In this paper, we investigate the asymptotic properties of Le Cam's one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the one-step estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator. An application for providing remotely computed indicators for time series is proposed.
翻译:在本文中, 我们调查了 Le Cam 的单步自动递减综合移动动作模型( FARIMA) 的单步测算器的无症状特性。 对于这些模型, 噪音不相干, 但不一定是独立的, 也不一定是martingale 差异错误。 我们根据一些常规假设显示, 单步测算器与最小正方形测算器一样, 与最小方形测算器一样, 高度一致且无症状常态。 我们通过模拟显示, 拟议的测算器减少了计算时间, 与最小方形测算器相比。 我们提议了为时间序列提供远程计算指标的应用程序 。