Bayesian Dynamic Factor Models - Department of Statistical Science ...

three relevant factors. Figure 8 shows results of time-varying loadings and sparsity, indicating that
the loadings of Factor4 are mostly shrunk in the entire periods. This finding implies that the LTM
structure can facilitate the data-driven model search in the factor models via shrinkage of time-
varying loadings.
Our experiences with various ordering of FX series in y t vectors are that the ordering re-
ported here yields more reasonable factor estimates with plausible implications than other ordering.
Therefore, we fix the ordering and the number of factors in the following portfolio analysis.
3 Factor1 (f 1t )
0
−3
2006 2007 2008 2009
3 Factor2 (f 2t )
0
−3
2006 2007 2008 2009
3 Factor3 (f 3t )
0
−3
2006 2007 2008 2009
3 Factor4 (f 4t )
0
−3
2006 2007 2008 2009
2 (w 1t )
1
2006 2007 2008 2009
2 (w 2t )
1
2006 2007 2008 2009
2 (w 3t )
1
2006 2007 2008 2009
2 (w 4t )
1
2006 2007 2008 2009
Figure 7: Results of 4 factors. Left panels: posterior means of factors fit. Right panels: posterior
means (solid) and 95% credible intervals (dotted) of factor stochastic volatility wit = exp(λit/2).
5 Portfolio allocation analysis
This section explores the forecasting performance of the LTDFMs in the context of dynamic
portfolio allocations. This portfolio analysis is related to some existing literature (Quintana (1992),
Putnum and Quintana (1994), Quintana and Putnum (1996), Aguilar and West (2000), Carvalho
and West (2007), Carvalho et al. (2011)). Our main focus here is the utility of the LTM structure
on the DFMs in forecast accuracy, considering how the dynamic sparsity/shrinkage in time-varying
factor loadings plays a relevant role in investment experiment. We compare six competing mod-
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