This interdisciplinary research includes elements of computing, optimization, and statistics for big data. Specifically, it addresses model order identification aspects of big time series data. Computing and minimizing information criteria, such as BIC, on a grid of integer orders becomes prohibitive for time series recorded at a large number of time points. We propose to compute information criteria only for a sample of integer orders and use kriging‐based methods to emulate the information criteria on the rest of the grid. Then we use an efficient global optimization (EGO) algorithm to identify the orders. The method is applied to both ARMA and ARMA‐GARCH models. We simulated times series from each type of model of prespecified orders and applied the method to identify the orders. We also used real big time series with tens of thousands of time points to illustrate the method. In particular, we used sentiment scores for news headlines on the economy for ARMA models, and the NASDAQ daily returns for ARMA‐GARCH models, from the beginning in 1971 to mid‐April 2020 in the early stages of the COVID‐19 pandemic. The proposed method identifies efficiently and accurately the orders of models for big time series data.

中文翻译：

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大时间序列数据模型的仿真订单识别

这项跨学科研究包括大数据的计算，优化和统计元素。具体来说，它解决了大时间序列数据的模型订单识别方面。对于在大量时间点记录的时间序列，在整数阶网格上计算和最小化诸如BIC之类的信息标准变得越来越困难。我们建议仅针对整数阶样本计算信息标准，并使用基于kriging的方法在网格的其余部分上模拟信息标准。然后，我们使用高效的全局优化（EGO）算法来识别订单。该方法适用于ARMA和ARMA-GARCH模型。我们从各种类型的预定订单模型中模拟了时间序列，并应用了该方法来识别订单。我们还使用了具有成千上万个时间点的真实大时间序列来说明该方法。特别是，从1971年初到2020年4月中旬COVID-19大流行的早期阶段，我们使用情绪得分来评价ARMA模型的经济新闻头条，以及纳斯达克的ARMA-GARCH模型的每日收益。所提出的方法可以有效，准确地识别大时间序列数据的模型顺序。