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

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2.0 1.5 GBP 2006 2007 2008 2009 0.012 JPY 0.010 0.008 2006 2007 2008 2009 1.0 AUD 0.8 2006 2007 2008 2009 3 0 −3 2006 2007 2008 2009 3 0 −3 GBP 2006 2007 2008 2009 5 0 −5 JPY AUD 2006 2007 2008 2009 (i) Exchange rates 1.6 EUR 1.4 1.2 1.0 0.8 2006 2007 2008 2009 CAD 2006 2007 2008 2009 1.0 CHF 0.9 0.8 (ii) Returns 2006 2007 2008 2009 0 −3 3 EUR 2006 2007 2008 2009 6 CAD 3 0 −3 2006 2007 2008 2009 3 0 CHF −3 2006 2007 2008 2009 Figure 1: Daily exchange rates and returns 8
3 2 1 GBP EUR JPY CAD AUD CHF 2006 2007 2008 2009 Figure 2: Estimated trajectories of univariate stochastic volatility (σit = exp(hit/2)) fit to each series separately. for ˜γ = (h, λ). The conditional prior for thresholds is U(di|0, |µi| + Kivi) with Ki = 3. MCMC used J = 100,000 iterations after discarding a burn-in period of 20,000 samples. Computations are obtained using Ox (Doornik 2006); code is available to interested readers. A determination of the number of factors has been a challenging issue in literature (see e.g. Lopes and West (2004) in Bayesian context). For the analysis here, we fit the LTDFM to the FX data and repeated the estimation across models with different number of factors k = 1, 2, 3, or 4. We evaluated each of the resulting suite of models by forecasting over the final five business days using first 930 observations, and repeated this five-step-ahead forecasting based on the first 930+5j observations for j = 1, . . . , 9, to obtain the 50-day forecasts. Based on the root mean squared errors (RMSE) for these out-of-sample forecasts, the LTDFM performs best when k = 3 is assumed, which is taken in the following analysis. 4.2 Summaries of posterior inference Figure 3 displays the posterior estimates of the time-varying factor loadings, as well as the posterior probabilities of sit = 0 for the LTDFM model. The estimated latent process exhibits a considerable time variation for several loadings, which can not be captured by a constant-loading factor model. In particular, JPY-Factor1 and AUD-Factor3 are estimated positive in 2006, but turns to be negative after 2007, reflecting a shift of correlated dynamics among the FX series. The 9 .
Page 1 and 2: Bayesian Dynamic Factor Models: Lat
Page 3 and 4: 2 Dynamic factor models 2.1 Standar
Page 5 and 6: series because process of their lat
Page 7: process for βit, with µi = µβi
Page 11 and 12: 1.0 0.5 β 2,1t (EUR−Factor) 2006
Page 13 and 14: 3 0 Factor1 (f 1t ) −3 2006 2007
Page 15 and 16: 0.5 0.0 β2,1t (EUR−Factor1) 2006
Page 17 and 18: • CM-IF: Constant means (ct ≡ c
Page 19 and 20: LT models provide averagely 20% les
Page 21 and 22: 0.5 GBP 0.0 0.5 0.0 0.4 0.0 CAD GBP
Page 23 and 24: References Aguilar, O. and West, M.
Page 25: West, M. (2003), “Bayesian factor

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