Vector Autoregressions and Macroeconomic Modeling: An Error Taxonomy
研究了有限滞后VAR(n)模型拟合无限阶VAR(∞)数据时的误差，将其分解为估计误差和近似误差，发现两者在实际应用中均可能严重，导致推断不可靠。
In this article we investigate the theoretical behaviour of finite lag VAR(n) models fitted totime series that in truth come from an infinite order VAR(∞) data generating mechanism. Weshow that the overall error can be broken down into two basic components, an estimation errorthat stems from the difference between the parameter estimates and their population ensembleVAR(n) counterparts, and an approximation error that stems from the difference between theVAR(n) and the true VAR(∞). The two sources of error are shown to be present in other performanceindicators previously employed in the literature to characterize, so called, truncationeffects. Our theoretical analysis indicates that the magnitude of the estimation error exceedsthat of the approximation error, but experimental results based upon a prototypical real businesscycle model and a practical example indicate that the approximation error approaches itsasymptotic position far more slowly than does the estimation error, their relative orders of magnitudenotwithstanding. The experimental results suggest that with sample sizes and lag lengthslike those commonly employed in practice VAR(n) models are likely to exhibit serious errorsof both types when attempting to replicate the dynamics of the true underlying process and thatinferences based on VAR(n) models can be very untrustworthy.