Seasonally adjusted series are usually used to analyse the business cycle and turning points. When the irregular is too high, it is preferable to smooth the series in order to analyse the trend-cycle component directly. This study focuses on the real-time estimation of the trend-cycle component around shocks and turning points. The linear moving averages classically used for estimating the trend-cycle, which are sensitive to the presence of atypical points, are compared with robust non-linear methods. We also propose a methodology for extending the Henderson and Musgrave moving averages to take account of external information and thus construct moving averages that are robust to the presence of certain shocks. We describe how to estimate confidence intervals for estimates derived from moving averages, thereby validating the use of these new moving averages. By comparing the methods on simulated and real series, we show that: building robust moving averages makes it possible to reduce revisions and better model turning points around shocks, without degrading the estimates when no shock is observed; robust non-linear methods do not make it possible to extract a trend-cycle component that is satisfactory for economic analysis, with sometimes significant revisions. This study is fully reproducible and all the codes used are available under https://github.com/AQLT/robustMA.

翻译：季节调整后的序列通常用于分析商业周期和转折点。当不规则成分过高时，最好对序列进行平滑处理，以便直接分析趋势-周期成分。本研究聚焦于冲击和转折点附近趋势-周期成分的实时估计。将经典用于估计趋势-周期但对异常点敏感的线性移动平均方法，与稳健的非线性方法进行比较。我们还提出了一种扩展Henderson和Musgrave移动平均的方法，以纳入外部信息，从而构建对特定冲击具有稳健性的移动平均。我们描述了如何估计移动平均所得估计值的置信区间，从而验证这些新移动平均方法的使用。通过在模拟序列和真实序列上比较各种方法，我们表明：构建稳健移动平均可以减少修订，并在冲击附近更好地建模转折点，同时在未观测到冲击时不会降低估计质量；稳健的非线性方法无法提取出满足经济分析需求的趋势-周期成分，有时会产生显著的修订。本研究完全可复现，所有使用的代码均可在 https://github.com/AQLT/robustMA 获取。