In time series analysis, multivariate dynamic factor models have gained popularity due to their time-varying nature that allows model parameters to vary over time. This exibility can allow models to capture patterns of change in time in model/forecast means that other models, such as ARMA and ARCH-GARCH models that have fixed parameters, fail to capture. However, in time series portfolio analysis, the increasing dimension of models poses challenges to parameter estimation, and calls for a need for more re_ned model and prior structuring. Recently developed Bayesian sparsity modeling approaches { such as graphical models (e.g. Carvalho and West, 2007; Wang and West, 2009; Wang, 2010) and sparse factor models (e.g. West, 2003; Carvalho et al., 2008; Yoshida and West, 2010; Carvalho, Lopes, and Aguilar, 2011) { address global sparsity, permitting data-based shrinkage of subsets of model parameters to zero using Bayesian sparsity priors. Nakajima and West improved this modeling perspective by introducing a general approach to local sparsity. This is based on latent threshold modeling that allows dynamic parameters to be zero for some periods of time but non-zero elsewhere. This latent threshold dynamic factor model shrinks down the number of parameters at certain periods by using speci_ed threshold mechanisms, thus encouraging reduced parameter dimensions when the data agree and so often improving the estimation process.(Nakajima and West, 2011) Nakajima and West applied the model to a multivariate time series model of a basket of 6 currencies, and showed that the new model consistently beats the non-threshold model for different scenarios.

In this paper, we further explore the application of the model in portfolio construction. Specifically, we apply the model to a portfolio of equity ETFs, an asset class that is more volatile than currency assets. What is different about equity ETFs is that they tend to have high correlations among themselves, that is to say, ETF on consumer product and retail equities tend to be highly correlated with ETF on industrial equities. This characteristic of ETFs poses a challenge to the non-correlation assumption in factor estimation we made in the original model. In order to address this problem, we allow the model to include correlation terms in our factor covariance matrix. This approach helps absorb more data variances in factor estimation, which in turn decreases variances in return predictions. We compare the new model with the original LTF model on a set of 10 equity ETFs and find that the new model outperforms the original one, thus validating our modification. This new model is highly applicable to all kinds of portfolio analysis as long as strong correlation is observed.

In section 2, we briefly explain the original LTF model proposed by Nakajima and West, followed by an introduction of our new model Latent Threshold Factor Correlation Model (LTDFCM). We evaluate the correlation behavior of a portfolio of 10 equity ETFs in section 3, and find our new model does a better job explaining data noises, approbating our assumption. In section 4, we further our analysis using the same portfolio and make daily return predictions over a period of 3 months. We construct our portfolio using maximum return portfolio algorism, i.e. maximizing portfolio return based on a pre-determined portfolio risk tolerance. Empirical results show that LTDFCM outperform the overall market and the original LTF model. We then give an extended future research direction in section 5 for interested scholars.