The decomposition of a time series is an essential task that helps to understand its very nature. It facilitates the analysis and forecasting of complex time series expressing various hidden components such as the trend, seasonal components, cyclic components and irregular fluctuations. Therefore, it is crucial in many fields for forecasting and decision processes. In recent years, many methods of time series decomposition have been developed, which extract and reveal different time series properties. Unfortunately, they neglect a very important property, i.e. time series variance. To deal with heteroscedasticity in time series, the method proposed in this work -- a seasonal-trend-dispersion decomposition (STD) -- extracts the trend, seasonal component and component related to the dispersion of the time series. We define STD decomposition in two ways: with and without an irregular component. We show how STD can be used for time series analysis and forecasting.
翻译:时间序列的分解是一项重要任务,有助于了解时间序列的本质,有助于分析和预测复杂的时间序列,表达各种隐蔽组成部分,如趋势、季节性成分、周期性成分和不规则波动。因此,对于预测和决策过程在许多领域至关重要。近年来,制定了许多时间序列分解方法,这些方法提取和揭示了不同的时间序列特性。不幸的是,这些方法忽视了一个非常重要的属性,即时间序列的差异。为了处理时间序列中的异变性,这项工作中建议的方法 -- -- 季节性趋势-趋势-分散分解分解(STD) -- -- 提取了与时间序列分散有关的趋势、季节性成分和组成部分。我们用两种方式定义了性病分解:与不规则性成分一起和不规则性分解。我们展示了性病如何用于时间序列分析和预测。