Dynamic Financial Conditions Index

The Financial Conditions Index is constructed with principal components. Principal components is easy to estimate but excludes any underlying time series data generation process applying to the factor structure. An alternative to principal components is to use a dynamic factor model. A factor model extracts a latent factor from a state-space process by capturing the time series transition behaviour. As with principal components more than 1 component is usually necessary to capture the significant common movement in a diverse group of time series. The significant common movement is extracted from the a vector autoregression (VAR) capturing the lagged cross dependencies for each series. For a single latent factor which follows as AR(2) process then the state-space structure is:

For the Australian Financial Conditions Index, nine components have eigenvalues greater than one, the significant changes in the eigenvalues occur after the first three.

Three latent factors following an AR(2) process has a transition equation in matrix form as:

Applied to the full dataset, for the period January 1996 to the following chart illustrates the first 3 principal components and the equipvalent autoregressive process from the dynamic factor model. The differences between the processes are realtively minor when considering the first and second principal component. The dynamics of the process vary more substantially in lower order components where the cross auto-correlations between factors have a stronger impact on the latent factor trends (as against idyiosyncractic innovations in the observation equation).

A key benefit of a the dynamic factor model is that the autoregressive structure produces forecast which highlight the momentum of the series and the potential speed of mean reversion (assuming the input data is stationary).