Unbiasedness of Predictions from Etimated Vector Autoregressions
证明，用OLS估计的向量自回归模型，即使阶数设定错误或变量缺失，其预测误差的分布仍关于零对称，即预测是无偏的，且该性质在有限样本下成立。
Forecasts from a univariate autoregressive model estimated by OLS are unbiased, irrespective of whether the model fitted has the correct order; this property only requires symmetry of the distribution of the innovations. In this paper, this result is generalized to vector autoregressions and a wide class of multivariate stochastic processes (which include Gaussian stationary multivariate stochastic processes) is described for which unbiasedness of predictions holds: specifically, if a vector autoregression of arbitrary finite order is fitted to a sample from any process in this class, the fitted model will produce unbiased forecasts, in the sense that the prediction errors have distributions symmetric about zero. Different numbers of lags may be used for each variable in each autoregression and variables may even be missing, without unbiasedness being affected. This property is exact in finite samples. Similarly, the residuals from the same autoregressions have distributions symmetric about zero.