In this paper we derive the asymptotic properties of the least squares estimator (LSE) of fractionally integrated autoregressive moving-average (FARIMA) models under the assumption that the errors are uncorrelated but not necessarily independent nor martingale differences. We relax considerably the independence and even the martingale difference assumptions on the innovation process to extend the range of application of the FARIMA models. We propose a consistent estimator of the asymptotic covariance matrix of the LSE which may be very different from that obtained in the standard framework. A self-normalized approach to confidence interval construction for weak FARIMA model parameters is also presented. All our results are done under a mixing assumption on the noise. Finally, some simulation studies and an application to the daily returns of stock market indices are presented to corroborate our theoretical work.

翻译：在本文中,我们得出了微小整合的自动递减移动平均(FARIMA)模型中最小方位估计值(LSE)的零点特征,其假设是错误不相干,但不一定独立,也不一定是马丁格尔差异。我们大大放松了创新过程的独立性,甚至对马丁格尔差异的假设,以扩大FARIMA模型的应用范围。我们提议了一个一致的LSE单位变量矩阵估计值,这可能与标准框架中获得的矩阵非常不同。还介绍了为弱的FARIMA模型参数构建信任间隔的自我规范方法。我们的所有结果都是在噪音混合假设下完成的。最后,一些模拟研究和应用股市指数的每日回报,以证实我们的理论工作。