Bayesian Dynamic Quantile Model Averaging

Abstract

This article introduces a novel dynamic framework to Bayesian model averaging for time-varying parameter quantile regressions. By employing sequential Markov chain Monte Carlo, we combine empirical estimates derived from dynamically chosen quantile regressions, thereby facilitating a comprehensive understanding of the quantile model instabilities. The effectiveness of our methodology is initially validated through the examination of simulated datasets and, subsequently, by two applications to the US inflation rates and to the US real estate market. Our empirical findings suggest that a more intricate and nuanced analysis is needed when examining different sub-period regimes, since the determinants of inflation and real estate prices are clearly shown to be time-varying. In conclusion, we suggest that our proposed approach could offer valuable insights to aid decision making in a rapidly changing environment.

Figures (11)

• Figure 1: The three main modeling and inference blocks (boxes) of our Bayesian Dynamic Quantile Model Averaging (BDQMA) framework together with the main features of the blocks (circles).
• Figure 2: Posterior mean of the regression parameters $\boldsymbol{\beta}_{t}=\left( \beta _{1,t},\beta _{2,t}, \beta _{3,t}\right)$, $t=1,2,\ldots ,T$, for the simulated data in Example \ref{['ex:sim_ex_1']}(left panel) and \ref{['ex:sim_ex_2']}(right panel), with quantile level $\tau =0.25$ and $N=100$ parallel chains. In each plot: true parameters (red), posterior medians (dark) and $95\%$ HPD regions (gray areas).
• Figure 3: US inflation data. Sequential estimates of the regression parameters by DMA (for the mean regression \ref{['fig:CPIAUCSL_beta_relevant']}) and BDQMA (for the quantile regression \ref{['fig:CPIAUCSL_beta010_relevant']}-\ref{['fig:CPIAUCSL_beta090_relevant']}) for the CPIAUCSL (Consumer Price Index for All Urban Consumers: All Items in U.S. City Average). For each quantile level $\tau$ the corresponding figure only reports those parameters having inclusion probability larger or equal to $0.7$ for at least one quarter. See Table \ref{['tab:table_US_inflation_data_CPIAUCSL_ss']} for a summary of the relevant covariate. The shaded areas identify two significant periods: the US Great Financial Crisis from 2007-Q4 to 2011-Q4 (blue), and the Russian-Ukraine crisis (red).
• Figure 4: US inflation dataset. Sequential update of the predicted inclusion probabilities $\pi _{t|t-1}$ by DMA (for the mean regression \ref{['fig:CPIAUCSL_incl_prob']}) and BDQMA (for the quantile regression \ref{['fig:CPIAUCSL_incl_prob010']}-\ref{['fig:CPIAUCSL_incl_prob090']}) for the CPIAUCSL (Consumer Price Index for All Urban Consumers: All Items in U.S. City Average). For each quantile level $\tau$ the corresponding figure only reports those parameters having inclusion probability larger or equal to $0.7$ for at least one quarter. See Table \ref{['tab:table_US_inflation_data_CPIAUCSL_ss']} for a summary of the relevant covariate. The shaded areas identify two significant periods: the US Great Financial Crisis from 2007-Q4 to 2011-Q4 (blue), and the Russian-Ukraine crisis (red).
• Figure 5: US Inflation dataset. Expected number of predictors over time for each quantile confidence levels. The quantiles are denoted as follows: $\tau=0.10$(gray dashed line), $\tau=0.25$(black dotted line), $\tau=0.50$(gray solid line), $\tau=0.75$(black dotted line), $\tau=0.90$(gray dashed line), and the mean (black solid line). The mean (Gaussian regression) is depicted by the black solid line. Additionally, the red line indicates the average number of predictors across all quantiles. The shaded areas identify two significant periods: the US Great Financial Crisis from 2007-Q4 to 2011-Q4 (blue), and the Russian-Ukraine crisis (red).

Theorems & Definitions (7)

• Theorem 2.1
• proof
• Theorem 2.2
• proof
• Remark 2.1
• proof : Proof of Theorem \ref{['th1']}
• proof : Proof of Theorem \ref{['th2']}