Predictive Inference for Locally Stationary Time Series With an Application to Climate Data
Predictive Inference for Locally Stationary Time Series With an Application to Climate Data
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DOI：
10.1080/01621459.2019.1708368
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发表时间：
2020-01-31
影响因子：
3.7
通讯作者：
Politis, Dimitris N.
中科院分区：
文献类型：
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作者：
Das, Srinjoy;Politis, Dimitris N.
无模型的肺炎预测原理已成功地应用于一般回归问题，以及涉及固定时间序列的问题。但是，例如，由于长期序列，每年的温度测量值超过100年或每日财务收益跨越了几年，因此在整个数据集的整个范围内都具有平稳性可能是不现实的。在本文中，我们展示了如何将无模型预测应用于处理仅本地固定的时间序列，也就是说，可以假定它们仅在短时间内固定。令人惊讶的是，即使在基于模型的设置中，对于一般本地固定时间序列的点预测，几乎没有文献预测，并且在局部固定时间序列的预测间隔的构建间隔中没有任何文献。我们也尝试在这里填补这一空白。构建了一个步骤的点预测指标和预测间隔，并使用结合趋势和/或异方差的模型将无模型的性能与基于模型的预测进行了比较。本文的两个方面都是无模型和基于模型的方面，在本地（但不是全球）固定的时间序列的背景下都是新颖的。我们还证明了我们基于模型和无模型的预测方法的应用，该方法表现出局部平稳性，并表明我们最佳的无模型点预测结果优于以前用于分析此类类型的rampfit算法获得的优胜。数据。本文可在线获得。
The model-free prediction principle of Politis has been successfully applied to general regression problems, as well as problems involving stationary time series. However, with long time series, for example, annual temperature measurements spanning over 100 years or daily financial returns spanning several years, it may be unrealistic to assume stationarity throughout the span of the dataset. In this article, we show how model-free prediction can be applied to handle time series that are only locally stationary, that is, they can be assumed to be stationary only over short time-windows. Surprisingly, there is little literature on point prediction for general locally stationary time series even in model-based setups, and there is no literature whatsoever on the construction of prediction intervals of locally stationary time series. We attempt to fill this gap here as well. Both one-step-ahead point predictors and prediction intervals are constructed, and the performance of model-free is compared to model-based prediction using models that incorporate a trend and/or heteroscedasticity. Both aspects of the article, model-free and model-based, are novel in the context of time-series that are locally (but not globally) stationary. We also demonstrate the application of our model-based and model-free prediction methods to speleothem climate data which exhibits local stationarity and show that our best model-free point prediction results outperform that obtained with the RAMPFIT algorithm previously used for analysis of this type of data. for this article are available online.