Bayesian averaging of classical estimates in asymmetric vector autoregressive models

ABSTRACT

The estimated vector autoregressive (VAR) model is sensitive to model misspecifications, resulting to biased and inconsistent parameter estimates. This article extends the Bayesian averaging of classical estimates, a robustness procedure in cross-section data, to a vector time-series that is estimated using a large number of asymmetric VAR models. The proposed procedure was applied to simulated data from various forms of model misspecifications. The results of the simulation suggest that, under misspecification problems, particularly if an important variable and moving average (MA) terms were omitted, the proposed procedure gives robust results and better forecasts than the automatically selected equal lag-length VAR model.

KEYWORDS:

• AVAR
• BACE
• Forecasting
• Robustness procedures

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M10 Time series
• auto-correlation
• regression
• 91B84 Economic time series analysis

Acknowledgments

The authors are grateful to the Statistical Research and Training Center (SRTC) for the thesis fellowship grant, and to the participants of the Colloquium on the Statistical Sciences at the School of Statistics, University of the Philippines, for their valuable comments.

Notes

1 Some of the studies that used BVAR and variants of it are from Po, Chi, Shyu, and Hsiao (2002), Chen and Leung (2003), Ramos (2003), and Carriero et al. (2009).

2 The he VAR operator is stable and the process is stationary if det A* (z) ≠ 0, where If this is the case, then the VAR(p) model can also be expressed as where Φ₀ = I_K if A*₀ = M₀* = I_K, and with A*_j = 0 or j > p The Φ_i's are popularly known as the impulse response function in the literature. In practice, researchers use the orthogonalized form of the IRF that can be expressed by Φ^o_i = Φ_iL here L's a lower triangular matrix of the Cholesky decomposition of Σ, that is, Σ = LL′ The interpretations of the VAR(p) model is coursed through the estimated IRF as it gives the reaction of the value of a variable when there is an abrupt change in the other variables.

3 The names KAIC and KSIC are adapted from Ozcicek and McMillin (1999).

4 A four-dimensional vector time-series data will be generated in the cases where one important variable is omitted.

5 The formula for the posterior probability involves the SSE being raised to the power − n/2. In the simulation, the posterior probability was zero for large sample size T for small SSE. The problem was remedied by raising the SSE to −(0.1T)/2 in Eq. (8(8) ) for the sample sizes T = 300 and T = 1,000. This stands only as a temporary remedy to the problem. SSE in time-series data may have a different rate of convergence to cross-section data.

Table 2. Average VAR lag-lengths from automatic selection procedure using AICc.