linear. Therefore, to understand the empirical properties of our proposed Sim-DCC model, we perform a simulation study in which we can compare correlation forecasts to the simulated series.In our simulation set-up we simulate the correlation process as a component process with a time-varying long-run correlation, depending on the realisations of an exogenous variable. None of the forecasting models considered will mimic the data generating process and hence we are working with misspecified models. We show that using economic variables in the Sim-DCC model provides better estimation and forecasting results of the Sim-DCC model compared to the DCC-MIDAS model.Our results demonstrate that the use of the Sim-DCC forecasting model can eliminate excess persistence in the conditional correlation process that is estimated in case the specified long-run correlation process is unable to capture the true underlying time variation. We further show that the improved estimation of the correlation dynamics also translates into better correlation forecasts, both in our simulation experiment and in an application. This is in addition to potentially earning useful insights in the complex relationship between the economy and asset return correlations.

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