Autoregressive moving average (ARMA) models are frequently used to analyze time series data. Despite the popularity of these models, algorithms for fitting ARMA models have weaknesses that are not well known. We provide a summary of parameter estimation via maximum likelihood and discuss common pitfalls that may lead to sub-optimal parameter estimates. We propose a random restart algorithm for parameter estimation that frequently yields higher likelihoods than traditional maximum likelihood estimation procedures. We then investigate the parameter uncertainty of maximum likelihood estimates, and propose the use of profile confidence intervals as a superior alternative to intervals derived from the Fisher's information matrix. Through a series of simulation studies, we demonstrate the efficacy of our proposed algorithm and the improved nominal coverage of profile confidence intervals compared to the normal approximation based on Fisher's Information.

翻译：自回归滑动平均(ARMA)模型常被用于分析时间序列数据。尽管这些模型应用广泛，但拟合ARMA模型的算法存在一些鲜为人知的缺陷。本文总结了基于最大似然的参数估计方法，并讨论了可能导致次优参数估计的常见陷阱。我们提出了一种随机重启算法进行参数估计，该算法通常能获得比传统最大似然估计方法更高的似然值。随后我们探究了最大似然估计的参数不确定性，并提出使用轮廓置信区间作为基于Fisher信息矩阵所得区间的更优替代方案。通过一系列模拟研究，我们验证了所提出算法的有效性，并证明了轮廓置信区间在名义覆盖率上优于基于Fisher信息法的正态近似方法。