Consistent order selection for ARFIMA processes
证明了贝叶斯信息准则（BIC）在自回归分数积分移动平均（ARFIMA）模型中选择阶数的一致性，适用于短记忆、长记忆和非平稳时间序列，并扩展到条件异方差误差情形，通过数值例子验证了有限样本表现。
Estimating the orders of the autoregressive fractionally integrated moving average (ARFIMA) model has been a long-standing problem in time series analysis. This paper tackles this challenge by establishing the consistency of the Bayesian information criterion (BIC) for ARFIMA models with independent errors. Since the memory parameter of the model can be any real number, this consistency result is valid for short memory, long memory and nonstationary time series. This paper further extends the consistency of the BIC to ARFIMA models with conditional heteroscedastic errors, thereby extending its applications to encompass many real-life situations. Finite-sample implications of the theoretical results are illustrated via numerical examples.