We establish a negative moment bound for the sample autocovariance matrix of a stationary process driven by conditional heteroscedastic errors. This moment bound enables us to asymptotically express the mean squared prediction error (MSPE) of the least squares predictor as the sum of three terms related to model complexity, model misspecification, and conditional heteroscedasticity. A direct application of this expression is the development of a model selection criterion that can asymptotically identify the best (in the sense of MSPE) subset AR model in the presence of misspecification and conditional heteroscedasticity. Finally, numerical simulations are conducted to confirm our theoretical results.

翻译：我们为一个由条件性混凝土误差驱动的固定过程的样本自动变异矩阵设定一个负点。 这一点会让我们能够以最小方预测器的平均平方预测误差(MSPE)表示最小方预测器的平均平方预测误差(MSPE),这是与模型复杂性、模型特性错误和有条件异体性有关的三个条件的总和。 这个表达式的直接应用是开发一个模型选择标准,能够在存在误差和条件性异体性的情况下,对最佳的(在MSPE意义上)亚瑟子模型进行随机识别。 最后,进行数字模拟,以确认我们的理论结果。