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LM-AF LM-IF CM-IF (i) One-step-ahead forecasts Target return: m = 0.02 1.033 1.007 1.185 0.04 1.149 1.187 1.062 0.06 1.232 1.407 0.969 Target-free (ii) Five-step-ahead forecasts 1.234 1.205 1.193 Target return: m = 0.02 1.067 1.027 1.178 0.04 1.158 1.102 1.058 0.06 1.223 1.150 0.979 Target-free 1.249 1.224 1.172 Table 3: Portfolio risk ratio: ex-ante ratio of portfolio standard deviation under the NT models relative to the LT models, averaged across 100 business days. 6 Concluding remarks We proposed the flexible structure of latent thresholding for time-varying loading matrix in context of dynamic factor models. Our substantive example of model fit and sequential portfolio allocation analysis using FX return series revealed the considerable utility of the LTM structure that plausibly dynamically selecting potential loadings in the factor analysis, eliminating unnecessary fluctuations of time-varying parameters as well as improving forecasting performance and model implication. There are a number of methodological and computational areas for further investiga- tion. Among them, we note the potential of more elaborate factor models such as factor-augmented VAR (FAVAR, Bernanke et al. (2005), Baumeister et al. (2010)) and other methodological approach including particle filter (also known as sequential Monte Carlo) and particle learning algorithm (Carvalho et al. (2010)) for the LTDFMs. 22
References Aguilar, O. and West, M. (2000), “Bayesian dynamic factor models and portfolio allocation,” Journal of Business and Economic Statistics, 18, 338–357. Baumeister, C., Liu, P., and Mumtaz, H. (2010), “Changes in the transmission of monetary policy: Evidence from a time-varying factor-augmented VAR,” Working Paper No.401, Bank of England. Bernanke, B., Boivin, J., and Eliasz, P. (2005), “Measuring the effects of monetary policy: A factor- augmented vector autoregressive (FAVAR) approach,” Quarterly Journal of Economics, 120, 387– 422. Carvalho, C. M., Chang, J., Lucas, J. E., Nevins, J. R., Wang, Q., and West, M. (2008), “High- dimensional sparse factor modeling: Applications in gene expression genomics,” Journal of the American Statistical Association, 103, 1438–1456. Carvalho, C. M., Johannes, M. S., Lopes, H. F., and Polson, N. G. (2010), “Particle learning and smoothing,” Statistical Science, 25, 88–106. Carvalho, C. M., Lopes, H. F., and Aguilar, O. (2011), “Dynamic stock selection strategies: A struc- tured factor model framework (with discussion),” in Bayesian Statistics 9, eds. Bernardo, J., Bayarri, M., Berger, J., Dawid, A., Heckerman, D., Smith, A., and West, M., Oxford University Press, pp. 69–90. Carvalho, C. M. and West, M. (2007), “Dynamic matrix-variate graphical models,” Bayesian Analy- sis, 2, 69–98. Clyde, M. and George, E. I. (2004), “Model uncertainty,” Statistical Science, 19, 81–94. Doornik, J. (2006), Ox: Object Oriented Matrix Programming, London: Timberlake Consultants Press. George, E. I. and McCulloch, R. E. (1993), “Variable selection via Gibbs sampling,” Journal of the American Statistical Association, 88, 881–889. — (1997), “Approaches for Bayesian variable selection,” Statistica Sinica, 7, 339–373. Jacquier, E., Polson, N. G., and Rossi, P. E. (1994), “Bayesian analysis of stochastic volatility models,” Journal of Business and Economic Statistics, 12, 371–389. Kim, S., Shephard, N., and Chib, S. (1998), “Stochastic volatility: likelihood inference and compar- ison with ARCH models,” Review of Economic Studies, 65, 361–393. 23
Page 1 and 2: Bayesian Dynamic Factor Models: Lat
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