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样本量与预测期同步增长时近单位根 AR(1) 模型的预测误差AI 解读

We develop asymptotic approximations to the distribution of forecast errors from an estimated AR(1) model with no drift when the true process is nearly I (1) and both the forecast horizon and the sample size are allowed to increase at the same rate. We find that the forecast errors are the sums of two components that are asymptotically independent. The first is asymptotically normal whereas the second is asymptotically nonnormal. This throws doubt on the suitability of a…

AR(1) 模型中预测误差的联合分布AI 解读

Second-order asymptotic expansion approximations to the joint distributions of dynamic forecast errors and of static forecast errors in the stationary Gaussian pure AR(1) model are derived. The approximation to the dynamic forecast errors distribution can be expressed as a multivariate normal distribution with modified mean vector and covariance matrix, thus generalizing the results of Phillips [12]. However, the approximation to the static forecast errors distribution…